/Users/scm/git/github/teem/src/seek/textract.c

Bug Summary

File:	src/seek/textract.c
Location:	line 204, column 3
Description:	The left operand of '-' is a garbage value

Annotated Source Code

Teem: Tools to process and visualize scientific data and images .

This library is free software; you can redistribute it and/or

modify it under the terms of the GNU Lesser General Public License

(LGPL) as published by the Free Software Foundation; either

version 2.1 of the License, or (at your option) any later version.

The terms of redistributing and/or modifying this software also

include exceptions to the LGPL that facilitate static linking.

This library is distributed in the hope that it will be useful,

but WITHOUT ANY WARRANTY; without even the implied warranty of

MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU

Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License

along with this library; if not, write to Free Software Foundation, Inc.,

51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA

/* This file collects functions that implement extraction of crease

* surfaces as proposed in Schultz / Theisel / Seidel, "Crease

* Surfaces: From Theory to Extraction and Application to Diffusion

* Tensor MRI", IEEE TVCG 16(1):109-119, 2010 */

#include "seek.h"

#include "privateSeek.h"

/* private helper routines for the T-based extraction */

/* Converts a Hessian into the transformed tensor T (cf. paper)

* T is a 9-vector representing the output

* evals is a 3-vector (eigenvalues of the Hessian)

* evecs is a 9-vector (eigenvectors of the Hessian)

* evalDiffThresh is the threshold parameter theta (cf. Eq. (4) in paper)

* ridge is non-zero if we are looking for a ridge (zero for valley)

void

_seekHess2T(double *T, const double *evals, const double *evecs,

const double evalDiffThresh, const char ridge) {

double lambdas[3]={0.0,0.0,0.0};

double tmpMat[9], diag[9], evecsT[9];

if (ridge) {

double diff = evals[1]-evals[2];

lambdas[0]=lambdas[1]=1.0;

if (diff<evalDiffThresh)

lambdas[2]=(1.0-diff/evalDiffThresh)*(1.0-diff/evalDiffThresh);

} else {

double diff = evals[0]-evals[1];

lambdas[1]=lambdas[2]=1.0;

if (diff<evalDiffThresh)

lambdas[0]=(1.0-diff/evalDiffThresh)*(1.0-diff/evalDiffThresh);

}

ELL_3M_ZERO_SET(diag)((((diag)+0)[0] = (0), ((diag)+0)[1] = (0), ((diag)+0)[2] = (
0)), (((diag)+3)[0] = (0), ((diag)+3)[1] = (0), ((diag)+3)[2]
= (0)), (((diag)+6)[0] = (0), ((diag)+6)[1] = (0), ((diag)+6
)[2] = (0)));

ELL_3M_DIAG_SET(diag, lambdas[0], lambdas[1], lambdas[2])((diag)[0] = (lambdas[0]), (diag)[4] = (lambdas[1]), (diag)[8
] = (lambdas[2]));

ELL_3M_TRANSPOSE(evecsT, evecs)((evecsT)[0] = (evecs)[0], (evecsT)[1] = (evecs)[3], (evecsT)
[2] = (evecs)[6], (evecsT)[3] = (evecs)[1], (evecsT)[4] = (evecs
)[4], (evecsT)[5] = (evecs)[7], (evecsT)[6] = (evecs)[2], (evecsT
)[7] = (evecs)[5], (evecsT)[8] = (evecs)[8]);

ELL_3M_MUL(tmpMat, diag, evecs)((tmpMat)[0] = (diag)[0]*(evecs)[0] + (diag)[1]*(evecs)[3] + (
diag)[2]*(evecs)[6], (tmpMat)[1] = (diag)[0]*(evecs)[1] + (diag
)[1]*(evecs)[4] + (diag)[2]*(evecs)[7], (tmpMat)[2] = (diag)[
0]*(evecs)[2] + (diag)[1]*(evecs)[5] + (diag)[2]*(evecs)[8], (
tmpMat)[3] = (diag)[3]*(evecs)[0] + (diag)[4]*(evecs)[3] + (diag
)[5]*(evecs)[6], (tmpMat)[4] = (diag)[3]*(evecs)[1] + (diag)[
4]*(evecs)[4] + (diag)[5]*(evecs)[7], (tmpMat)[5] = (diag)[3]
*(evecs)[2] + (diag)[4]*(evecs)[5] + (diag)[5]*(evecs)[8], (tmpMat
)[6] = (diag)[6]*(evecs)[0] + (diag)[7]*(evecs)[3] + (diag)[8
]*(evecs)[6], (tmpMat)[7] = (diag)[6]*(evecs)[1] + (diag)[7]*
(evecs)[4] + (diag)[8]*(evecs)[7], (tmpMat)[8] = (diag)[6]*(evecs
)[2] + (diag)[7]*(evecs)[5] + (diag)[8]*(evecs)[8]);

ELL_3M_MUL(T, evecsT, tmpMat)((T)[0] = (evecsT)[0]*(tmpMat)[0] + (evecsT)[1]*(tmpMat)[3] +
(evecsT)[2]*(tmpMat)[6], (T)[1] = (evecsT)[0]*(tmpMat)[1] + (
evecsT)[1]*(tmpMat)[4] + (evecsT)[2]*(tmpMat)[7], (T)[2] = (evecsT
)[0]*(tmpMat)[2] + (evecsT)[1]*(tmpMat)[5] + (evecsT)[2]*(tmpMat
)[8], (T)[3] = (evecsT)[3]*(tmpMat)[0] + (evecsT)[4]*(tmpMat)
[3] + (evecsT)[5]*(tmpMat)[6], (T)[4] = (evecsT)[3]*(tmpMat)[
1] + (evecsT)[4]*(tmpMat)[4] + (evecsT)[5]*(tmpMat)[7], (T)[5
] = (evecsT)[3]*(tmpMat)[2] + (evecsT)[4]*(tmpMat)[5] + (evecsT
)[5]*(tmpMat)[8], (T)[6] = (evecsT)[6]*(tmpMat)[0] + (evecsT)
[7]*(tmpMat)[3] + (evecsT)[8]*(tmpMat)[6], (T)[7] = (evecsT)[
6]*(tmpMat)[1] + (evecsT)[7]*(tmpMat)[4] + (evecsT)[8]*(tmpMat
)[7], (T)[8] = (evecsT)[6]*(tmpMat)[2] + (evecsT)[7]*(tmpMat)
[5] + (evecsT)[8]*(tmpMat)[8]);

}

/* Converts a Hessian derivative into a derivative of the transformed

* tensor field T

* Tder is a 9-vector representing the output

* hessder is a 9-vector (Hessian derivative)

* evals is a 3-vector (eigenvalues of the Hessian value)

* evecs is a 9-vector (eigenvectors of the Hessian value)

* evalDiffThresh is the threshold parameter theta (cf. Eq. (4) in the paper)

* ridge is non-zero if we are looking for a ridge (zero for valley)

void

_seekHessder2Tder(double *Tder, const double *hessder, const double *evals,

const double *evecs, const double evalDiffThresh,

const char ridge) {

double evecTrans[9];

double hessderE[9]; /* Hessian derivative in eigenframe */

double tmp[9];

ELL_3M_TRANSPOSE(evecTrans,evecs)((evecTrans)[0] = (evecs)[0], (evecTrans)[1] = (evecs)[3], (evecTrans
)[2] = (evecs)[6], (evecTrans)[3] = (evecs)[1], (evecTrans)[4
] = (evecs)[4], (evecTrans)[5] = (evecs)[7], (evecTrans)[6] =
(evecs)[2], (evecTrans)[7] = (evecs)[5], (evecTrans)[8] = (evecs
)[8]);

ell_3m_mul_d(tmp,hessder,evecTrans);

ell_3m_mul_d(hessderE,evecs,tmp);

if (ridge) {

double diff=evals[1]-evals[2];

double l3;

double l3der;

if (diff<evalDiffThresh)

l3=(1.0-diff/evalDiffThresh)*(1.0-diff/evalDiffThresh);

else l3=0.0;

hessderE[2]*=(1.0-l3)/(evals[0]-evals[2]);

hessderE[6]=hessderE[2];

hessderE[5]*=(1.0-l3)/(evals[1]-evals[2]);

hessderE[7]=hessderE[5];

if (diff<evalDiffThresh)

l3der = 2/evalDiffThresh*(1-diff/evalDiffThresh)*

(hessderE[8]-hessderE[4]);

else

100

l3der=0;

101

hessderE[8]=l3der;

102

hessderE[0]=hessderE[1]=hessderE[3]=hessderE[4]=0.0;

103

} else {

104

double diff=evals[0]-evals[1];

105

double l1;

106

double l1der;

107

if (diff<evalDiffThresh)

108

l1=(1.0-diff/evalDiffThresh)*(1.0-diff/evalDiffThresh);

109

else l1=0.0;

110

hessderE[1]*=(l1-1.0)/(evals[0]-evals[1]);

111

hessderE[3]=hessderE[1];

112

hessderE[2]*=(l1-1.0)/(evals[0]-evals[2]);

113

hessderE[6]=hessderE[2];

114

115

if (diff<evalDiffThresh)

116

l1der = 2/evalDiffThresh*(1-diff/evalDiffThresh)*

117

(hessderE[4]-hessderE[0]);

118

else

119

l1der = 0;

120

hessderE[0]=l1der;

121

hessderE[4]=hessderE[5]=hessderE[7]=hessderE[8]=0.0;

122

}

123

124

ell_3m_mul_d(tmp,hessderE,evecs);

125

ell_3m_mul_d(Tder,evecTrans,tmp);

126

}

127

128

static int

129

findFeatureIntersection(double *results, double *Tleft,

130

double *hessleft, double *gleft,

131

double *Tright, double *hessright,

132

double *gright, double idxleft,

133

double idxright, char ridge,

134

const double evalDiffThresh,

135

const double dotThresh) {

136

double Tdp = ELL_3V_DOT(Tleft, Tright)((Tleft)[0]*(Tright)[0] + (Tleft)[1]*(Tright)[1] + (Tleft)[2]
*(Tright)[2]) + ELL_3V_DOT(Tleft+3,Tright+3)((Tleft+3)[0]*(Tright+3)[0] + (Tleft+3)[1]*(Tright+3)[1] + (Tleft
+3)[2]*(Tright+3)[2]) +

137

ELL_3V_DOT(Tleft+6,Tright+6)((Tleft+6)[0]*(Tright+6)[0] + (Tleft+6)[1]*(Tright+6)[1] + (Tleft
+6)[2]*(Tright+6)[2]);

138

double denom_l = sqrt(ELL_3V_DOT(Tleft, Tleft)((Tleft)[0]*(Tleft)[0] + (Tleft)[1]*(Tleft)[1] + (Tleft)[2]*(
Tleft)[2]) + ELL_3V_DOT(Tleft+3, Tleft+3)((Tleft+3)[0]*(Tleft+3)[0] + (Tleft+3)[1]*(Tleft+3)[1] + (Tleft
+3)[2]*(Tleft+3)[2])

139

+ ELL_3V_DOT(Tleft+6, Tleft+6)((Tleft+6)[0]*(Tleft+6)[0] + (Tleft+6)[1]*(Tleft+6)[1] + (Tleft
+6)[2]*(Tleft+6)[2])),

140

denom_r = sqrt(ELL_3V_DOT(Tright,Tright)((Tright)[0]*(Tright)[0] + (Tright)[1]*(Tright)[1] + (Tright)
[2]*(Tright)[2]) + ELL_3V_DOT(Tright+3, Tright+3)((Tright+3)[0]*(Tright+3)[0] + (Tright+3)[1]*(Tright+3)[1] + (
Tright+3)[2]*(Tright+3)[2])

141

+ ELL_3V_DOT(Tright+6, Tright+6)((Tright+6)[0]*(Tright+6)[0] + (Tright+6)[1]*(Tright+6)[1] + (
Tright+6)[2]*(Tright+6)[2]));

142

143

if (Tdp/(denom_l*denom_r)<dotThresh &&

144

idxright-idxleft>0.24) { /* do a recursive step */

145

double idxcenter = 0.5*(idxleft+idxright);

146

/* simply interpolate Hessian linearly */

147

double hessnew[9];

148

double evals[3],evecs[9];

149

double Tnew[9], gradnew[3];

150

int retval;

151

152

ELL_3M_LERP(hessnew,0.5,hessleft,hessright)((((hessnew)+0)[0] = ((((0.5)))*((((hessright)+0)[0]) - (((hessleft
)+0)[0])) + (((hessleft)+0)[0])), ((hessnew)+0)[1] = ((((0.5)
))*((((hessright)+0)[1]) - (((hessleft)+0)[1])) + (((hessleft
)+0)[1])), ((hessnew)+0)[2] = ((((0.5)))*((((hessright)+0)[2]
) - (((hessleft)+0)[2])) + (((hessleft)+0)[2]))), (((hessnew)
+3)[0] = ((((0.5)))*((((hessright)+3)[0]) - (((hessleft)+3)[0
])) + (((hessleft)+3)[0])), ((hessnew)+3)[1] = ((((0.5)))*(((
(hessright)+3)[1]) - (((hessleft)+3)[1])) + (((hessleft)+3)[1
])), ((hessnew)+3)[2] = ((((0.5)))*((((hessright)+3)[2]) - ((
(hessleft)+3)[2])) + (((hessleft)+3)[2]))), (((hessnew)+6)[0]
= ((((0.5)))*((((hessright)+6)[0]) - (((hessleft)+6)[0])) + (
((hessleft)+6)[0])), ((hessnew)+6)[1] = ((((0.5)))*((((hessright
)+6)[1]) - (((hessleft)+6)[1])) + (((hessleft)+6)[1])), ((hessnew
)+6)[2] = ((((0.5)))*((((hessright)+6)[2]) - (((hessleft)+6)[
2])) + (((hessleft)+6)[2]))));

153

ell_3m_eigensolve_d(evals, evecs, hessnew, AIR_TRUE1);

154

155

_seekHess2T(Tnew, evals, evecs, evalDiffThresh, ridge);

156

157

ELL_3V_LERP(gradnew,0.5,gleft,gright)((gradnew)[0] = (((0.5))*(((gright)[0]) - ((gleft)[0])) + ((gleft
)[0])), (gradnew)[1] = (((0.5))*(((gright)[1]) - ((gleft)[1])
) + ((gleft)[1])), (gradnew)[2] = (((0.5))*(((gright)[2]) - (
(gleft)[2])) + ((gleft)[2])));

158

retval = findFeatureIntersection(results, Tleft, hessleft,

159

gleft, Tnew, hessnew, gradnew,

160

idxleft, idxcenter,

161

ridge, evalDiffThresh, dotThresh);

162

retval += findFeatureIntersection(results+retval, Tnew, hessnew,

163

gradnew, Tright, hessright, gright,

164

idxcenter, idxright,

165

ridge, evalDiffThresh, dotThresh);

166

return retval;

167

} else {

168

double d1[3], d4[3];

169

ell_3mv_mul_d(d1, Tleft, gleft);

170

ELL_3V_SUB(d1,d1,gleft)((d1)[0] = (d1)[0] - (gleft)[0], (d1)[1] = (d1)[1] - (gleft)[
1], (d1)[2] = (d1)[2] - (gleft)[2]);

171

ell_3mv_mul_d(d4, Tright, gright);

172

ELL_3V_SUB(d4,d4,gright)((d4)[0] = (d4)[0] - (gright)[0], (d4)[1] = (d4)[1] - (gright
)[1], (d4)[2] = (d4)[2] - (gright)[2]);

173

174

if (ELL_3V_DOT(d1,d4)((d1)[0]*(d4)[0] + (d1)[1]*(d4)[1] + (d1)[2]*(d4)[2])<0) { /* mark edge as crossed */

175

/* find assumed intersection point */

176

double diff[3], dlen, alpha;

177

ELL_3V_SUB(diff,d4,d1)((diff)[0] = (d4)[0] - (d1)[0], (diff)[1] = (d4)[1] - (d1)[1]
, (diff)[2] = (d4)[2] - (d1)[2]);

178

dlen=ELL_3V_LEN(diff)(sqrt((((diff))[0]*((diff))[0] + ((diff))[1]*((diff))[1] + ((
diff))[2]*((diff))[2])));

179

if (dlen>1e-5) {

180

double ap=-ELL_3V_DOT(d1,diff)((d1)[0]*(diff)[0] + (d1)[1]*(diff)[1] + (d1)[2]*(diff)[2])/dlen;

181

alpha = ap/dlen;

182

} else

183

alpha = 0.5;

184

185

*results = (1-alpha)*idxleft+alpha*idxright;

186

return 1;

187

}

188

}

189

return 0;

190

}

191

192

/* Assuming (simplistic) linearly interpolated Hessians and gradients,

193

* computes the analytical normal of the crease surface.

194

* The result is _not_ normalized. */

195

static void

196

computeGradientLin(double *result, double *T, double *g,

197

double *Txm, double *gxm, double *Txp, double *gxp,

198

double *Tym, double *gym, double *Typ, double *gyp,

199

double *Tzm, double *gzm, double *Tzp, double *gzp) {

200

double Tder[9];

201

double gder[3];

202

double tmp[3], tmp1[3], tmp2[3];

203

double derxv[3], deryv[3], derzv[3];

204

ELL_3M_SUB(Tder,Txp,Txm)((Tder)[0] = (Txp)[0] - (Txm)[0], (Tder)[1] = (Txp)[1] - (Txm
)[1], (Tder)[2] = (Txp)[2] - (Txm)[2], (Tder)[3] = (Txp)[3] -
(Txm)[3], (Tder)[4] = (Txp)[4] - (Txm)[4], (Tder)[5] = (Txp)
[5] - (Txm)[5], (Tder)[6] = (Txp)[6] - (Txm)[6], (Tder)[7] = (
Txp)[7] - (Txm)[7], (Tder)[8] = (Txp)[8] - (Txm)[8]);

←

Within the expansion of the macro 'ELL_3M_SUB':

a	The left operand of '-' is a garbage value

205

ELL_3V_SUB(gder,gxp,gxm)((gder)[0] = (gxp)[0] - (gxm)[0], (gder)[1] = (gxp)[1] - (gxm
)[1], (gder)[2] = (gxp)[2] - (gxm)[2]);

206

ell_3mv_mul_d(tmp,T,gder);

207

ELL_3V_SUB(tmp,tmp,gder)((tmp)[0] = (tmp)[0] - (gder)[0], (tmp)[1] = (tmp)[1] - (gder
)[1], (tmp)[2] = (tmp)[2] - (gder)[2]);

208

ell_3mv_mul_d(derxv,Tder,g);

209

ELL_3V_ADD2(derxv,derxv,tmp)((derxv)[0] = (derxv)[0] + (tmp)[0], (derxv)[1] = (derxv)[1] +
(tmp)[1], (derxv)[2] = (derxv)[2] + (tmp)[2]);

210

211

ELL_3M_SUB(Tder,Typ,Tym)((Tder)[0] = (Typ)[0] - (Tym)[0], (Tder)[1] = (Typ)[1] - (Tym
)[1], (Tder)[2] = (Typ)[2] - (Tym)[2], (Tder)[3] = (Typ)[3] -
(Tym)[3], (Tder)[4] = (Typ)[4] - (Tym)[4], (Tder)[5] = (Typ)
[5] - (Tym)[5], (Tder)[6] = (Typ)[6] - (Tym)[6], (Tder)[7] = (
Typ)[7] - (Tym)[7], (Tder)[8] = (Typ)[8] - (Tym)[8]);

212

ELL_3V_SUB(gder,gyp,gym)((gder)[0] = (gyp)[0] - (gym)[0], (gder)[1] = (gyp)[1] - (gym
)[1], (gder)[2] = (gyp)[2] - (gym)[2]);

213

ell_3mv_mul_d(tmp,T,gder);

214

ELL_3V_SUB(tmp,tmp,gder)((tmp)[0] = (tmp)[0] - (gder)[0], (tmp)[1] = (tmp)[1] - (gder
)[1], (tmp)[2] = (tmp)[2] - (gder)[2]);

215

ell_3mv_mul_d(deryv,Tder,g);

216

ELL_3V_ADD2(deryv,deryv,tmp)((deryv)[0] = (deryv)[0] + (tmp)[0], (deryv)[1] = (deryv)[1] +
(tmp)[1], (deryv)[2] = (deryv)[2] + (tmp)[2]);

217

218

ELL_3M_SUB(Tder,Tzp,Tzm)((Tder)[0] = (Tzp)[0] - (Tzm)[0], (Tder)[1] = (Tzp)[1] - (Tzm
)[1], (Tder)[2] = (Tzp)[2] - (Tzm)[2], (Tder)[3] = (Tzp)[3] -
(Tzm)[3], (Tder)[4] = (Tzp)[4] - (Tzm)[4], (Tder)[5] = (Tzp)
[5] - (Tzm)[5], (Tder)[6] = (Tzp)[6] - (Tzm)[6], (Tder)[7] = (
Tzp)[7] - (Tzm)[7], (Tder)[8] = (Tzp)[8] - (Tzm)[8]);

219

ELL_3V_SUB(gder,gzp,gzm)((gder)[0] = (gzp)[0] - (gzm)[0], (gder)[1] = (gzp)[1] - (gzm
)[1], (gder)[2] = (gzp)[2] - (gzm)[2]);

220

ell_3mv_mul_d(tmp,T,gder);

221

ELL_3V_SUB(tmp,tmp,gder)((tmp)[0] = (tmp)[0] - (gder)[0], (tmp)[1] = (tmp)[1] - (gder
)[1], (tmp)[2] = (tmp)[2] - (gder)[2]);

222

ell_3mv_mul_d(derzv,Tder,g);

223

ELL_3V_ADD2(derzv,derzv,tmp)((derzv)[0] = (derzv)[0] + (tmp)[0], (derzv)[1] = (derzv)[1] +
(tmp)[1], (derzv)[2] = (derzv)[2] + (tmp)[2]);

224

225

/* accumulate a gradient */

226

tmp1[0]=derxv[0]; tmp1[1]=deryv[0]; tmp1[2]=derzv[0];

227

tmp2[0]=derxv[1]; tmp2[1]=deryv[1]; tmp2[2]=derzv[1];

228

if (ELL_3V_DOT(tmp1,tmp2)((tmp1)[0]*(tmp2)[0] + (tmp1)[1]*(tmp2)[1] + (tmp1)[2]*(tmp2)
[2])<0)

229

ELL_3V_SCALE(tmp2,-1.0,tmp2)((tmp2)[0] = (-1.0)*(tmp2)[0], (tmp2)[1] = (-1.0)*(tmp2)[1], (
tmp2)[2] = (-1.0)*(tmp2)[2]);

230

ELL_3V_ADD2(tmp1,tmp1,tmp2)((tmp1)[0] = (tmp1)[0] + (tmp2)[0], (tmp1)[1] = (tmp1)[1] + (
tmp2)[1], (tmp1)[2] = (tmp1)[2] + (tmp2)[2]);

231

tmp2[0]=derxv[2]; tmp2[1]=deryv[2]; tmp2[2]=derzv[2];

232

if (ELL_3V_DOT(tmp1,tmp2)((tmp1)[0]*(tmp2)[0] + (tmp1)[1]*(tmp2)[1] + (tmp1)[2]*(tmp2)
[2])<0)

233

ELL_3V_SCALE(tmp2,-1.0,tmp2)((tmp2)[0] = (-1.0)*(tmp2)[0], (tmp2)[1] = (-1.0)*(tmp2)[1], (
tmp2)[2] = (-1.0)*(tmp2)[2]);

234

ELL_3V_ADD2(result,tmp1,tmp2)((result)[0] = (tmp1)[0] + (tmp2)[0], (result)[1] = (tmp1)[1]
+ (tmp2)[1], (result)[2] = (tmp1)[2] + (tmp2)[2]);

235

}

236

237

/* Given a unique edge ID and an intersection point given by some value

238

* alpha \in [0,1], compute the crease surface normal at that point */

239

static void

240

computeEdgeGradient(seekContext *sctx, baggage *bag, double *res,

241

unsigned int xi, unsigned int yi, char edgeid, double alpha)

242

{

243

double Txm[9], Txp[9], Tym[9], Typ[9], Tzm[9], Tzp[9], T[9],

244

gxm[3], gxp[3], gym[3], gyp[3], gzm[3], gzp[3], g[3];

245

246

unsigned int sx = AIR_CAST(unsigned int, sctx->sx)((unsigned int)(sctx->sx));

247

unsigned int sy = AIR_CAST(unsigned int, sctx->sy)((unsigned int)(sctx->sy));

248

unsigned int sz = AIR_CAST(unsigned int, sctx->sz)((unsigned int)(sctx->sz));

249

unsigned int si = xi + sx*yi;

250

unsigned int six = xi + 1 + sx*yi, siX = xi - 1 + sx*yi;

251

unsigned int siy = xi + sx*(yi+1), siY = xi + sx*(yi-1);

252

unsigned int sixy = xi + 1 + sx*(yi+1),

253

sixY = xi + 1 + sx*(yi-1),

254

siXy = xi - 1 + sx*(yi+1);

255

/* many special cases needed to fill Txm, gxm, etc. :-( */

256

switch (edgeid) {

257

case 0:

258

ELL_3M_LERP(T, alpha, sctx->t + 9*(0+2*si), sctx->t + 9*(0+2*six))((((T)+0)[0] = ((((alpha)))*((((sctx->t + 9*(0+2*six))+0)[
0]) - (((sctx->t + 9*(0+2*si))+0)[0])) + (((sctx->t + 9
*(0+2*si))+0)[0])), ((T)+0)[1] = ((((alpha)))*((((sctx->t +
9*(0+2*six))+0)[1]) - (((sctx->t + 9*(0+2*si))+0)[1])) + (
((sctx->t + 9*(0+2*si))+0)[1])), ((T)+0)[2] = ((((alpha)))
*((((sctx->t + 9*(0+2*six))+0)[2]) - (((sctx->t + 9*(0+
2*si))+0)[2])) + (((sctx->t + 9*(0+2*si))+0)[2]))), (((T)+
3)[0] = ((((alpha)))*((((sctx->t + 9*(0+2*six))+3)[0]) - (
((sctx->t + 9*(0+2*si))+3)[0])) + (((sctx->t + 9*(0+2*si
))+3)[0])), ((T)+3)[1] = ((((alpha)))*((((sctx->t + 9*(0+2
*six))+3)[1]) - (((sctx->t + 9*(0+2*si))+3)[1])) + (((sctx
->t + 9*(0+2*si))+3)[1])), ((T)+3)[2] = ((((alpha)))*((((sctx
->t + 9*(0+2*six))+3)[2]) - (((sctx->t + 9*(0+2*si))+3)
[2])) + (((sctx->t + 9*(0+2*si))+3)[2]))), (((T)+6)[0] = (
(((alpha)))*((((sctx->t + 9*(0+2*six))+6)[0]) - (((sctx->
t + 9*(0+2*si))+6)[0])) + (((sctx->t + 9*(0+2*si))+6)[0]))
, ((T)+6)[1] = ((((alpha)))*((((sctx->t + 9*(0+2*six))+6)[
1]) - (((sctx->t + 9*(0+2*si))+6)[1])) + (((sctx->t + 9
*(0+2*si))+6)[1])), ((T)+6)[2] = ((((alpha)))*((((sctx->t +
9*(0+2*six))+6)[2]) - (((sctx->t + 9*(0+2*si))+6)[2])) + (
((sctx->t + 9*(0+2*si))+6)[2]))));

259

ELL_3V_LERP(g, alpha, sctx->grad + 3*(0+2*si), sctx->grad + 3*(0+2*six))((g)[0] = (((alpha))*(((sctx->grad + 3*(0+2*six))[0]) - ((
sctx->grad + 3*(0+2*si))[0])) + ((sctx->grad + 3*(0+2*si
))[0])), (g)[1] = (((alpha))*(((sctx->grad + 3*(0+2*six))[
1]) - ((sctx->grad + 3*(0+2*si))[1])) + ((sctx->grad + 3
*(0+2*si))[1])), (g)[2] = (((alpha))*(((sctx->grad + 3*(0+
2*six))[2]) - ((sctx->grad + 3*(0+2*si))[2])) + ((sctx->
grad + 3*(0+2*si))[2])));

260

ELL_3M_LERP(Tzp, alpha, sctx->t + 9*(1+2*si), sctx->t + 9*(1+2*six))((((Tzp)+0)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*six))+0
)[0]) - (((sctx->t + 9*(1+2*si))+0)[0])) + (((sctx->t +
9*(1+2*si))+0)[0])), ((Tzp)+0)[1] = ((((alpha)))*((((sctx->
t + 9*(1+2*six))+0)[1]) - (((sctx->t + 9*(1+2*si))+0)[1]))
+ (((sctx->t + 9*(1+2*si))+0)[1])), ((Tzp)+0)[2] = ((((alpha
)))*((((sctx->t + 9*(1+2*six))+0)[2]) - (((sctx->t + 9*
(1+2*si))+0)[2])) + (((sctx->t + 9*(1+2*si))+0)[2]))), (((
Tzp)+3)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*six))+3)[0]
) - (((sctx->t + 9*(1+2*si))+3)[0])) + (((sctx->t + 9*(
1+2*si))+3)[0])), ((Tzp)+3)[1] = ((((alpha)))*((((sctx->t +
9*(1+2*six))+3)[1]) - (((sctx->t + 9*(1+2*si))+3)[1])) + (
((sctx->t + 9*(1+2*si))+3)[1])), ((Tzp)+3)[2] = ((((alpha)
))*((((sctx->t + 9*(1+2*six))+3)[2]) - (((sctx->t + 9*(
1+2*si))+3)[2])) + (((sctx->t + 9*(1+2*si))+3)[2]))), (((Tzp
)+6)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*six))+6)[0]) -
(((sctx->t + 9*(1+2*si))+6)[0])) + (((sctx->t + 9*(1+2
*si))+6)[0])), ((Tzp)+6)[1] = ((((alpha)))*((((sctx->t + 9
*(1+2*six))+6)[1]) - (((sctx->t + 9*(1+2*si))+6)[1])) + ((
(sctx->t + 9*(1+2*si))+6)[1])), ((Tzp)+6)[2] = ((((alpha))
)*((((sctx->t + 9*(1+2*six))+6)[2]) - (((sctx->t + 9*(1
+2*si))+6)[2])) + (((sctx->t + 9*(1+2*si))+6)[2]))));

261

ELL_3V_LERP(gzp, alpha, sctx->grad + 3*(1+2*si), sctx->grad + 3*(1+2*six))((gzp)[0] = (((alpha))*(((sctx->grad + 3*(1+2*six))[0]) - (
(sctx->grad + 3*(1+2*si))[0])) + ((sctx->grad + 3*(1+2*
si))[0])), (gzp)[1] = (((alpha))*(((sctx->grad + 3*(1+2*six
))[1]) - ((sctx->grad + 3*(1+2*si))[1])) + ((sctx->grad
+ 3*(1+2*si))[1])), (gzp)[2] = (((alpha))*(((sctx->grad +
3*(1+2*six))[2]) - ((sctx->grad + 3*(1+2*si))[2])) + ((sctx
->grad + 3*(1+2*si))[2])));

262

if (bag->zi==0) {

263

ELL_3M_COPY(Tzm, T)((((Tzm)+0)[0] = ((T)+0)[0], ((Tzm)+0)[1] = ((T)+0)[1], ((Tzm
)+0)[2] = ((T)+0)[2]), (((Tzm)+3)[0] = ((T)+3)[0], ((Tzm)+3)[
1] = ((T)+3)[1], ((Tzm)+3)[2] = ((T)+3)[2]), (((Tzm)+6)[0] = (
(T)+6)[0], ((Tzm)+6)[1] = ((T)+6)[1], ((Tzm)+6)[2] = ((T)+6)[
2])); ELL_3V_COPY(gzm, g)((gzm)[0] = (g)[0], (gzm)[1] = (g)[1], (gzm)[2] = (g)[2]);

264

} else {

265

ELL_3M_LERP(Tzm, alpha, sctx->tcontext + 9*(0+2*si),((((Tzm)+0)[0] = ((((alpha)))*((((sctx->tcontext + 9*(0+2*
six))+0)[0]) - (((sctx->tcontext + 9*(0+2*si))+0)[0])) + (
((sctx->tcontext + 9*(0+2*si))+0)[0])), ((Tzm)+0)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(0+2*six))+0)[1]) - (((sctx
->tcontext + 9*(0+2*si))+0)[1])) + (((sctx->tcontext + 9
*(0+2*si))+0)[1])), ((Tzm)+0)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(0+2*six))+0)[2]) - (((sctx->tcontext + 9*(0+
2*si))+0)[2])) + (((sctx->tcontext + 9*(0+2*si))+0)[2]))),
(((Tzm)+3)[0] = ((((alpha)))*((((sctx->tcontext + 9*(0+2*
six))+3)[0]) - (((sctx->tcontext + 9*(0+2*si))+3)[0])) + (
((sctx->tcontext + 9*(0+2*si))+3)[0])), ((Tzm)+3)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(0+2*six))+3)[1]) - (((sctx
->tcontext + 9*(0+2*si))+3)[1])) + (((sctx->tcontext + 9
*(0+2*si))+3)[1])), ((Tzm)+3)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(0+2*six))+3)[2]) - (((sctx->tcontext + 9*(0+
2*si))+3)[2])) + (((sctx->tcontext + 9*(0+2*si))+3)[2]))),
(((Tzm)+6)[0] = ((((alpha)))*((((sctx->tcontext + 9*(0+2*
six))+6)[0]) - (((sctx->tcontext + 9*(0+2*si))+6)[0])) + (
((sctx->tcontext + 9*(0+2*si))+6)[0])), ((Tzm)+6)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(0+2*six))+6)[1]) - (((sctx
->tcontext + 9*(0+2*si))+6)[1])) + (((sctx->tcontext + 9
*(0+2*si))+6)[1])), ((Tzm)+6)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(0+2*six))+6)[2]) - (((sctx->tcontext + 9*(0+
2*si))+6)[2])) + (((sctx->tcontext + 9*(0+2*si))+6)[2]))))

266

sctx->tcontext + 9*(0+2*six))((((Tzm)+0)[0] = ((((alpha)))*((((sctx->tcontext + 9*(0+2*
six))+0)[0]) - (((sctx->tcontext + 9*(0+2*si))+0)[0])) + (
((sctx->tcontext + 9*(0+2*si))+0)[0])), ((Tzm)+0)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(0+2*six))+0)[1]) - (((sctx
->tcontext + 9*(0+2*si))+0)[1])) + (((sctx->tcontext + 9
*(0+2*si))+0)[1])), ((Tzm)+0)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(0+2*six))+0)[2]) - (((sctx->tcontext + 9*(0+
2*si))+0)[2])) + (((sctx->tcontext + 9*(0+2*si))+0)[2]))),
(((Tzm)+3)[0] = ((((alpha)))*((((sctx->tcontext + 9*(0+2*
six))+3)[0]) - (((sctx->tcontext + 9*(0+2*si))+3)[0])) + (
((sctx->tcontext + 9*(0+2*si))+3)[0])), ((Tzm)+3)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(0+2*six))+3)[1]) - (((sctx
->tcontext + 9*(0+2*si))+3)[1])) + (((sctx->tcontext + 9
*(0+2*si))+3)[1])), ((Tzm)+3)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(0+2*six))+3)[2]) - (((sctx->tcontext + 9*(0+
2*si))+3)[2])) + (((sctx->tcontext + 9*(0+2*si))+3)[2]))),
(((Tzm)+6)[0] = ((((alpha)))*((((sctx->tcontext + 9*(0+2*
six))+6)[0]) - (((sctx->tcontext + 9*(0+2*si))+6)[0])) + (
((sctx->tcontext + 9*(0+2*si))+6)[0])), ((Tzm)+6)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(0+2*six))+6)[1]) - (((sctx
->tcontext + 9*(0+2*si))+6)[1])) + (((sctx->tcontext + 9
*(0+2*si))+6)[1])), ((Tzm)+6)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(0+2*six))+6)[2]) - (((sctx->tcontext + 9*(0+
2*si))+6)[2])) + (((sctx->tcontext + 9*(0+2*si))+6)[2]))));

267

ELL_3V_LERP(gzm, alpha, sctx->gradcontext + 3*(0+2*si),((gzm)[0] = (((alpha))*(((sctx->gradcontext + 3*(0+2*six))
[0]) - ((sctx->gradcontext + 3*(0+2*si))[0])) + ((sctx->
gradcontext + 3*(0+2*si))[0])), (gzm)[1] = (((alpha))*(((sctx
->gradcontext + 3*(0+2*six))[1]) - ((sctx->gradcontext +
3*(0+2*si))[1])) + ((sctx->gradcontext + 3*(0+2*si))[1]))
, (gzm)[2] = (((alpha))*(((sctx->gradcontext + 3*(0+2*six)
)[2]) - ((sctx->gradcontext + 3*(0+2*si))[2])) + ((sctx->
gradcontext + 3*(0+2*si))[2])))

268

sctx->gradcontext + 3*(0+2*six))((gzm)[0] = (((alpha))*(((sctx->gradcontext + 3*(0+2*six))
[0]) - ((sctx->gradcontext + 3*(0+2*si))[0])) + ((sctx->
gradcontext + 3*(0+2*si))[0])), (gzm)[1] = (((alpha))*(((sctx
->gradcontext + 3*(0+2*six))[1]) - ((sctx->gradcontext +
3*(0+2*si))[1])) + ((sctx->gradcontext + 3*(0+2*si))[1]))
, (gzm)[2] = (((alpha))*(((sctx->gradcontext + 3*(0+2*six)
)[2]) - ((sctx->gradcontext + 3*(0+2*si))[2])) + ((sctx->
gradcontext + 3*(0+2*si))[2])));

269

ELL_3M_SCALE(Tzm, 0.5, Tzm)((((Tzm)+0)[0] = ((0.5))*((Tzm)+0)[0], ((Tzm)+0)[1] = ((0.5))
*((Tzm)+0)[1], ((Tzm)+0)[2] = ((0.5))*((Tzm)+0)[2]), (((Tzm)+
3)[0] = ((0.5))*((Tzm)+3)[0], ((Tzm)+3)[1] = ((0.5))*((Tzm)+3
)[1], ((Tzm)+3)[2] = ((0.5))*((Tzm)+3)[2]), (((Tzm)+6)[0] = (
(0.5))*((Tzm)+6)[0], ((Tzm)+6)[1] = ((0.5))*((Tzm)+6)[1], ((Tzm
)+6)[2] = ((0.5))*((Tzm)+6)[2])); ELL_3M_SCALE(Tzp, 0.5, Tzp)((((Tzp)+0)[0] = ((0.5))*((Tzp)+0)[0], ((Tzp)+0)[1] = ((0.5))
*((Tzp)+0)[1], ((Tzp)+0)[2] = ((0.5))*((Tzp)+0)[2]), (((Tzp)+
3)[0] = ((0.5))*((Tzp)+3)[0], ((Tzp)+3)[1] = ((0.5))*((Tzp)+3
)[1], ((Tzp)+3)[2] = ((0.5))*((Tzp)+3)[2]), (((Tzp)+6)[0] = (
(0.5))*((Tzp)+6)[0], ((Tzp)+6)[1] = ((0.5))*((Tzp)+6)[1], ((Tzp
)+6)[2] = ((0.5))*((Tzp)+6)[2]));

270

ELL_3V_SCALE(gzm, 0.5, gzm)((gzm)[0] = (0.5)*(gzm)[0], (gzm)[1] = (0.5)*(gzm)[1], (gzm)[
2] = (0.5)*(gzm)[2]); ELL_3V_SCALE(gzp, 0.5, gzp)((gzp)[0] = (0.5)*(gzp)[0], (gzp)[1] = (0.5)*(gzp)[1], (gzp)[
2] = (0.5)*(gzp)[2]);

271

}

272

if (yi==0) {

273

ELL_3M_COPY(Tym, T)((((Tym)+0)[0] = ((T)+0)[0], ((Tym)+0)[1] = ((T)+0)[1], ((Tym
)+0)[2] = ((T)+0)[2]), (((Tym)+3)[0] = ((T)+3)[0], ((Tym)+3)[
1] = ((T)+3)[1], ((Tym)+3)[2] = ((T)+3)[2]), (((Tym)+6)[0] = (
(T)+6)[0], ((Tym)+6)[1] = ((T)+6)[1], ((Tym)+6)[2] = ((T)+6)[
2])); ELL_3V_COPY(gym, g)((gym)[0] = (g)[0], (gym)[1] = (g)[1], (gym)[2] = (g)[2]);

274

} else {

275

ELL_3M_LERP(Tym, alpha, sctx->t + 9*(0+2*siY), sctx->t + 9*(0+2*sixY))((((Tym)+0)[0] = ((((alpha)))*((((sctx->t + 9*(0+2*sixY))+
0)[0]) - (((sctx->t + 9*(0+2*siY))+0)[0])) + (((sctx->t
+ 9*(0+2*siY))+0)[0])), ((Tym)+0)[1] = ((((alpha)))*((((sctx
->t + 9*(0+2*sixY))+0)[1]) - (((sctx->t + 9*(0+2*siY))+
0)[1])) + (((sctx->t + 9*(0+2*siY))+0)[1])), ((Tym)+0)[2] =
((((alpha)))*((((sctx->t + 9*(0+2*sixY))+0)[2]) - (((sctx
->t + 9*(0+2*siY))+0)[2])) + (((sctx->t + 9*(0+2*siY))+
0)[2]))), (((Tym)+3)[0] = ((((alpha)))*((((sctx->t + 9*(0+
2*sixY))+3)[0]) - (((sctx->t + 9*(0+2*siY))+3)[0])) + (((sctx
->t + 9*(0+2*siY))+3)[0])), ((Tym)+3)[1] = ((((alpha)))*((
((sctx->t + 9*(0+2*sixY))+3)[1]) - (((sctx->t + 9*(0+2*
siY))+3)[1])) + (((sctx->t + 9*(0+2*siY))+3)[1])), ((Tym)+
3)[2] = ((((alpha)))*((((sctx->t + 9*(0+2*sixY))+3)[2]) - (
((sctx->t + 9*(0+2*siY))+3)[2])) + (((sctx->t + 9*(0+2*
siY))+3)[2]))), (((Tym)+6)[0] = ((((alpha)))*((((sctx->t +
9*(0+2*sixY))+6)[0]) - (((sctx->t + 9*(0+2*siY))+6)[0])) +
(((sctx->t + 9*(0+2*siY))+6)[0])), ((Tym)+6)[1] = ((((alpha
)))*((((sctx->t + 9*(0+2*sixY))+6)[1]) - (((sctx->t + 9
*(0+2*siY))+6)[1])) + (((sctx->t + 9*(0+2*siY))+6)[1])), (
(Tym)+6)[2] = ((((alpha)))*((((sctx->t + 9*(0+2*sixY))+6)[
2]) - (((sctx->t + 9*(0+2*siY))+6)[2])) + (((sctx->t + 9
*(0+2*siY))+6)[2]))));

276

ELL_3V_LERP(gym, alpha, sctx->grad + 3*(0+2*siY),((gym)[0] = (((alpha))*(((sctx->grad + 3*(0+2*sixY))[0]) -
((sctx->grad + 3*(0+2*siY))[0])) + ((sctx->grad + 3*(0
+2*siY))[0])), (gym)[1] = (((alpha))*(((sctx->grad + 3*(0+
2*sixY))[1]) - ((sctx->grad + 3*(0+2*siY))[1])) + ((sctx->
grad + 3*(0+2*siY))[1])), (gym)[2] = (((alpha))*(((sctx->grad
+ 3*(0+2*sixY))[2]) - ((sctx->grad + 3*(0+2*siY))[2])) + (
(sctx->grad + 3*(0+2*siY))[2])))

277

sctx->grad + 3*(0+2*sixY))((gym)[0] = (((alpha))*(((sctx->grad + 3*(0+2*sixY))[0]) -
((sctx->grad + 3*(0+2*siY))[0])) + ((sctx->grad + 3*(0
+2*siY))[0])), (gym)[1] = (((alpha))*(((sctx->grad + 3*(0+
2*sixY))[1]) - ((sctx->grad + 3*(0+2*siY))[1])) + ((sctx->
grad + 3*(0+2*siY))[1])), (gym)[2] = (((alpha))*(((sctx->grad
+ 3*(0+2*sixY))[2]) - ((sctx->grad + 3*(0+2*siY))[2])) + (
(sctx->grad + 3*(0+2*siY))[2])));

278

}

279

if (yi==sy-1) {

280

ELL_3M_COPY(Typ, T)((((Typ)+0)[0] = ((T)+0)[0], ((Typ)+0)[1] = ((T)+0)[1], ((Typ
)+0)[2] = ((T)+0)[2]), (((Typ)+3)[0] = ((T)+3)[0], ((Typ)+3)[
1] = ((T)+3)[1], ((Typ)+3)[2] = ((T)+3)[2]), (((Typ)+6)[0] = (
(T)+6)[0], ((Typ)+6)[1] = ((T)+6)[1], ((Typ)+6)[2] = ((T)+6)[
2])); ELL_3V_COPY(gyp, g)((gyp)[0] = (g)[0], (gyp)[1] = (g)[1], (gyp)[2] = (g)[2]);

281

} else {

282

ELL_3M_LERP(Typ, alpha, sctx->t + 9*(0+2*siy), sctx->t + 9*(0+2*sixy))((((Typ)+0)[0] = ((((alpha)))*((((sctx->t + 9*(0+2*sixy))+
0)[0]) - (((sctx->t + 9*(0+2*siy))+0)[0])) + (((sctx->t
+ 9*(0+2*siy))+0)[0])), ((Typ)+0)[1] = ((((alpha)))*((((sctx
->t + 9*(0+2*sixy))+0)[1]) - (((sctx->t + 9*(0+2*siy))+
0)[1])) + (((sctx->t + 9*(0+2*siy))+0)[1])), ((Typ)+0)[2] =
((((alpha)))*((((sctx->t + 9*(0+2*sixy))+0)[2]) - (((sctx
->t + 9*(0+2*siy))+0)[2])) + (((sctx->t + 9*(0+2*siy))+
0)[2]))), (((Typ)+3)[0] = ((((alpha)))*((((sctx->t + 9*(0+
2*sixy))+3)[0]) - (((sctx->t + 9*(0+2*siy))+3)[0])) + (((sctx
->t + 9*(0+2*siy))+3)[0])), ((Typ)+3)[1] = ((((alpha)))*((
((sctx->t + 9*(0+2*sixy))+3)[1]) - (((sctx->t + 9*(0+2*
siy))+3)[1])) + (((sctx->t + 9*(0+2*siy))+3)[1])), ((Typ)+
3)[2] = ((((alpha)))*((((sctx->t + 9*(0+2*sixy))+3)[2]) - (
((sctx->t + 9*(0+2*siy))+3)[2])) + (((sctx->t + 9*(0+2*
siy))+3)[2]))), (((Typ)+6)[0] = ((((alpha)))*((((sctx->t +
9*(0+2*sixy))+6)[0]) - (((sctx->t + 9*(0+2*siy))+6)[0])) +
(((sctx->t + 9*(0+2*siy))+6)[0])), ((Typ)+6)[1] = ((((alpha
)))*((((sctx->t + 9*(0+2*sixy))+6)[1]) - (((sctx->t + 9
*(0+2*siy))+6)[1])) + (((sctx->t + 9*(0+2*siy))+6)[1])), (
(Typ)+6)[2] = ((((alpha)))*((((sctx->t + 9*(0+2*sixy))+6)[
2]) - (((sctx->t + 9*(0+2*siy))+6)[2])) + (((sctx->t + 9
*(0+2*siy))+6)[2]))));

283

ELL_3V_LERP(gyp, alpha, sctx->grad + 3*(0+2*siy),((gyp)[0] = (((alpha))*(((sctx->grad + 3*(0+2*sixy))[0]) -
((sctx->grad + 3*(0+2*siy))[0])) + ((sctx->grad + 3*(0
+2*siy))[0])), (gyp)[1] = (((alpha))*(((sctx->grad + 3*(0+
2*sixy))[1]) - ((sctx->grad + 3*(0+2*siy))[1])) + ((sctx->
grad + 3*(0+2*siy))[1])), (gyp)[2] = (((alpha))*(((sctx->grad
+ 3*(0+2*sixy))[2]) - ((sctx->grad + 3*(0+2*siy))[2])) + (
(sctx->grad + 3*(0+2*siy))[2])))

284

sctx->grad + 3*(0+2*sixy))((gyp)[0] = (((alpha))*(((sctx->grad + 3*(0+2*sixy))[0]) -
((sctx->grad + 3*(0+2*siy))[0])) + ((sctx->grad + 3*(0
+2*siy))[0])), (gyp)[1] = (((alpha))*(((sctx->grad + 3*(0+
2*sixy))[1]) - ((sctx->grad + 3*(0+2*siy))[1])) + ((sctx->
grad + 3*(0+2*siy))[1])), (gyp)[2] = (((alpha))*(((sctx->grad
+ 3*(0+2*sixy))[2]) - ((sctx->grad + 3*(0+2*siy))[2])) + (
(sctx->grad + 3*(0+2*siy))[2])));

285

}

286

if (yi!=0 && yi!=sy-1) {

287

ELL_3M_SCALE(Tym, 0.5, Tym)((((Tym)+0)[0] = ((0.5))*((Tym)+0)[0], ((Tym)+0)[1] = ((0.5))
*((Tym)+0)[1], ((Tym)+0)[2] = ((0.5))*((Tym)+0)[2]), (((Tym)+
3)[0] = ((0.5))*((Tym)+3)[0], ((Tym)+3)[1] = ((0.5))*((Tym)+3
)[1], ((Tym)+3)[2] = ((0.5))*((Tym)+3)[2]), (((Tym)+6)[0] = (
(0.5))*((Tym)+6)[0], ((Tym)+6)[1] = ((0.5))*((Tym)+6)[1], ((Tym
)+6)[2] = ((0.5))*((Tym)+6)[2])); ELL_3M_SCALE(Typ, 0.5, Typ)((((Typ)+0)[0] = ((0.5))*((Typ)+0)[0], ((Typ)+0)[1] = ((0.5))
*((Typ)+0)[1], ((Typ)+0)[2] = ((0.5))*((Typ)+0)[2]), (((Typ)+
3)[0] = ((0.5))*((Typ)+3)[0], ((Typ)+3)[1] = ((0.5))*((Typ)+3
)[1], ((Typ)+3)[2] = ((0.5))*((Typ)+3)[2]), (((Typ)+6)[0] = (
(0.5))*((Typ)+6)[0], ((Typ)+6)[1] = ((0.5))*((Typ)+6)[1], ((Typ
)+6)[2] = ((0.5))*((Typ)+6)[2]));

288

ELL_3V_SCALE(gym, 0.5, gym)((gym)[0] = (0.5)*(gym)[0], (gym)[1] = (0.5)*(gym)[1], (gym)[
2] = (0.5)*(gym)[2]); ELL_3V_SCALE(gyp, 0.5, gyp)((gyp)[0] = (0.5)*(gyp)[0], (gyp)[1] = (0.5)*(gyp)[1], (gyp)[
2] = (0.5)*(gyp)[2]);

289

}

290

computeGradientLin(res, T, g,

291

sctx->t + 9*(0+2*si), sctx->grad + 3*(0+2*si),

292

sctx->t + 9*(0+2*six), sctx->grad + 3*(0+2*six),

293

Tym, gym, Typ, gyp,

294

Tzm, gzm, Tzp, gzp);

295

break;

296

case 1:

297

ELL_3M_LERP(T, alpha, sctx->t + 9*(0+2*si), sctx->t + 9*(0+2*siy))((((T)+0)[0] = ((((alpha)))*((((sctx->t + 9*(0+2*siy))+0)[
0]) - (((sctx->t + 9*(0+2*si))+0)[0])) + (((sctx->t + 9
*(0+2*si))+0)[0])), ((T)+0)[1] = ((((alpha)))*((((sctx->t +
9*(0+2*siy))+0)[1]) - (((sctx->t + 9*(0+2*si))+0)[1])) + (
((sctx->t + 9*(0+2*si))+0)[1])), ((T)+0)[2] = ((((alpha)))
*((((sctx->t + 9*(0+2*siy))+0)[2]) - (((sctx->t + 9*(0+
2*si))+0)[2])) + (((sctx->t + 9*(0+2*si))+0)[2]))), (((T)+
3)[0] = ((((alpha)))*((((sctx->t + 9*(0+2*siy))+3)[0]) - (
((sctx->t + 9*(0+2*si))+3)[0])) + (((sctx->t + 9*(0+2*si
))+3)[0])), ((T)+3)[1] = ((((alpha)))*((((sctx->t + 9*(0+2
*siy))+3)[1]) - (((sctx->t + 9*(0+2*si))+3)[1])) + (((sctx
->t + 9*(0+2*si))+3)[1])), ((T)+3)[2] = ((((alpha)))*((((sctx
->t + 9*(0+2*siy))+3)[2]) - (((sctx->t + 9*(0+2*si))+3)
[2])) + (((sctx->t + 9*(0+2*si))+3)[2]))), (((T)+6)[0] = (
(((alpha)))*((((sctx->t + 9*(0+2*siy))+6)[0]) - (((sctx->
t + 9*(0+2*si))+6)[0])) + (((sctx->t + 9*(0+2*si))+6)[0]))
, ((T)+6)[1] = ((((alpha)))*((((sctx->t + 9*(0+2*siy))+6)[
1]) - (((sctx->t + 9*(0+2*si))+6)[1])) + (((sctx->t + 9
*(0+2*si))+6)[1])), ((T)+6)[2] = ((((alpha)))*((((sctx->t +
9*(0+2*siy))+6)[2]) - (((sctx->t + 9*(0+2*si))+6)[2])) + (
((sctx->t + 9*(0+2*si))+6)[2]))));

298

ELL_3V_LERP(g, alpha, sctx->grad + 3*(0+2*si), sctx->grad + 3*(0+2*siy))((g)[0] = (((alpha))*(((sctx->grad + 3*(0+2*siy))[0]) - ((
sctx->grad + 3*(0+2*si))[0])) + ((sctx->grad + 3*(0+2*si
))[0])), (g)[1] = (((alpha))*(((sctx->grad + 3*(0+2*siy))[
1]) - ((sctx->grad + 3*(0+2*si))[1])) + ((sctx->grad + 3
*(0+2*si))[1])), (g)[2] = (((alpha))*(((sctx->grad + 3*(0+
2*siy))[2]) - ((sctx->grad + 3*(0+2*si))[2])) + ((sctx->
grad + 3*(0+2*si))[2])));

299

ELL_3M_LERP(Tzp, alpha, sctx->t + 9*(1+2*si), sctx->t + 9*(1+2*siy))((((Tzp)+0)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*siy))+0
)[0]) - (((sctx->t + 9*(1+2*si))+0)[0])) + (((sctx->t +
9*(1+2*si))+0)[0])), ((Tzp)+0)[1] = ((((alpha)))*((((sctx->
t + 9*(1+2*siy))+0)[1]) - (((sctx->t + 9*(1+2*si))+0)[1]))
+ (((sctx->t + 9*(1+2*si))+0)[1])), ((Tzp)+0)[2] = ((((alpha
)))*((((sctx->t + 9*(1+2*siy))+0)[2]) - (((sctx->t + 9*
(1+2*si))+0)[2])) + (((sctx->t + 9*(1+2*si))+0)[2]))), (((
Tzp)+3)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*siy))+3)[0]
) - (((sctx->t + 9*(1+2*si))+3)[0])) + (((sctx->t + 9*(
1+2*si))+3)[0])), ((Tzp)+3)[1] = ((((alpha)))*((((sctx->t +
9*(1+2*siy))+3)[1]) - (((sctx->t + 9*(1+2*si))+3)[1])) + (
((sctx->t + 9*(1+2*si))+3)[1])), ((Tzp)+3)[2] = ((((alpha)
))*((((sctx->t + 9*(1+2*siy))+3)[2]) - (((sctx->t + 9*(
1+2*si))+3)[2])) + (((sctx->t + 9*(1+2*si))+3)[2]))), (((Tzp
)+6)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*siy))+6)[0]) -
(((sctx->t + 9*(1+2*si))+6)[0])) + (((sctx->t + 9*(1+2
*si))+6)[0])), ((Tzp)+6)[1] = ((((alpha)))*((((sctx->t + 9
*(1+2*siy))+6)[1]) - (((sctx->t + 9*(1+2*si))+6)[1])) + ((
(sctx->t + 9*(1+2*si))+6)[1])), ((Tzp)+6)[2] = ((((alpha))
)*((((sctx->t + 9*(1+2*siy))+6)[2]) - (((sctx->t + 9*(1
+2*si))+6)[2])) + (((sctx->t + 9*(1+2*si))+6)[2]))));

300

ELL_3V_LERP(gzp, alpha, sctx->grad + 3*(1+2*si), sctx->grad + 3*(1+2*siy))((gzp)[0] = (((alpha))*(((sctx->grad + 3*(1+2*siy))[0]) - (
(sctx->grad + 3*(1+2*si))[0])) + ((sctx->grad + 3*(1+2*
si))[0])), (gzp)[1] = (((alpha))*(((sctx->grad + 3*(1+2*siy
))[1]) - ((sctx->grad + 3*(1+2*si))[1])) + ((sctx->grad
+ 3*(1+2*si))[1])), (gzp)[2] = (((alpha))*(((sctx->grad +
3*(1+2*siy))[2]) - ((sctx->grad + 3*(1+2*si))[2])) + ((sctx
->grad + 3*(1+2*si))[2])));

301

if (bag->zi==0) {

302

303

} else {

304

ELL_3M_LERP(Tzm, alpha, sctx->tcontext + 9*(0+2*si),((((Tzm)+0)[0] = ((((alpha)))*((((sctx->tcontext + 9*(0+2*
siy))+0)[0]) - (((sctx->tcontext + 9*(0+2*si))+0)[0])) + (
((sctx->tcontext + 9*(0+2*si))+0)[0])), ((Tzm)+0)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(0+2*siy))+0)[1]) - (((sctx
->tcontext + 9*(0+2*si))+0)[1])) + (((sctx->tcontext + 9
*(0+2*si))+0)[1])), ((Tzm)+0)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(0+2*siy))+0)[2]) - (((sctx->tcontext + 9*(0+
2*si))+0)[2])) + (((sctx->tcontext + 9*(0+2*si))+0)[2]))),
(((Tzm)+3)[0] = ((((alpha)))*((((sctx->tcontext + 9*(0+2*
siy))+3)[0]) - (((sctx->tcontext + 9*(0+2*si))+3)[0])) + (
((sctx->tcontext + 9*(0+2*si))+3)[0])), ((Tzm)+3)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(0+2*siy))+3)[1]) - (((sctx
->tcontext + 9*(0+2*si))+3)[1])) + (((sctx->tcontext + 9
*(0+2*si))+3)[1])), ((Tzm)+3)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(0+2*siy))+3)[2]) - (((sctx->tcontext + 9*(0+
2*si))+3)[2])) + (((sctx->tcontext + 9*(0+2*si))+3)[2]))),
(((Tzm)+6)[0] = ((((alpha)))*((((sctx->tcontext + 9*(0+2*
siy))+6)[0]) - (((sctx->tcontext + 9*(0+2*si))+6)[0])) + (
((sctx->tcontext + 9*(0+2*si))+6)[0])), ((Tzm)+6)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(0+2*siy))+6)[1]) - (((sctx
->tcontext + 9*(0+2*si))+6)[1])) + (((sctx->tcontext + 9
*(0+2*si))+6)[1])), ((Tzm)+6)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(0+2*siy))+6)[2]) - (((sctx->tcontext + 9*(0+
2*si))+6)[2])) + (((sctx->tcontext + 9*(0+2*si))+6)[2]))))

305

sctx->tcontext + 9*(0+2*siy))((((Tzm)+0)[0] = ((((alpha)))*((((sctx->tcontext + 9*(0+2*
siy))+0)[0]) - (((sctx->tcontext + 9*(0+2*si))+0)[0])) + (
((sctx->tcontext + 9*(0+2*si))+0)[0])), ((Tzm)+0)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(0+2*siy))+0)[1]) - (((sctx
->tcontext + 9*(0+2*si))+0)[1])) + (((sctx->tcontext + 9
*(0+2*si))+0)[1])), ((Tzm)+0)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(0+2*siy))+0)[2]) - (((sctx->tcontext + 9*(0+
2*si))+0)[2])) + (((sctx->tcontext + 9*(0+2*si))+0)[2]))),
(((Tzm)+3)[0] = ((((alpha)))*((((sctx->tcontext + 9*(0+2*
siy))+3)[0]) - (((sctx->tcontext + 9*(0+2*si))+3)[0])) + (
((sctx->tcontext + 9*(0+2*si))+3)[0])), ((Tzm)+3)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(0+2*siy))+3)[1]) - (((sctx
->tcontext + 9*(0+2*si))+3)[1])) + (((sctx->tcontext + 9
*(0+2*si))+3)[1])), ((Tzm)+3)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(0+2*siy))+3)[2]) - (((sctx->tcontext + 9*(0+
2*si))+3)[2])) + (((sctx->tcontext + 9*(0+2*si))+3)[2]))),
(((Tzm)+6)[0] = ((((alpha)))*((((sctx->tcontext + 9*(0+2*
siy))+6)[0]) - (((sctx->tcontext + 9*(0+2*si))+6)[0])) + (
((sctx->tcontext + 9*(0+2*si))+6)[0])), ((Tzm)+6)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(0+2*siy))+6)[1]) - (((sctx
->tcontext + 9*(0+2*si))+6)[1])) + (((sctx->tcontext + 9
*(0+2*si))+6)[1])), ((Tzm)+6)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(0+2*siy))+6)[2]) - (((sctx->tcontext + 9*(0+
2*si))+6)[2])) + (((sctx->tcontext + 9*(0+2*si))+6)[2]))));

306

ELL_3V_LERP(gzm, alpha, sctx->gradcontext + 3*(0+2*si),((gzm)[0] = (((alpha))*(((sctx->gradcontext + 3*(0+2*siy))
[0]) - ((sctx->gradcontext + 3*(0+2*si))[0])) + ((sctx->
gradcontext + 3*(0+2*si))[0])), (gzm)[1] = (((alpha))*(((sctx
->gradcontext + 3*(0+2*siy))[1]) - ((sctx->gradcontext +
3*(0+2*si))[1])) + ((sctx->gradcontext + 3*(0+2*si))[1]))
, (gzm)[2] = (((alpha))*(((sctx->gradcontext + 3*(0+2*siy)
)[2]) - ((sctx->gradcontext + 3*(0+2*si))[2])) + ((sctx->
gradcontext + 3*(0+2*si))[2])))

307

sctx->gradcontext + 3*(0+2*siy))((gzm)[0] = (((alpha))*(((sctx->gradcontext + 3*(0+2*siy))
[0]) - ((sctx->gradcontext + 3*(0+2*si))[0])) + ((sctx->
gradcontext + 3*(0+2*si))[0])), (gzm)[1] = (((alpha))*(((sctx
->gradcontext + 3*(0+2*siy))[1]) - ((sctx->gradcontext +
3*(0+2*si))[1])) + ((sctx->gradcontext + 3*(0+2*si))[1]))
, (gzm)[2] = (((alpha))*(((sctx->gradcontext + 3*(0+2*siy)
)[2]) - ((sctx->gradcontext + 3*(0+2*si))[2])) + ((sctx->
gradcontext + 3*(0+2*si))[2])));

308

309

310

}

311

if (xi==0) {

312

ELL_3M_COPY(Txm, T)((((Txm)+0)[0] = ((T)+0)[0], ((Txm)+0)[1] = ((T)+0)[1], ((Txm
)+0)[2] = ((T)+0)[2]), (((Txm)+3)[0] = ((T)+3)[0], ((Txm)+3)[
1] = ((T)+3)[1], ((Txm)+3)[2] = ((T)+3)[2]), (((Txm)+6)[0] = (
(T)+6)[0], ((Txm)+6)[1] = ((T)+6)[1], ((Txm)+6)[2] = ((T)+6)[
2])); ELL_3V_COPY(gxm, g)((gxm)[0] = (g)[0], (gxm)[1] = (g)[1], (gxm)[2] = (g)[2]);

313

} else {

314

ELL_3M_LERP(Txm, alpha, sctx->t + 9*(0+2*siX), sctx->t + 9*(0+2*siXy))((((Txm)+0)[0] = ((((alpha)))*((((sctx->t + 9*(0+2*siXy))+
0)[0]) - (((sctx->t + 9*(0+2*siX))+0)[0])) + (((sctx->t
+ 9*(0+2*siX))+0)[0])), ((Txm)+0)[1] = ((((alpha)))*((((sctx
->t + 9*(0+2*siXy))+0)[1]) - (((sctx->t + 9*(0+2*siX))+
0)[1])) + (((sctx->t + 9*(0+2*siX))+0)[1])), ((Txm)+0)[2] =
((((alpha)))*((((sctx->t + 9*(0+2*siXy))+0)[2]) - (((sctx
->t + 9*(0+2*siX))+0)[2])) + (((sctx->t + 9*(0+2*siX))+
0)[2]))), (((Txm)+3)[0] = ((((alpha)))*((((sctx->t + 9*(0+
2*siXy))+3)[0]) - (((sctx->t + 9*(0+2*siX))+3)[0])) + (((sctx
->t + 9*(0+2*siX))+3)[0])), ((Txm)+3)[1] = ((((alpha)))*((
((sctx->t + 9*(0+2*siXy))+3)[1]) - (((sctx->t + 9*(0+2*
siX))+3)[1])) + (((sctx->t + 9*(0+2*siX))+3)[1])), ((Txm)+
3)[2] = ((((alpha)))*((((sctx->t + 9*(0+2*siXy))+3)[2]) - (
((sctx->t + 9*(0+2*siX))+3)[2])) + (((sctx->t + 9*(0+2*
siX))+3)[2]))), (((Txm)+6)[0] = ((((alpha)))*((((sctx->t +
9*(0+2*siXy))+6)[0]) - (((sctx->t + 9*(0+2*siX))+6)[0])) +
(((sctx->t + 9*(0+2*siX))+6)[0])), ((Txm)+6)[1] = ((((alpha
)))*((((sctx->t + 9*(0+2*siXy))+6)[1]) - (((sctx->t + 9
*(0+2*siX))+6)[1])) + (((sctx->t + 9*(0+2*siX))+6)[1])), (
(Txm)+6)[2] = ((((alpha)))*((((sctx->t + 9*(0+2*siXy))+6)[
2]) - (((sctx->t + 9*(0+2*siX))+6)[2])) + (((sctx->t + 9
*(0+2*siX))+6)[2]))));

315

ELL_3V_LERP(gxm, alpha, sctx->grad + 3*(0+2*siX),((gxm)[0] = (((alpha))*(((sctx->grad + 3*(0+2*siXy))[0]) -
((sctx->grad + 3*(0+2*siX))[0])) + ((sctx->grad + 3*(0
+2*siX))[0])), (gxm)[1] = (((alpha))*(((sctx->grad + 3*(0+
2*siXy))[1]) - ((sctx->grad + 3*(0+2*siX))[1])) + ((sctx->
grad + 3*(0+2*siX))[1])), (gxm)[2] = (((alpha))*(((sctx->grad
+ 3*(0+2*siXy))[2]) - ((sctx->grad + 3*(0+2*siX))[2])) + (
(sctx->grad + 3*(0+2*siX))[2])))

316

sctx->grad + 3*(0+2*siXy))((gxm)[0] = (((alpha))*(((sctx->grad + 3*(0+2*siXy))[0]) -
((sctx->grad + 3*(0+2*siX))[0])) + ((sctx->grad + 3*(0
+2*siX))[0])), (gxm)[1] = (((alpha))*(((sctx->grad + 3*(0+
2*siXy))[1]) - ((sctx->grad + 3*(0+2*siX))[1])) + ((sctx->
grad + 3*(0+2*siX))[1])), (gxm)[2] = (((alpha))*(((sctx->grad
+ 3*(0+2*siXy))[2]) - ((sctx->grad + 3*(0+2*siX))[2])) + (
(sctx->grad + 3*(0+2*siX))[2])));

317

}

318

if (xi==sx-1) {

319

ELL_3M_COPY(Txp, T)((((Txp)+0)[0] = ((T)+0)[0], ((Txp)+0)[1] = ((T)+0)[1], ((Txp
)+0)[2] = ((T)+0)[2]), (((Txp)+3)[0] = ((T)+3)[0], ((Txp)+3)[
1] = ((T)+3)[1], ((Txp)+3)[2] = ((T)+3)[2]), (((Txp)+6)[0] = (
(T)+6)[0], ((Txp)+6)[1] = ((T)+6)[1], ((Txp)+6)[2] = ((T)+6)[
2])); ELL_3V_COPY(gxm, g)((gxm)[0] = (g)[0], (gxm)[1] = (g)[1], (gxm)[2] = (g)[2]);

320

} else {

321

ELL_3M_LERP(Txp, alpha, sctx->t + 9*(0+2*six), sctx->t + 9*(0+2*sixy))((((Txp)+0)[0] = ((((alpha)))*((((sctx->t + 9*(0+2*sixy))+
0)[0]) - (((sctx->t + 9*(0+2*six))+0)[0])) + (((sctx->t
+ 9*(0+2*six))+0)[0])), ((Txp)+0)[1] = ((((alpha)))*((((sctx
->t + 9*(0+2*sixy))+0)[1]) - (((sctx->t + 9*(0+2*six))+
0)[1])) + (((sctx->t + 9*(0+2*six))+0)[1])), ((Txp)+0)[2] =
((((alpha)))*((((sctx->t + 9*(0+2*sixy))+0)[2]) - (((sctx
->t + 9*(0+2*six))+0)[2])) + (((sctx->t + 9*(0+2*six))+
0)[2]))), (((Txp)+3)[0] = ((((alpha)))*((((sctx->t + 9*(0+
2*sixy))+3)[0]) - (((sctx->t + 9*(0+2*six))+3)[0])) + (((sctx
->t + 9*(0+2*six))+3)[0])), ((Txp)+3)[1] = ((((alpha)))*((
((sctx->t + 9*(0+2*sixy))+3)[1]) - (((sctx->t + 9*(0+2*
six))+3)[1])) + (((sctx->t + 9*(0+2*six))+3)[1])), ((Txp)+
3)[2] = ((((alpha)))*((((sctx->t + 9*(0+2*sixy))+3)[2]) - (
((sctx->t + 9*(0+2*six))+3)[2])) + (((sctx->t + 9*(0+2*
six))+3)[2]))), (((Txp)+6)[0] = ((((alpha)))*((((sctx->t +
9*(0+2*sixy))+6)[0]) - (((sctx->t + 9*(0+2*six))+6)[0])) +
(((sctx->t + 9*(0+2*six))+6)[0])), ((Txp)+6)[1] = ((((alpha
)))*((((sctx->t + 9*(0+2*sixy))+6)[1]) - (((sctx->t + 9
*(0+2*six))+6)[1])) + (((sctx->t + 9*(0+2*six))+6)[1])), (
(Txp)+6)[2] = ((((alpha)))*((((sctx->t + 9*(0+2*sixy))+6)[
2]) - (((sctx->t + 9*(0+2*six))+6)[2])) + (((sctx->t + 9
*(0+2*six))+6)[2]))));

322

ELL_3V_LERP(gxp, alpha, sctx->grad + 3*(0+2*six),((gxp)[0] = (((alpha))*(((sctx->grad + 3*(0+2*sixy))[0]) -
((sctx->grad + 3*(0+2*six))[0])) + ((sctx->grad + 3*(0
+2*six))[0])), (gxp)[1] = (((alpha))*(((sctx->grad + 3*(0+
2*sixy))[1]) - ((sctx->grad + 3*(0+2*six))[1])) + ((sctx->
grad + 3*(0+2*six))[1])), (gxp)[2] = (((alpha))*(((sctx->grad
+ 3*(0+2*sixy))[2]) - ((sctx->grad + 3*(0+2*six))[2])) + (
(sctx->grad + 3*(0+2*six))[2])))

323

sctx->grad + 3*(0+2*sixy))((gxp)[0] = (((alpha))*(((sctx->grad + 3*(0+2*sixy))[0]) -
((sctx->grad + 3*(0+2*six))[0])) + ((sctx->grad + 3*(0
+2*six))[0])), (gxp)[1] = (((alpha))*(((sctx->grad + 3*(0+
2*sixy))[1]) - ((sctx->grad + 3*(0+2*six))[1])) + ((sctx->
grad + 3*(0+2*six))[1])), (gxp)[2] = (((alpha))*(((sctx->grad
+ 3*(0+2*sixy))[2]) - ((sctx->grad + 3*(0+2*six))[2])) + (
(sctx->grad + 3*(0+2*six))[2])));

324

}

325

if (xi!=0 && xi!=sx-1) {

326

ELL_3M_SCALE(Txm, 0.5, Txm)((((Txm)+0)[0] = ((0.5))*((Txm)+0)[0], ((Txm)+0)[1] = ((0.5))
*((Txm)+0)[1], ((Txm)+0)[2] = ((0.5))*((Txm)+0)[2]), (((Txm)+
3)[0] = ((0.5))*((Txm)+3)[0], ((Txm)+3)[1] = ((0.5))*((Txm)+3
)[1], ((Txm)+3)[2] = ((0.5))*((Txm)+3)[2]), (((Txm)+6)[0] = (
(0.5))*((Txm)+6)[0], ((Txm)+6)[1] = ((0.5))*((Txm)+6)[1], ((Txm
)+6)[2] = ((0.5))*((Txm)+6)[2])); ELL_3M_SCALE(Txp, 0.5, Txp)((((Txp)+0)[0] = ((0.5))*((Txp)+0)[0], ((Txp)+0)[1] = ((0.5))
*((Txp)+0)[1], ((Txp)+0)[2] = ((0.5))*((Txp)+0)[2]), (((Txp)+
3)[0] = ((0.5))*((Txp)+3)[0], ((Txp)+3)[1] = ((0.5))*((Txp)+3
)[1], ((Txp)+3)[2] = ((0.5))*((Txp)+3)[2]), (((Txp)+6)[0] = (
(0.5))*((Txp)+6)[0], ((Txp)+6)[1] = ((0.5))*((Txp)+6)[1], ((Txp
)+6)[2] = ((0.5))*((Txp)+6)[2]));

327

ELL_3V_SCALE(gxm, 0.5, gxm)((gxm)[0] = (0.5)*(gxm)[0], (gxm)[1] = (0.5)*(gxm)[1], (gxm)[
2] = (0.5)*(gxm)[2]); ELL_3V_SCALE(gxp, 0.5, gxp)((gxp)[0] = (0.5)*(gxp)[0], (gxp)[1] = (0.5)*(gxp)[1], (gxp)[
2] = (0.5)*(gxp)[2]);

328

}

329

computeGradientLin(res, T, g,

330

Txm, gxm, Txp, gxp,

331

sctx->t + 9*(0+2*si), sctx->grad + 3*(0+2*si),

332

sctx->t + 9*(0+2*siy), sctx->grad + 3*(0+2*siy),

333

T, g, Tzp, gzp);

334

break;

335

case 2:

336

ELL_3M_LERP(T, alpha, sctx->t + 9*(0+2*si), sctx->t + 9*(1+2*si))((((T)+0)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*si))+0)[0
]) - (((sctx->t + 9*(0+2*si))+0)[0])) + (((sctx->t + 9*
(0+2*si))+0)[0])), ((T)+0)[1] = ((((alpha)))*((((sctx->t +
9*(1+2*si))+0)[1]) - (((sctx->t + 9*(0+2*si))+0)[1])) + (
((sctx->t + 9*(0+2*si))+0)[1])), ((T)+0)[2] = ((((alpha)))
*((((sctx->t + 9*(1+2*si))+0)[2]) - (((sctx->t + 9*(0+2
*si))+0)[2])) + (((sctx->t + 9*(0+2*si))+0)[2]))), (((T)+3
)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*si))+3)[0]) - (((
sctx->t + 9*(0+2*si))+3)[0])) + (((sctx->t + 9*(0+2*si)
)+3)[0])), ((T)+3)[1] = ((((alpha)))*((((sctx->t + 9*(1+2*
si))+3)[1]) - (((sctx->t + 9*(0+2*si))+3)[1])) + (((sctx->
t + 9*(0+2*si))+3)[1])), ((T)+3)[2] = ((((alpha)))*((((sctx->
t + 9*(1+2*si))+3)[2]) - (((sctx->t + 9*(0+2*si))+3)[2])) +
(((sctx->t + 9*(0+2*si))+3)[2]))), (((T)+6)[0] = ((((alpha
)))*((((sctx->t + 9*(1+2*si))+6)[0]) - (((sctx->t + 9*(
0+2*si))+6)[0])) + (((sctx->t + 9*(0+2*si))+6)[0])), ((T)+
6)[1] = ((((alpha)))*((((sctx->t + 9*(1+2*si))+6)[1]) - ((
(sctx->t + 9*(0+2*si))+6)[1])) + (((sctx->t + 9*(0+2*si
))+6)[1])), ((T)+6)[2] = ((((alpha)))*((((sctx->t + 9*(1+2
*si))+6)[2]) - (((sctx->t + 9*(0+2*si))+6)[2])) + (((sctx->
t + 9*(0+2*si))+6)[2]))));

337

ELL_3V_LERP(g, alpha, sctx->grad + 3*(0+2*si), sctx->grad + 3*(1+2*si))((g)[0] = (((alpha))*(((sctx->grad + 3*(1+2*si))[0]) - ((sctx
->grad + 3*(0+2*si))[0])) + ((sctx->grad + 3*(0+2*si))[
0])), (g)[1] = (((alpha))*(((sctx->grad + 3*(1+2*si))[1]) -
((sctx->grad + 3*(0+2*si))[1])) + ((sctx->grad + 3*(0+
2*si))[1])), (g)[2] = (((alpha))*(((sctx->grad + 3*(1+2*si
))[2]) - ((sctx->grad + 3*(0+2*si))[2])) + ((sctx->grad
+ 3*(0+2*si))[2])));

338

if (xi==0) {

339

340

} else {

341

ELL_3M_LERP(Txm, alpha, sctx->t + 9*(0+2*siX), sctx->t + 9*(1+2*siX))((((Txm)+0)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*siX))+0
)[0]) - (((sctx->t + 9*(0+2*siX))+0)[0])) + (((sctx->t +
9*(0+2*siX))+0)[0])), ((Txm)+0)[1] = ((((alpha)))*((((sctx->
t + 9*(1+2*siX))+0)[1]) - (((sctx->t + 9*(0+2*siX))+0)[1])
) + (((sctx->t + 9*(0+2*siX))+0)[1])), ((Txm)+0)[2] = ((((
alpha)))*((((sctx->t + 9*(1+2*siX))+0)[2]) - (((sctx->t
+ 9*(0+2*siX))+0)[2])) + (((sctx->t + 9*(0+2*siX))+0)[2])
)), (((Txm)+3)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*siX)
)+3)[0]) - (((sctx->t + 9*(0+2*siX))+3)[0])) + (((sctx->
t + 9*(0+2*siX))+3)[0])), ((Txm)+3)[1] = ((((alpha)))*((((sctx
->t + 9*(1+2*siX))+3)[1]) - (((sctx->t + 9*(0+2*siX))+3
)[1])) + (((sctx->t + 9*(0+2*siX))+3)[1])), ((Txm)+3)[2] =
((((alpha)))*((((sctx->t + 9*(1+2*siX))+3)[2]) - (((sctx->
t + 9*(0+2*siX))+3)[2])) + (((sctx->t + 9*(0+2*siX))+3)[2]
))), (((Txm)+6)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*siX
))+6)[0]) - (((sctx->t + 9*(0+2*siX))+6)[0])) + (((sctx->
t + 9*(0+2*siX))+6)[0])), ((Txm)+6)[1] = ((((alpha)))*((((sctx
->t + 9*(1+2*siX))+6)[1]) - (((sctx->t + 9*(0+2*siX))+6
)[1])) + (((sctx->t + 9*(0+2*siX))+6)[1])), ((Txm)+6)[2] =
((((alpha)))*((((sctx->t + 9*(1+2*siX))+6)[2]) - (((sctx->
t + 9*(0+2*siX))+6)[2])) + (((sctx->t + 9*(0+2*siX))+6)[2]
))));

342

ELL_3V_LERP(gxm, alpha, sctx->grad + 3*(0+2*siX),((gxm)[0] = (((alpha))*(((sctx->grad + 3*(1+2*siX))[0]) - (
(sctx->grad + 3*(0+2*siX))[0])) + ((sctx->grad + 3*(0+2
*siX))[0])), (gxm)[1] = (((alpha))*(((sctx->grad + 3*(1+2*
siX))[1]) - ((sctx->grad + 3*(0+2*siX))[1])) + ((sctx->
grad + 3*(0+2*siX))[1])), (gxm)[2] = (((alpha))*(((sctx->grad
+ 3*(1+2*siX))[2]) - ((sctx->grad + 3*(0+2*siX))[2])) + (
(sctx->grad + 3*(0+2*siX))[2])))

343

sctx->grad + 3*(1+2*siX))((gxm)[0] = (((alpha))*(((sctx->grad + 3*(1+2*siX))[0]) - (
(sctx->grad + 3*(0+2*siX))[0])) + ((sctx->grad + 3*(0+2
*siX))[0])), (gxm)[1] = (((alpha))*(((sctx->grad + 3*(1+2*
siX))[1]) - ((sctx->grad + 3*(0+2*siX))[1])) + ((sctx->
grad + 3*(0+2*siX))[1])), (gxm)[2] = (((alpha))*(((sctx->grad
+ 3*(1+2*siX))[2]) - ((sctx->grad + 3*(0+2*siX))[2])) + (
(sctx->grad + 3*(0+2*siX))[2])));

344

}

345

if (xi==sx-1) {

346

ELL_3M_COPY(Txp, T)((((Txp)+0)[0] = ((T)+0)[0], ((Txp)+0)[1] = ((T)+0)[1], ((Txp
)+0)[2] = ((T)+0)[2]), (((Txp)+3)[0] = ((T)+3)[0], ((Txp)+3)[
1] = ((T)+3)[1], ((Txp)+3)[2] = ((T)+3)[2]), (((Txp)+6)[0] = (
(T)+6)[0], ((Txp)+6)[1] = ((T)+6)[1], ((Txp)+6)[2] = ((T)+6)[
2])); ELL_3V_COPY(gxp, g)((gxp)[0] = (g)[0], (gxp)[1] = (g)[1], (gxp)[2] = (g)[2]);

347

} else {

348

ELL_3M_LERP(Txp, alpha, sctx->t + 9*(0+2*six), sctx->t + 9*(1+2*six))((((Txp)+0)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*six))+0
)[0]) - (((sctx->t + 9*(0+2*six))+0)[0])) + (((sctx->t +
9*(0+2*six))+0)[0])), ((Txp)+0)[1] = ((((alpha)))*((((sctx->
t + 9*(1+2*six))+0)[1]) - (((sctx->t + 9*(0+2*six))+0)[1])
) + (((sctx->t + 9*(0+2*six))+0)[1])), ((Txp)+0)[2] = ((((
alpha)))*((((sctx->t + 9*(1+2*six))+0)[2]) - (((sctx->t
+ 9*(0+2*six))+0)[2])) + (((sctx->t + 9*(0+2*six))+0)[2])
)), (((Txp)+3)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*six)
)+3)[0]) - (((sctx->t + 9*(0+2*six))+3)[0])) + (((sctx->
t + 9*(0+2*six))+3)[0])), ((Txp)+3)[1] = ((((alpha)))*((((sctx
->t + 9*(1+2*six))+3)[1]) - (((sctx->t + 9*(0+2*six))+3
)[1])) + (((sctx->t + 9*(0+2*six))+3)[1])), ((Txp)+3)[2] =
((((alpha)))*((((sctx->t + 9*(1+2*six))+3)[2]) - (((sctx->
t + 9*(0+2*six))+3)[2])) + (((sctx->t + 9*(0+2*six))+3)[2]
))), (((Txp)+6)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*six
))+6)[0]) - (((sctx->t + 9*(0+2*six))+6)[0])) + (((sctx->
t + 9*(0+2*six))+6)[0])), ((Txp)+6)[1] = ((((alpha)))*((((sctx
->t + 9*(1+2*six))+6)[1]) - (((sctx->t + 9*(0+2*six))+6
)[1])) + (((sctx->t + 9*(0+2*six))+6)[1])), ((Txp)+6)[2] =
((((alpha)))*((((sctx->t + 9*(1+2*six))+6)[2]) - (((sctx->
t + 9*(0+2*six))+6)[2])) + (((sctx->t + 9*(0+2*six))+6)[2]
))));

349

ELL_3V_LERP(gxp, alpha, sctx->grad + 3*(0+2*six),((gxp)[0] = (((alpha))*(((sctx->grad + 3*(1+2*six))[0]) - (
(sctx->grad + 3*(0+2*six))[0])) + ((sctx->grad + 3*(0+2
*six))[0])), (gxp)[1] = (((alpha))*(((sctx->grad + 3*(1+2*
six))[1]) - ((sctx->grad + 3*(0+2*six))[1])) + ((sctx->
grad + 3*(0+2*six))[1])), (gxp)[2] = (((alpha))*(((sctx->grad
+ 3*(1+2*six))[2]) - ((sctx->grad + 3*(0+2*six))[2])) + (
(sctx->grad + 3*(0+2*six))[2])))

350

sctx->grad + 3*(1+2*six))((gxp)[0] = (((alpha))*(((sctx->grad + 3*(1+2*six))[0]) - (
(sctx->grad + 3*(0+2*six))[0])) + ((sctx->grad + 3*(0+2
*six))[0])), (gxp)[1] = (((alpha))*(((sctx->grad + 3*(1+2*
six))[1]) - ((sctx->grad + 3*(0+2*six))[1])) + ((sctx->
grad + 3*(0+2*six))[1])), (gxp)[2] = (((alpha))*(((sctx->grad
+ 3*(1+2*six))[2]) - ((sctx->grad + 3*(0+2*six))[2])) + (
(sctx->grad + 3*(0+2*six))[2])));

351

}

352

if (xi!=0 && xi!=sx-1) {

353

354

355

}

356

if (yi==0) {

357

358

} else {

359

ELL_3M_LERP(Tym, alpha, sctx->t + 9*(0+2*siY), sctx->t + 9*(1+2*siY))((((Tym)+0)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*siY))+0
)[0]) - (((sctx->t + 9*(0+2*siY))+0)[0])) + (((sctx->t +
9*(0+2*siY))+0)[0])), ((Tym)+0)[1] = ((((alpha)))*((((sctx->
t + 9*(1+2*siY))+0)[1]) - (((sctx->t + 9*(0+2*siY))+0)[1])
) + (((sctx->t + 9*(0+2*siY))+0)[1])), ((Tym)+0)[2] = ((((
alpha)))*((((sctx->t + 9*(1+2*siY))+0)[2]) - (((sctx->t
+ 9*(0+2*siY))+0)[2])) + (((sctx->t + 9*(0+2*siY))+0)[2])
)), (((Tym)+3)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*siY)
)+3)[0]) - (((sctx->t + 9*(0+2*siY))+3)[0])) + (((sctx->
t + 9*(0+2*siY))+3)[0])), ((Tym)+3)[1] = ((((alpha)))*((((sctx
->t + 9*(1+2*siY))+3)[1]) - (((sctx->t + 9*(0+2*siY))+3
)[1])) + (((sctx->t + 9*(0+2*siY))+3)[1])), ((Tym)+3)[2] =
((((alpha)))*((((sctx->t + 9*(1+2*siY))+3)[2]) - (((sctx->
t + 9*(0+2*siY))+3)[2])) + (((sctx->t + 9*(0+2*siY))+3)[2]
))), (((Tym)+6)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*siY
))+6)[0]) - (((sctx->t + 9*(0+2*siY))+6)[0])) + (((sctx->
t + 9*(0+2*siY))+6)[0])), ((Tym)+6)[1] = ((((alpha)))*((((sctx
->t + 9*(1+2*siY))+6)[1]) - (((sctx->t + 9*(0+2*siY))+6
)[1])) + (((sctx->t + 9*(0+2*siY))+6)[1])), ((Tym)+6)[2] =
((((alpha)))*((((sctx->t + 9*(1+2*siY))+6)[2]) - (((sctx->
t + 9*(0+2*siY))+6)[2])) + (((sctx->t + 9*(0+2*siY))+6)[2]
))));

360

ELL_3V_LERP(gym, alpha, sctx->grad + 3*(0+2*siY),((gym)[0] = (((alpha))*(((sctx->grad + 3*(1+2*siY))[0]) - (
(sctx->grad + 3*(0+2*siY))[0])) + ((sctx->grad + 3*(0+2
*siY))[0])), (gym)[1] = (((alpha))*(((sctx->grad + 3*(1+2*
siY))[1]) - ((sctx->grad + 3*(0+2*siY))[1])) + ((sctx->
grad + 3*(0+2*siY))[1])), (gym)[2] = (((alpha))*(((sctx->grad
+ 3*(1+2*siY))[2]) - ((sctx->grad + 3*(0+2*siY))[2])) + (
(sctx->grad + 3*(0+2*siY))[2])))

361

sctx->grad + 3*(1+2*siY))((gym)[0] = (((alpha))*(((sctx->grad + 3*(1+2*siY))[0]) - (
(sctx->grad + 3*(0+2*siY))[0])) + ((sctx->grad + 3*(0+2
*siY))[0])), (gym)[1] = (((alpha))*(((sctx->grad + 3*(1+2*
siY))[1]) - ((sctx->grad + 3*(0+2*siY))[1])) + ((sctx->
grad + 3*(0+2*siY))[1])), (gym)[2] = (((alpha))*(((sctx->grad
+ 3*(1+2*siY))[2]) - ((sctx->grad + 3*(0+2*siY))[2])) + (
(sctx->grad + 3*(0+2*siY))[2])));

362

}

363

if (yi==sy-1) {

364

365

} else {

366

ELL_3M_LERP(Typ, alpha, sctx->t + 9*(0+2*siy), sctx->t + 9*(1+2*siy))((((Typ)+0)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*siy))+0
)[0]) - (((sctx->t + 9*(0+2*siy))+0)[0])) + (((sctx->t +
9*(0+2*siy))+0)[0])), ((Typ)+0)[1] = ((((alpha)))*((((sctx->
t + 9*(1+2*siy))+0)[1]) - (((sctx->t + 9*(0+2*siy))+0)[1])
) + (((sctx->t + 9*(0+2*siy))+0)[1])), ((Typ)+0)[2] = ((((
alpha)))*((((sctx->t + 9*(1+2*siy))+0)[2]) - (((sctx->t
+ 9*(0+2*siy))+0)[2])) + (((sctx->t + 9*(0+2*siy))+0)[2])
)), (((Typ)+3)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*siy)
)+3)[0]) - (((sctx->t + 9*(0+2*siy))+3)[0])) + (((sctx->
t + 9*(0+2*siy))+3)[0])), ((Typ)+3)[1] = ((((alpha)))*((((sctx
->t + 9*(1+2*siy))+3)[1]) - (((sctx->t + 9*(0+2*siy))+3
)[1])) + (((sctx->t + 9*(0+2*siy))+3)[1])), ((Typ)+3)[2] =
((((alpha)))*((((sctx->t + 9*(1+2*siy))+3)[2]) - (((sctx->
t + 9*(0+2*siy))+3)[2])) + (((sctx->t + 9*(0+2*siy))+3)[2]
))), (((Typ)+6)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*siy
))+6)[0]) - (((sctx->t + 9*(0+2*siy))+6)[0])) + (((sctx->
t + 9*(0+2*siy))+6)[0])), ((Typ)+6)[1] = ((((alpha)))*((((sctx
->t + 9*(1+2*siy))+6)[1]) - (((sctx->t + 9*(0+2*siy))+6
)[1])) + (((sctx->t + 9*(0+2*siy))+6)[1])), ((Typ)+6)[2] =
((((alpha)))*((((sctx->t + 9*(1+2*siy))+6)[2]) - (((sctx->
t + 9*(0+2*siy))+6)[2])) + (((sctx->t + 9*(0+2*siy))+6)[2]
))));

367

ELL_3V_LERP(gyp, alpha, sctx->grad + 3*(0+2*siy),((gyp)[0] = (((alpha))*(((sctx->grad + 3*(1+2*siy))[0]) - (
(sctx->grad + 3*(0+2*siy))[0])) + ((sctx->grad + 3*(0+2
*siy))[0])), (gyp)[1] = (((alpha))*(((sctx->grad + 3*(1+2*
siy))[1]) - ((sctx->grad + 3*(0+2*siy))[1])) + ((sctx->
grad + 3*(0+2*siy))[1])), (gyp)[2] = (((alpha))*(((sctx->grad
+ 3*(1+2*siy))[2]) - ((sctx->grad + 3*(0+2*siy))[2])) + (
(sctx->grad + 3*(0+2*siy))[2])))

368

sctx->grad + 3*(1+2*siy))((gyp)[0] = (((alpha))*(((sctx->grad + 3*(1+2*siy))[0]) - (
(sctx->grad + 3*(0+2*siy))[0])) + ((sctx->grad + 3*(0+2
*siy))[0])), (gyp)[1] = (((alpha))*(((sctx->grad + 3*(1+2*
siy))[1]) - ((sctx->grad + 3*(0+2*siy))[1])) + ((sctx->
grad + 3*(0+2*siy))[1])), (gyp)[2] = (((alpha))*(((sctx->grad
+ 3*(1+2*siy))[2]) - ((sctx->grad + 3*(0+2*siy))[2])) + (
(sctx->grad + 3*(0+2*siy))[2])));

369

}

370

if (yi!=0 && yi!=sy-1) {

371

372

373

}

374

if (bag->zi>0 && bag->zi<sz-2) {

375

ELL_3M_LERP(Tzm, alpha, sctx->tcontext + 9*(0+2*si),((((Tzm)+0)[0] = ((((alpha)))*((((sctx->t + 9*(0+2*si))+0)
[0]) - (((sctx->tcontext + 9*(0+2*si))+0)[0])) + (((sctx->
tcontext + 9*(0+2*si))+0)[0])), ((Tzm)+0)[1] = ((((alpha)))*(
(((sctx->t + 9*(0+2*si))+0)[1]) - (((sctx->tcontext + 9
*(0+2*si))+0)[1])) + (((sctx->tcontext + 9*(0+2*si))+0)[1]
)), ((Tzm)+0)[2] = ((((alpha)))*((((sctx->t + 9*(0+2*si))+
0)[2]) - (((sctx->tcontext + 9*(0+2*si))+0)[2])) + (((sctx
->tcontext + 9*(0+2*si))+0)[2]))), (((Tzm)+3)[0] = ((((alpha
)))*((((sctx->t + 9*(0+2*si))+3)[0]) - (((sctx->tcontext
+ 9*(0+2*si))+3)[0])) + (((sctx->tcontext + 9*(0+2*si))+3
)[0])), ((Tzm)+3)[1] = ((((alpha)))*((((sctx->t + 9*(0+2*si
))+3)[1]) - (((sctx->tcontext + 9*(0+2*si))+3)[1])) + (((sctx
->tcontext + 9*(0+2*si))+3)[1])), ((Tzm)+3)[2] = ((((alpha
)))*((((sctx->t + 9*(0+2*si))+3)[2]) - (((sctx->tcontext
+ 9*(0+2*si))+3)[2])) + (((sctx->tcontext + 9*(0+2*si))+3
)[2]))), (((Tzm)+6)[0] = ((((alpha)))*((((sctx->t + 9*(0+2
*si))+6)[0]) - (((sctx->tcontext + 9*(0+2*si))+6)[0])) + (
((sctx->tcontext + 9*(0+2*si))+6)[0])), ((Tzm)+6)[1] = (((
(alpha)))*((((sctx->t + 9*(0+2*si))+6)[1]) - (((sctx->tcontext
+ 9*(0+2*si))+6)[1])) + (((sctx->tcontext + 9*(0+2*si))+6
)[1])), ((Tzm)+6)[2] = ((((alpha)))*((((sctx->t + 9*(0+2*si
))+6)[2]) - (((sctx->tcontext + 9*(0+2*si))+6)[2])) + (((sctx
->tcontext + 9*(0+2*si))+6)[2]))))

376

sctx->t + 9*(0+2*si))((((Tzm)+0)[0] = ((((alpha)))*((((sctx->t + 9*(0+2*si))+0)
[0]) - (((sctx->tcontext + 9*(0+2*si))+0)[0])) + (((sctx->
tcontext + 9*(0+2*si))+0)[0])), ((Tzm)+0)[1] = ((((alpha)))*(
(((sctx->t + 9*(0+2*si))+0)[1]) - (((sctx->tcontext + 9
*(0+2*si))+0)[1])) + (((sctx->tcontext + 9*(0+2*si))+0)[1]
)), ((Tzm)+0)[2] = ((((alpha)))*((((sctx->t + 9*(0+2*si))+
0)[2]) - (((sctx->tcontext + 9*(0+2*si))+0)[2])) + (((sctx
->tcontext + 9*(0+2*si))+0)[2]))), (((Tzm)+3)[0] = ((((alpha
)))*((((sctx->t + 9*(0+2*si))+3)[0]) - (((sctx->tcontext
+ 9*(0+2*si))+3)[0])) + (((sctx->tcontext + 9*(0+2*si))+3
)[0])), ((Tzm)+3)[1] = ((((alpha)))*((((sctx->t + 9*(0+2*si
))+3)[1]) - (((sctx->tcontext + 9*(0+2*si))+3)[1])) + (((sctx
->tcontext + 9*(0+2*si))+3)[1])), ((Tzm)+3)[2] = ((((alpha
)))*((((sctx->t + 9*(0+2*si))+3)[2]) - (((sctx->tcontext
+ 9*(0+2*si))+3)[2])) + (((sctx->tcontext + 9*(0+2*si))+3
)[2]))), (((Tzm)+6)[0] = ((((alpha)))*((((sctx->t + 9*(0+2
*si))+6)[0]) - (((sctx->tcontext + 9*(0+2*si))+6)[0])) + (
((sctx->tcontext + 9*(0+2*si))+6)[0])), ((Tzm)+6)[1] = (((
(alpha)))*((((sctx->t + 9*(0+2*si))+6)[1]) - (((sctx->tcontext
+ 9*(0+2*si))+6)[1])) + (((sctx->tcontext + 9*(0+2*si))+6
)[1])), ((Tzm)+6)[2] = ((((alpha)))*((((sctx->t + 9*(0+2*si
))+6)[2]) - (((sctx->tcontext + 9*(0+2*si))+6)[2])) + (((sctx
->tcontext + 9*(0+2*si))+6)[2]))));

377

ELL_3V_LERP(gzm, alpha, sctx->gradcontext + 3*(0+2*si),((gzm)[0] = (((alpha))*(((sctx->grad + 3*(0+2*si))[0]) - (
(sctx->gradcontext + 3*(0+2*si))[0])) + ((sctx->gradcontext
+ 3*(0+2*si))[0])), (gzm)[1] = (((alpha))*(((sctx->grad +
3*(0+2*si))[1]) - ((sctx->gradcontext + 3*(0+2*si))[1])) +
((sctx->gradcontext + 3*(0+2*si))[1])), (gzm)[2] = (((alpha
))*(((sctx->grad + 3*(0+2*si))[2]) - ((sctx->gradcontext
+ 3*(0+2*si))[2])) + ((sctx->gradcontext + 3*(0+2*si))[2]
)))

378

sctx->grad + 3*(0+2*si))((gzm)[0] = (((alpha))*(((sctx->grad + 3*(0+2*si))[0]) - (
(sctx->gradcontext + 3*(0+2*si))[0])) + ((sctx->gradcontext
+ 3*(0+2*si))[0])), (gzm)[1] = (((alpha))*(((sctx->grad +
3*(0+2*si))[1]) - ((sctx->gradcontext + 3*(0+2*si))[1])) +
((sctx->gradcontext + 3*(0+2*si))[1])), (gzm)[2] = (((alpha
))*(((sctx->grad + 3*(0+2*si))[2]) - ((sctx->gradcontext
+ 3*(0+2*si))[2])) + ((sctx->gradcontext + 3*(0+2*si))[2]
)));

379

ELL_3M_LERP(Tzp, alpha, sctx->t + 9*(1+2*si),((((Tzp)+0)[0] = ((((alpha)))*((((sctx->tcontext + 9*(1+2*
si))+0)[0]) - (((sctx->t + 9*(1+2*si))+0)[0])) + (((sctx->
t + 9*(1+2*si))+0)[0])), ((Tzp)+0)[1] = ((((alpha)))*((((sctx
->tcontext + 9*(1+2*si))+0)[1]) - (((sctx->t + 9*(1+2*si
))+0)[1])) + (((sctx->t + 9*(1+2*si))+0)[1])), ((Tzp)+0)[2
] = ((((alpha)))*((((sctx->tcontext + 9*(1+2*si))+0)[2]) -
(((sctx->t + 9*(1+2*si))+0)[2])) + (((sctx->t + 9*(1+2
*si))+0)[2]))), (((Tzp)+3)[0] = ((((alpha)))*((((sctx->tcontext
+ 9*(1+2*si))+3)[0]) - (((sctx->t + 9*(1+2*si))+3)[0])) +
(((sctx->t + 9*(1+2*si))+3)[0])), ((Tzp)+3)[1] = ((((alpha
)))*((((sctx->tcontext + 9*(1+2*si))+3)[1]) - (((sctx->
t + 9*(1+2*si))+3)[1])) + (((sctx->t + 9*(1+2*si))+3)[1]))
, ((Tzp)+3)[2] = ((((alpha)))*((((sctx->tcontext + 9*(1+2*
si))+3)[2]) - (((sctx->t + 9*(1+2*si))+3)[2])) + (((sctx->
t + 9*(1+2*si))+3)[2]))), (((Tzp)+6)[0] = ((((alpha)))*((((sctx
->tcontext + 9*(1+2*si))+6)[0]) - (((sctx->t + 9*(1+2*si
))+6)[0])) + (((sctx->t + 9*(1+2*si))+6)[0])), ((Tzp)+6)[1
] = ((((alpha)))*((((sctx->tcontext + 9*(1+2*si))+6)[1]) -
(((sctx->t + 9*(1+2*si))+6)[1])) + (((sctx->t + 9*(1+2
*si))+6)[1])), ((Tzp)+6)[2] = ((((alpha)))*((((sctx->tcontext
+ 9*(1+2*si))+6)[2]) - (((sctx->t + 9*(1+2*si))+6)[2])) +
(((sctx->t + 9*(1+2*si))+6)[2]))))

380

sctx->tcontext + 9*(1+2*si))((((Tzp)+0)[0] = ((((alpha)))*((((sctx->tcontext + 9*(1+2*
si))+0)[0]) - (((sctx->t + 9*(1+2*si))+0)[0])) + (((sctx->
t + 9*(1+2*si))+0)[0])), ((Tzp)+0)[1] = ((((alpha)))*((((sctx
->tcontext + 9*(1+2*si))+0)[1]) - (((sctx->t + 9*(1+2*si
))+0)[1])) + (((sctx->t + 9*(1+2*si))+0)[1])), ((Tzp)+0)[2
] = ((((alpha)))*((((sctx->tcontext + 9*(1+2*si))+0)[2]) -
(((sctx->t + 9*(1+2*si))+0)[2])) + (((sctx->t + 9*(1+2
*si))+0)[2]))), (((Tzp)+3)[0] = ((((alpha)))*((((sctx->tcontext
+ 9*(1+2*si))+3)[0]) - (((sctx->t + 9*(1+2*si))+3)[0])) +
(((sctx->t + 9*(1+2*si))+3)[0])), ((Tzp)+3)[1] = ((((alpha
)))*((((sctx->tcontext + 9*(1+2*si))+3)[1]) - (((sctx->
t + 9*(1+2*si))+3)[1])) + (((sctx->t + 9*(1+2*si))+3)[1]))
, ((Tzp)+3)[2] = ((((alpha)))*((((sctx->tcontext + 9*(1+2*
si))+3)[2]) - (((sctx->t + 9*(1+2*si))+3)[2])) + (((sctx->
t + 9*(1+2*si))+3)[2]))), (((Tzp)+6)[0] = ((((alpha)))*((((sctx
->tcontext + 9*(1+2*si))+6)[0]) - (((sctx->t + 9*(1+2*si
))+6)[0])) + (((sctx->t + 9*(1+2*si))+6)[0])), ((Tzp)+6)[1
] = ((((alpha)))*((((sctx->tcontext + 9*(1+2*si))+6)[1]) -
(((sctx->t + 9*(1+2*si))+6)[1])) + (((sctx->t + 9*(1+2
*si))+6)[1])), ((Tzp)+6)[2] = ((((alpha)))*((((sctx->tcontext
+ 9*(1+2*si))+6)[2]) - (((sctx->t + 9*(1+2*si))+6)[2])) +
(((sctx->t + 9*(1+2*si))+6)[2]))));

381

ELL_3V_LERP(gzp, alpha, sctx->grad + 3*(1+2*si),((gzp)[0] = (((alpha))*(((sctx->gradcontext + 3*(1+2*si))[
0]) - ((sctx->grad + 3*(1+2*si))[0])) + ((sctx->grad + 3
*(1+2*si))[0])), (gzp)[1] = (((alpha))*(((sctx->gradcontext
+ 3*(1+2*si))[1]) - ((sctx->grad + 3*(1+2*si))[1])) + ((sctx
->grad + 3*(1+2*si))[1])), (gzp)[2] = (((alpha))*(((sctx->
gradcontext + 3*(1+2*si))[2]) - ((sctx->grad + 3*(1+2*si))
[2])) + ((sctx->grad + 3*(1+2*si))[2])))

382

sctx->gradcontext + 3*(1+2*si))((gzp)[0] = (((alpha))*(((sctx->gradcontext + 3*(1+2*si))[
0]) - ((sctx->grad + 3*(1+2*si))[0])) + ((sctx->grad + 3
*(1+2*si))[0])), (gzp)[1] = (((alpha))*(((sctx->gradcontext
+ 3*(1+2*si))[1]) - ((sctx->grad + 3*(1+2*si))[1])) + ((sctx
->grad + 3*(1+2*si))[1])), (gzp)[2] = (((alpha))*(((sctx->
gradcontext + 3*(1+2*si))[2]) - ((sctx->grad + 3*(1+2*si))
[2])) + ((sctx->grad + 3*(1+2*si))[2])));

383

384

385

} else {

386

ELL_3M_COPY(Tzm, sctx->t + 9*(0+2*si))((((Tzm)+0)[0] = ((sctx->t + 9*(0+2*si))+0)[0], ((Tzm)+0)[
1] = ((sctx->t + 9*(0+2*si))+0)[1], ((Tzm)+0)[2] = ((sctx->
t + 9*(0+2*si))+0)[2]), (((Tzm)+3)[0] = ((sctx->t + 9*(0+2
*si))+3)[0], ((Tzm)+3)[1] = ((sctx->t + 9*(0+2*si))+3)[1],
((Tzm)+3)[2] = ((sctx->t + 9*(0+2*si))+3)[2]), (((Tzm)+6)
[0] = ((sctx->t + 9*(0+2*si))+6)[0], ((Tzm)+6)[1] = ((sctx
->t + 9*(0+2*si))+6)[1], ((Tzm)+6)[2] = ((sctx->t + 9*(
0+2*si))+6)[2]));

387

ELL_3V_COPY(gzm, sctx->grad + 3*(0+2*si))((gzm)[0] = (sctx->grad + 3*(0+2*si))[0], (gzm)[1] = (sctx
->grad + 3*(0+2*si))[1], (gzm)[2] = (sctx->grad + 3*(0+
2*si))[2]);

388

ELL_3M_COPY(Tzp, sctx->t + 9*(1+2*si))((((Tzp)+0)[0] = ((sctx->t + 9*(1+2*si))+0)[0], ((Tzp)+0)[
1] = ((sctx->t + 9*(1+2*si))+0)[1], ((Tzp)+0)[2] = ((sctx->
t + 9*(1+2*si))+0)[2]), (((Tzp)+3)[0] = ((sctx->t + 9*(1+2
*si))+3)[0], ((Tzp)+3)[1] = ((sctx->t + 9*(1+2*si))+3)[1],
((Tzp)+3)[2] = ((sctx->t + 9*(1+2*si))+3)[2]), (((Tzp)+6)
[0] = ((sctx->t + 9*(1+2*si))+6)[0], ((Tzp)+6)[1] = ((sctx
->t + 9*(1+2*si))+6)[1], ((Tzp)+6)[2] = ((sctx->t + 9*(
1+2*si))+6)[2]));

389

ELL_3V_COPY(gzp, sctx->grad + 3*(1+2*si))((gzp)[0] = (sctx->grad + 3*(1+2*si))[0], (gzp)[1] = (sctx
->grad + 3*(1+2*si))[1], (gzp)[2] = (sctx->grad + 3*(1+
2*si))[2]);

390

}

391

computeGradientLin(res, T, g,

392

Txm, gxm, Txp, gxp,

393

Tym, gym, Typ, gyp,

394

Tzm, gzm, Tzp, gzp);

395

break;

396

case 3:

397

ELL_3M_LERP(T, alpha, sctx->t + 9*(1+2*si), sctx->t + 9*(1+2*six))((((T)+0)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*six))+0)[
0]) - (((sctx->t + 9*(1+2*si))+0)[0])) + (((sctx->t + 9
*(1+2*si))+0)[0])), ((T)+0)[1] = ((((alpha)))*((((sctx->t +
9*(1+2*six))+0)[1]) - (((sctx->t + 9*(1+2*si))+0)[1])) + (
((sctx->t + 9*(1+2*si))+0)[1])), ((T)+0)[2] = ((((alpha)))
*((((sctx->t + 9*(1+2*six))+0)[2]) - (((sctx->t + 9*(1+
2*si))+0)[2])) + (((sctx->t + 9*(1+2*si))+0)[2]))), (((T)+
3)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*six))+3)[0]) - (
((sctx->t + 9*(1+2*si))+3)[0])) + (((sctx->t + 9*(1+2*si
))+3)[0])), ((T)+3)[1] = ((((alpha)))*((((sctx->t + 9*(1+2
*six))+3)[1]) - (((sctx->t + 9*(1+2*si))+3)[1])) + (((sctx
->t + 9*(1+2*si))+3)[1])), ((T)+3)[2] = ((((alpha)))*((((sctx
->t + 9*(1+2*six))+3)[2]) - (((sctx->t + 9*(1+2*si))+3)
[2])) + (((sctx->t + 9*(1+2*si))+3)[2]))), (((T)+6)[0] = (
(((alpha)))*((((sctx->t + 9*(1+2*six))+6)[0]) - (((sctx->
t + 9*(1+2*si))+6)[0])) + (((sctx->t + 9*(1+2*si))+6)[0]))
, ((T)+6)[1] = ((((alpha)))*((((sctx->t + 9*(1+2*six))+6)[
1]) - (((sctx->t + 9*(1+2*si))+6)[1])) + (((sctx->t + 9
*(1+2*si))+6)[1])), ((T)+6)[2] = ((((alpha)))*((((sctx->t +
9*(1+2*six))+6)[2]) - (((sctx->t + 9*(1+2*si))+6)[2])) + (
((sctx->t + 9*(1+2*si))+6)[2]))));

398

ELL_3V_LERP(g, alpha, sctx->grad + 3*(1+2*si), sctx->grad + 3*(1+2*six))((g)[0] = (((alpha))*(((sctx->grad + 3*(1+2*six))[0]) - ((
sctx->grad + 3*(1+2*si))[0])) + ((sctx->grad + 3*(1+2*si
))[0])), (g)[1] = (((alpha))*(((sctx->grad + 3*(1+2*six))[
1]) - ((sctx->grad + 3*(1+2*si))[1])) + ((sctx->grad + 3
*(1+2*si))[1])), (g)[2] = (((alpha))*(((sctx->grad + 3*(1+
2*six))[2]) - ((sctx->grad + 3*(1+2*si))[2])) + ((sctx->
grad + 3*(1+2*si))[2])));

399

ELL_3M_LERP(Tzm, alpha, sctx->t + 9*(0+2*si), sctx->t + 9*(0+2*six))((((Tzm)+0)[0] = ((((alpha)))*((((sctx->t + 9*(0+2*six))+0
)[0]) - (((sctx->t + 9*(0+2*si))+0)[0])) + (((sctx->t +
9*(0+2*si))+0)[0])), ((Tzm)+0)[1] = ((((alpha)))*((((sctx->
t + 9*(0+2*six))+0)[1]) - (((sctx->t + 9*(0+2*si))+0)[1]))
+ (((sctx->t + 9*(0+2*si))+0)[1])), ((Tzm)+0)[2] = ((((alpha
)))*((((sctx->t + 9*(0+2*six))+0)[2]) - (((sctx->t + 9*
(0+2*si))+0)[2])) + (((sctx->t + 9*(0+2*si))+0)[2]))), (((
Tzm)+3)[0] = ((((alpha)))*((((sctx->t + 9*(0+2*six))+3)[0]
) - (((sctx->t + 9*(0+2*si))+3)[0])) + (((sctx->t + 9*(
0+2*si))+3)[0])), ((Tzm)+3)[1] = ((((alpha)))*((((sctx->t +
9*(0+2*six))+3)[1]) - (((sctx->t + 9*(0+2*si))+3)[1])) + (
((sctx->t + 9*(0+2*si))+3)[1])), ((Tzm)+3)[2] = ((((alpha)
))*((((sctx->t + 9*(0+2*six))+3)[2]) - (((sctx->t + 9*(
0+2*si))+3)[2])) + (((sctx->t + 9*(0+2*si))+3)[2]))), (((Tzm
)+6)[0] = ((((alpha)))*((((sctx->t + 9*(0+2*six))+6)[0]) -
(((sctx->t + 9*(0+2*si))+6)[0])) + (((sctx->t + 9*(0+2
*si))+6)[0])), ((Tzm)+6)[1] = ((((alpha)))*((((sctx->t + 9
*(0+2*six))+6)[1]) - (((sctx->t + 9*(0+2*si))+6)[1])) + ((
(sctx->t + 9*(0+2*si))+6)[1])), ((Tzm)+6)[2] = ((((alpha))
)*((((sctx->t + 9*(0+2*six))+6)[2]) - (((sctx->t + 9*(0
+2*si))+6)[2])) + (((sctx->t + 9*(0+2*si))+6)[2]))));

400

ELL_3V_LERP(gzm, alpha, sctx->grad + 3*(0+2*si), sctx->grad + 3*(0+2*six))((gzm)[0] = (((alpha))*(((sctx->grad + 3*(0+2*six))[0]) - (
(sctx->grad + 3*(0+2*si))[0])) + ((sctx->grad + 3*(0+2*
si))[0])), (gzm)[1] = (((alpha))*(((sctx->grad + 3*(0+2*six
))[1]) - ((sctx->grad + 3*(0+2*si))[1])) + ((sctx->grad
+ 3*(0+2*si))[1])), (gzm)[2] = (((alpha))*(((sctx->grad +
3*(0+2*six))[2]) - ((sctx->grad + 3*(0+2*si))[2])) + ((sctx
->grad + 3*(0+2*si))[2])));

401

if (bag->zi==sz-2) {

402

ELL_3M_COPY(Tzp, T)((((Tzp)+0)[0] = ((T)+0)[0], ((Tzp)+0)[1] = ((T)+0)[1], ((Tzp
)+0)[2] = ((T)+0)[2]), (((Tzp)+3)[0] = ((T)+3)[0], ((Tzp)+3)[
1] = ((T)+3)[1], ((Tzp)+3)[2] = ((T)+3)[2]), (((Tzp)+6)[0] = (
(T)+6)[0], ((Tzp)+6)[1] = ((T)+6)[1], ((Tzp)+6)[2] = ((T)+6)[
2])); ELL_3V_COPY(gzp, g)((gzp)[0] = (g)[0], (gzp)[1] = (g)[1], (gzp)[2] = (g)[2]);

403

} else {

404

ELL_3M_LERP(Tzp, alpha, sctx->tcontext + 9*(1+2*si),((((Tzp)+0)[0] = ((((alpha)))*((((sctx->tcontext + 9*(1+2*
six))+0)[0]) - (((sctx->tcontext + 9*(1+2*si))+0)[0])) + (
((sctx->tcontext + 9*(1+2*si))+0)[0])), ((Tzp)+0)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(1+2*six))+0)[1]) - (((sctx
->tcontext + 9*(1+2*si))+0)[1])) + (((sctx->tcontext + 9
*(1+2*si))+0)[1])), ((Tzp)+0)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(1+2*six))+0)[2]) - (((sctx->tcontext + 9*(1+
2*si))+0)[2])) + (((sctx->tcontext + 9*(1+2*si))+0)[2]))),
(((Tzp)+3)[0] = ((((alpha)))*((((sctx->tcontext + 9*(1+2*
six))+3)[0]) - (((sctx->tcontext + 9*(1+2*si))+3)[0])) + (
((sctx->tcontext + 9*(1+2*si))+3)[0])), ((Tzp)+3)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(1+2*six))+3)[1]) - (((sctx
->tcontext + 9*(1+2*si))+3)[1])) + (((sctx->tcontext + 9
*(1+2*si))+3)[1])), ((Tzp)+3)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(1+2*six))+3)[2]) - (((sctx->tcontext + 9*(1+
2*si))+3)[2])) + (((sctx->tcontext + 9*(1+2*si))+3)[2]))),
(((Tzp)+6)[0] = ((((alpha)))*((((sctx->tcontext + 9*(1+2*
six))+6)[0]) - (((sctx->tcontext + 9*(1+2*si))+6)[0])) + (
((sctx->tcontext + 9*(1+2*si))+6)[0])), ((Tzp)+6)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(1+2*six))+6)[1]) - (((sctx
->tcontext + 9*(1+2*si))+6)[1])) + (((sctx->tcontext + 9
*(1+2*si))+6)[1])), ((Tzp)+6)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(1+2*six))+6)[2]) - (((sctx->tcontext + 9*(1+
2*si))+6)[2])) + (((sctx->tcontext + 9*(1+2*si))+6)[2]))))

405

sctx->tcontext + 9*(1+2*six))((((Tzp)+0)[0] = ((((alpha)))*((((sctx->tcontext + 9*(1+2*
six))+0)[0]) - (((sctx->tcontext + 9*(1+2*si))+0)[0])) + (
((sctx->tcontext + 9*(1+2*si))+0)[0])), ((Tzp)+0)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(1+2*six))+0)[1]) - (((sctx
->tcontext + 9*(1+2*si))+0)[1])) + (((sctx->tcontext + 9
*(1+2*si))+0)[1])), ((Tzp)+0)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(1+2*six))+0)[2]) - (((sctx->tcontext + 9*(1+
2*si))+0)[2])) + (((sctx->tcontext + 9*(1+2*si))+0)[2]))),
(((Tzp)+3)[0] = ((((alpha)))*((((sctx->tcontext + 9*(1+2*
six))+3)[0]) - (((sctx->tcontext + 9*(1+2*si))+3)[0])) + (
((sctx->tcontext + 9*(1+2*si))+3)[0])), ((Tzp)+3)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(1+2*six))+3)[1]) - (((sctx
->tcontext + 9*(1+2*si))+3)[1])) + (((sctx->tcontext + 9
*(1+2*si))+3)[1])), ((Tzp)+3)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(1+2*six))+3)[2]) - (((sctx->tcontext + 9*(1+
2*si))+3)[2])) + (((sctx->tcontext + 9*(1+2*si))+3)[2]))),
(((Tzp)+6)[0] = ((((alpha)))*((((sctx->tcontext + 9*(1+2*
six))+6)[0]) - (((sctx->tcontext + 9*(1+2*si))+6)[0])) + (
((sctx->tcontext + 9*(1+2*si))+6)[0])), ((Tzp)+6)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(1+2*six))+6)[1]) - (((sctx
->tcontext + 9*(1+2*si))+6)[1])) + (((sctx->tcontext + 9
*(1+2*si))+6)[1])), ((Tzp)+6)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(1+2*six))+6)[2]) - (((sctx->tcontext + 9*(1+
2*si))+6)[2])) + (((sctx->tcontext + 9*(1+2*si))+6)[2]))));

406

ELL_3V_LERP(gzp, alpha, sctx->gradcontext + 3*(1+2*si),((gzp)[0] = (((alpha))*(((sctx->gradcontext + 3*(1+2*six))
[0]) - ((sctx->gradcontext + 3*(1+2*si))[0])) + ((sctx->
gradcontext + 3*(1+2*si))[0])), (gzp)[1] = (((alpha))*(((sctx
->gradcontext + 3*(1+2*six))[1]) - ((sctx->gradcontext +
3*(1+2*si))[1])) + ((sctx->gradcontext + 3*(1+2*si))[1]))
, (gzp)[2] = (((alpha))*(((sctx->gradcontext + 3*(1+2*six)
)[2]) - ((sctx->gradcontext + 3*(1+2*si))[2])) + ((sctx->
gradcontext + 3*(1+2*si))[2])))

407

sctx->gradcontext + 3*(1+2*six))((gzp)[0] = (((alpha))*(((sctx->gradcontext + 3*(1+2*six))
[0]) - ((sctx->gradcontext + 3*(1+2*si))[0])) + ((sctx->
gradcontext + 3*(1+2*si))[0])), (gzp)[1] = (((alpha))*(((sctx
->gradcontext + 3*(1+2*six))[1]) - ((sctx->gradcontext +
3*(1+2*si))[1])) + ((sctx->gradcontext + 3*(1+2*si))[1]))
, (gzp)[2] = (((alpha))*(((sctx->gradcontext + 3*(1+2*six)
)[2]) - ((sctx->gradcontext + 3*(1+2*si))[2])) + ((sctx->
gradcontext + 3*(1+2*si))[2])));

408

409

410

}

411

if (xi>0 && xi<sx-2) {

412

unsigned int sixx = xi + 2 + sx*yi;

413

ELL_3M_LERP(Txm, alpha, sctx->t + 9*(1+2*siX), sctx->t + 9*(1+2*si))((((Txm)+0)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*si))+0)
[0]) - (((sctx->t + 9*(1+2*siX))+0)[0])) + (((sctx->t +
9*(1+2*siX))+0)[0])), ((Txm)+0)[1] = ((((alpha)))*((((sctx->
t + 9*(1+2*si))+0)[1]) - (((sctx->t + 9*(1+2*siX))+0)[1]))
+ (((sctx->t + 9*(1+2*siX))+0)[1])), ((Txm)+0)[2] = ((((alpha
)))*((((sctx->t + 9*(1+2*si))+0)[2]) - (((sctx->t + 9*(
1+2*siX))+0)[2])) + (((sctx->t + 9*(1+2*siX))+0)[2]))), ((
(Txm)+3)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*si))+3)[0]
) - (((sctx->t + 9*(1+2*siX))+3)[0])) + (((sctx->t + 9*
(1+2*siX))+3)[0])), ((Txm)+3)[1] = ((((alpha)))*((((sctx->
t + 9*(1+2*si))+3)[1]) - (((sctx->t + 9*(1+2*siX))+3)[1]))
+ (((sctx->t + 9*(1+2*siX))+3)[1])), ((Txm)+3)[2] = ((((alpha
)))*((((sctx->t + 9*(1+2*si))+3)[2]) - (((sctx->t + 9*(
1+2*siX))+3)[2])) + (((sctx->t + 9*(1+2*siX))+3)[2]))), ((
(Txm)+6)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*si))+6)[0]
) - (((sctx->t + 9*(1+2*siX))+6)[0])) + (((sctx->t + 9*
(1+2*siX))+6)[0])), ((Txm)+6)[1] = ((((alpha)))*((((sctx->
t + 9*(1+2*si))+6)[1]) - (((sctx->t + 9*(1+2*siX))+6)[1]))
+ (((sctx->t + 9*(1+2*siX))+6)[1])), ((Txm)+6)[2] = ((((alpha
)))*((((sctx->t + 9*(1+2*si))+6)[2]) - (((sctx->t + 9*(
1+2*siX))+6)[2])) + (((sctx->t + 9*(1+2*siX))+6)[2]))));

414

ELL_3V_LERP(gxm, alpha, sctx->grad + 3*(1+2*siX),((gxm)[0] = (((alpha))*(((sctx->grad + 3*(1+2*si))[0]) - (
(sctx->grad + 3*(1+2*siX))[0])) + ((sctx->grad + 3*(1+2
*siX))[0])), (gxm)[1] = (((alpha))*(((sctx->grad + 3*(1+2*
si))[1]) - ((sctx->grad + 3*(1+2*siX))[1])) + ((sctx->grad
+ 3*(1+2*siX))[1])), (gxm)[2] = (((alpha))*(((sctx->grad +
3*(1+2*si))[2]) - ((sctx->grad + 3*(1+2*siX))[2])) + ((sctx
->grad + 3*(1+2*siX))[2])))

415

sctx->grad + 3*(1+2*si))((gxm)[0] = (((alpha))*(((sctx->grad + 3*(1+2*si))[0]) - (
(sctx->grad + 3*(1+2*siX))[0])) + ((sctx->grad + 3*(1+2
*siX))[0])), (gxm)[1] = (((alpha))*(((sctx->grad + 3*(1+2*
si))[1]) - ((sctx->grad + 3*(1+2*siX))[1])) + ((sctx->grad
+ 3*(1+2*siX))[1])), (gxm)[2] = (((alpha))*(((sctx->grad +
3*(1+2*si))[2]) - ((sctx->grad + 3*(1+2*siX))[2])) + ((sctx
->grad + 3*(1+2*siX))[2])));

416

ELL_3M_LERP(Txp, alpha, sctx->t + 9*(1+2*six), sctx->t + 9*(1+2*sixx))((((Txp)+0)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*sixx))+
0)[0]) - (((sctx->t + 9*(1+2*six))+0)[0])) + (((sctx->t
+ 9*(1+2*six))+0)[0])), ((Txp)+0)[1] = ((((alpha)))*((((sctx
->t + 9*(1+2*sixx))+0)[1]) - (((sctx->t + 9*(1+2*six))+
0)[1])) + (((sctx->t + 9*(1+2*six))+0)[1])), ((Txp)+0)[2] =
((((alpha)))*((((sctx->t + 9*(1+2*sixx))+0)[2]) - (((sctx
->t + 9*(1+2*six))+0)[2])) + (((sctx->t + 9*(1+2*six))+
0)[2]))), (((Txp)+3)[0] = ((((alpha)))*((((sctx->t + 9*(1+
2*sixx))+3)[0]) - (((sctx->t + 9*(1+2*six))+3)[0])) + (((sctx
->t + 9*(1+2*six))+3)[0])), ((Txp)+3)[1] = ((((alpha)))*((
((sctx->t + 9*(1+2*sixx))+3)[1]) - (((sctx->t + 9*(1+2*
six))+3)[1])) + (((sctx->t + 9*(1+2*six))+3)[1])), ((Txp)+
3)[2] = ((((alpha)))*((((sctx->t + 9*(1+2*sixx))+3)[2]) - (
((sctx->t + 9*(1+2*six))+3)[2])) + (((sctx->t + 9*(1+2*
six))+3)[2]))), (((Txp)+6)[0] = ((((alpha)))*((((sctx->t +
9*(1+2*sixx))+6)[0]) - (((sctx->t + 9*(1+2*six))+6)[0])) +
(((sctx->t + 9*(1+2*six))+6)[0])), ((Txp)+6)[1] = ((((alpha
)))*((((sctx->t + 9*(1+2*sixx))+6)[1]) - (((sctx->t + 9
*(1+2*six))+6)[1])) + (((sctx->t + 9*(1+2*six))+6)[1])), (
(Txp)+6)[2] = ((((alpha)))*((((sctx->t + 9*(1+2*sixx))+6)[
2]) - (((sctx->t + 9*(1+2*six))+6)[2])) + (((sctx->t + 9
*(1+2*six))+6)[2]))));

417

ELL_3V_LERP(gxp, alpha, sctx->grad + 3*(1+2*six),((gxp)[0] = (((alpha))*(((sctx->grad + 3*(1+2*sixx))[0]) -
((sctx->grad + 3*(1+2*six))[0])) + ((sctx->grad + 3*(1
+2*six))[0])), (gxp)[1] = (((alpha))*(((sctx->grad + 3*(1+
2*sixx))[1]) - ((sctx->grad + 3*(1+2*six))[1])) + ((sctx->
grad + 3*(1+2*six))[1])), (gxp)[2] = (((alpha))*(((sctx->grad
+ 3*(1+2*sixx))[2]) - ((sctx->grad + 3*(1+2*six))[2])) + (
(sctx->grad + 3*(1+2*six))[2])))

418

sctx->grad + 3*(1+2*sixx))((gxp)[0] = (((alpha))*(((sctx->grad + 3*(1+2*sixx))[0]) -
((sctx->grad + 3*(1+2*six))[0])) + ((sctx->grad + 3*(1
+2*six))[0])), (gxp)[1] = (((alpha))*(((sctx->grad + 3*(1+
2*sixx))[1]) - ((sctx->grad + 3*(1+2*six))[1])) + ((sctx->
grad + 3*(1+2*six))[1])), (gxp)[2] = (((alpha))*(((sctx->grad
+ 3*(1+2*sixx))[2]) - ((sctx->grad + 3*(1+2*six))[2])) + (
(sctx->grad + 3*(1+2*six))[2])));

419

420

421

} else {

422

ELL_3M_COPY(Txm, sctx->t + 9*(1+2*si))((((Txm)+0)[0] = ((sctx->t + 9*(1+2*si))+0)[0], ((Txm)+0)[
1] = ((sctx->t + 9*(1+2*si))+0)[1], ((Txm)+0)[2] = ((sctx->
t + 9*(1+2*si))+0)[2]), (((Txm)+3)[0] = ((sctx->t + 9*(1+2
*si))+3)[0], ((Txm)+3)[1] = ((sctx->t + 9*(1+2*si))+3)[1],
((Txm)+3)[2] = ((sctx->t + 9*(1+2*si))+3)[2]), (((Txm)+6)
[0] = ((sctx->t + 9*(1+2*si))+6)[0], ((Txm)+6)[1] = ((sctx
->t + 9*(1+2*si))+6)[1], ((Txm)+6)[2] = ((sctx->t + 9*(
1+2*si))+6)[2]));

423

ELL_3V_COPY(gxm, sctx->grad + 3*(1+2*si))((gxm)[0] = (sctx->grad + 3*(1+2*si))[0], (gxm)[1] = (sctx
->grad + 3*(1+2*si))[1], (gxm)[2] = (sctx->grad + 3*(1+
2*si))[2]);

424

ELL_3M_COPY(Txp, sctx->t + 9*(1+2*six))((((Txp)+0)[0] = ((sctx->t + 9*(1+2*six))+0)[0], ((Txp)+0)
[1] = ((sctx->t + 9*(1+2*six))+0)[1], ((Txp)+0)[2] = ((sctx
->t + 9*(1+2*six))+0)[2]), (((Txp)+3)[0] = ((sctx->t + 9
*(1+2*six))+3)[0], ((Txp)+3)[1] = ((sctx->t + 9*(1+2*six))
+3)[1], ((Txp)+3)[2] = ((sctx->t + 9*(1+2*six))+3)[2]), ((
(Txp)+6)[0] = ((sctx->t + 9*(1+2*six))+6)[0], ((Txp)+6)[1]
= ((sctx->t + 9*(1+2*six))+6)[1], ((Txp)+6)[2] = ((sctx->
t + 9*(1+2*six))+6)[2]));

425

ELL_3V_COPY(gxp, sctx->grad + 3*(1+2*six))((gxp)[0] = (sctx->grad + 3*(1+2*six))[0], (gxp)[1] = (sctx
->grad + 3*(1+2*six))[1], (gxp)[2] = (sctx->grad + 3*(1
+2*six))[2]);

426

}

427

if (yi==0) {

428

429

} else {

430

ELL_3M_LERP(Tym, alpha, sctx->t + 9*(1+2*siY), sctx->t + 9*(1+2*sixY))((((Tym)+0)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*sixY))+
0)[0]) - (((sctx->t + 9*(1+2*siY))+0)[0])) + (((sctx->t
+ 9*(1+2*siY))+0)[0])), ((Tym)+0)[1] = ((((alpha)))*((((sctx
->t + 9*(1+2*sixY))+0)[1]) - (((sctx->t + 9*(1+2*siY))+
0)[1])) + (((sctx->t + 9*(1+2*siY))+0)[1])), ((Tym)+0)[2] =
((((alpha)))*((((sctx->t + 9*(1+2*sixY))+0)[2]) - (((sctx
->t + 9*(1+2*siY))+0)[2])) + (((sctx->t + 9*(1+2*siY))+
0)[2]))), (((Tym)+3)[0] = ((((alpha)))*((((sctx->t + 9*(1+
2*sixY))+3)[0]) - (((sctx->t + 9*(1+2*siY))+3)[0])) + (((sctx
->t + 9*(1+2*siY))+3)[0])), ((Tym)+3)[1] = ((((alpha)))*((
((sctx->t + 9*(1+2*sixY))+3)[1]) - (((sctx->t + 9*(1+2*
siY))+3)[1])) + (((sctx->t + 9*(1+2*siY))+3)[1])), ((Tym)+
3)[2] = ((((alpha)))*((((sctx->t + 9*(1+2*sixY))+3)[2]) - (
((sctx->t + 9*(1+2*siY))+3)[2])) + (((sctx->t + 9*(1+2*
siY))+3)[2]))), (((Tym)+6)[0] = ((((alpha)))*((((sctx->t +
9*(1+2*sixY))+6)[0]) - (((sctx->t + 9*(1+2*siY))+6)[0])) +
(((sctx->t + 9*(1+2*siY))+6)[0])), ((Tym)+6)[1] = ((((alpha
)))*((((sctx->t + 9*(1+2*sixY))+6)[1]) - (((sctx->t + 9
*(1+2*siY))+6)[1])) + (((sctx->t + 9*(1+2*siY))+6)[1])), (
(Tym)+6)[2] = ((((alpha)))*((((sctx->t + 9*(1+2*sixY))+6)[
2]) - (((sctx->t + 9*(1+2*siY))+6)[2])) + (((sctx->t + 9
*(1+2*siY))+6)[2]))));

431

ELL_3V_LERP(gym, alpha, sctx->grad + 3*(1+2*siY),((gym)[0] = (((alpha))*(((sctx->grad + 3*(1+2*sixY))[0]) -
((sctx->grad + 3*(1+2*siY))[0])) + ((sctx->grad + 3*(1
+2*siY))[0])), (gym)[1] = (((alpha))*(((sctx->grad + 3*(1+
2*sixY))[1]) - ((sctx->grad + 3*(1+2*siY))[1])) + ((sctx->
grad + 3*(1+2*siY))[1])), (gym)[2] = (((alpha))*(((sctx->grad
+ 3*(1+2*sixY))[2]) - ((sctx->grad + 3*(1+2*siY))[2])) + (
(sctx->grad + 3*(1+2*siY))[2])))

432

sctx->grad + 3*(1+2*sixY))((gym)[0] = (((alpha))*(((sctx->grad + 3*(1+2*sixY))[0]) -
((sctx->grad + 3*(1+2*siY))[0])) + ((sctx->grad + 3*(1
+2*siY))[0])), (gym)[1] = (((alpha))*(((sctx->grad + 3*(1+
2*sixY))[1]) - ((sctx->grad + 3*(1+2*siY))[1])) + ((sctx->
grad + 3*(1+2*siY))[1])), (gym)[2] = (((alpha))*(((sctx->grad
+ 3*(1+2*sixY))[2]) - ((sctx->grad + 3*(1+2*siY))[2])) + (
(sctx->grad + 3*(1+2*siY))[2])));

433

}

434

if (yi==sy-1) {

435

436

} else {

437

ELL_3M_LERP(Typ, alpha, sctx->t + 9*(1+2*siy), sctx->t + 9*(1+2*sixy))((((Typ)+0)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*sixy))+
0)[0]) - (((sctx->t + 9*(1+2*siy))+0)[0])) + (((sctx->t
+ 9*(1+2*siy))+0)[0])), ((Typ)+0)[1] = ((((alpha)))*((((sctx
->t + 9*(1+2*sixy))+0)[1]) - (((sctx->t + 9*(1+2*siy))+
0)[1])) + (((sctx->t + 9*(1+2*siy))+0)[1])), ((Typ)+0)[2] =
((((alpha)))*((((sctx->t + 9*(1+2*sixy))+0)[2]) - (((sctx
->t + 9*(1+2*siy))+0)[2])) + (((sctx->t + 9*(1+2*siy))+
0)[2]))), (((Typ)+3)[0] = ((((alpha)))*((((sctx->t + 9*(1+
2*sixy))+3)[0]) - (((sctx->t + 9*(1+2*siy))+3)[0])) + (((sctx
->t + 9*(1+2*siy))+3)[0])), ((Typ)+3)[1] = ((((alpha)))*((
((sctx->t + 9*(1+2*sixy))+3)[1]) - (((sctx->t + 9*(1+2*
siy))+3)[1])) + (((sctx->t + 9*(1+2*siy))+3)[1])), ((Typ)+
3)[2] = ((((alpha)))*((((sctx->t + 9*(1+2*sixy))+3)[2]) - (
((sctx->t + 9*(1+2*siy))+3)[2])) + (((sctx->t + 9*(1+2*
siy))+3)[2]))), (((Typ)+6)[0] = ((((alpha)))*((((sctx->t +
9*(1+2*sixy))+6)[0]) - (((sctx->t + 9*(1+2*siy))+6)[0])) +
(((sctx->t + 9*(1+2*siy))+6)[0])), ((Typ)+6)[1] = ((((alpha
)))*((((sctx->t + 9*(1+2*sixy))+6)[1]) - (((sctx->t + 9
*(1+2*siy))+6)[1])) + (((sctx->t + 9*(1+2*siy))+6)[1])), (
(Typ)+6)[2] = ((((alpha)))*((((sctx->t + 9*(1+2*sixy))+6)[
2]) - (((sctx->t + 9*(1+2*siy))+6)[2])) + (((sctx->t + 9
*(1+2*siy))+6)[2]))));

438

ELL_3V_LERP(gyp, alpha, sctx->grad + 3*(1+2*siy),((gyp)[0] = (((alpha))*(((sctx->grad + 3*(1+2*sixy))[0]) -
((sctx->grad + 3*(1+2*siy))[0])) + ((sctx->grad + 3*(1
+2*siy))[0])), (gyp)[1] = (((alpha))*(((sctx->grad + 3*(1+
2*sixy))[1]) - ((sctx->grad + 3*(1+2*siy))[1])) + ((sctx->
grad + 3*(1+2*siy))[1])), (gyp)[2] = (((alpha))*(((sctx->grad
+ 3*(1+2*sixy))[2]) - ((sctx->grad + 3*(1+2*siy))[2])) + (
(sctx->grad + 3*(1+2*siy))[2])))

439

sctx->grad + 3*(1+2*sixy))((gyp)[0] = (((alpha))*(((sctx->grad + 3*(1+2*sixy))[0]) -
((sctx->grad + 3*(1+2*siy))[0])) + ((sctx->grad + 3*(1
+2*siy))[0])), (gyp)[1] = (((alpha))*(((sctx->grad + 3*(1+
2*sixy))[1]) - ((sctx->grad + 3*(1+2*siy))[1])) + ((sctx->
grad + 3*(1+2*siy))[1])), (gyp)[2] = (((alpha))*(((sctx->grad
+ 3*(1+2*sixy))[2]) - ((sctx->grad + 3*(1+2*siy))[2])) + (
(sctx->grad + 3*(1+2*siy))[2])));

440

}

441

if (yi!=0 && yi!=sy-1) {

442

443

444

}

445

computeGradientLin(res, T, g,

446

Txm, gxm, Txp, gxp,

447

Tym, gym, Typ, gyp,

448

Tzm, gzm, Tzp, gzp);

449

break;

450

case 4:

451

ELL_3M_LERP(T, alpha, sctx->t + 9*(1+2*si), sctx->t + 9*(1+2*siy))((((T)+0)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*siy))+0)[
0]) - (((sctx->t + 9*(1+2*si))+0)[0])) + (((sctx->t + 9
*(1+2*si))+0)[0])), ((T)+0)[1] = ((((alpha)))*((((sctx->t +
9*(1+2*siy))+0)[1]) - (((sctx->t + 9*(1+2*si))+0)[1])) + (
((sctx->t + 9*(1+2*si))+0)[1])), ((T)+0)[2] = ((((alpha)))
*((((sctx->t + 9*(1+2*siy))+0)[2]) - (((sctx->t + 9*(1+
2*si))+0)[2])) + (((sctx->t + 9*(1+2*si))+0)[2]))), (((T)+
3)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*siy))+3)[0]) - (
((sctx->t + 9*(1+2*si))+3)[0])) + (((sctx->t + 9*(1+2*si
))+3)[0])), ((T)+3)[1] = ((((alpha)))*((((sctx->t + 9*(1+2
*siy))+3)[1]) - (((sctx->t + 9*(1+2*si))+3)[1])) + (((sctx
->t + 9*(1+2*si))+3)[1])), ((T)+3)[2] = ((((alpha)))*((((sctx
->t + 9*(1+2*siy))+3)[2]) - (((sctx->t + 9*(1+2*si))+3)
[2])) + (((sctx->t + 9*(1+2*si))+3)[2]))), (((T)+6)[0] = (
(((alpha)))*((((sctx->t + 9*(1+2*siy))+6)[0]) - (((sctx->
t + 9*(1+2*si))+6)[0])) + (((sctx->t + 9*(1+2*si))+6)[0]))
, ((T)+6)[1] = ((((alpha)))*((((sctx->t + 9*(1+2*siy))+6)[
1]) - (((sctx->t + 9*(1+2*si))+6)[1])) + (((sctx->t + 9
*(1+2*si))+6)[1])), ((T)+6)[2] = ((((alpha)))*((((sctx->t +
9*(1+2*siy))+6)[2]) - (((sctx->t + 9*(1+2*si))+6)[2])) + (
((sctx->t + 9*(1+2*si))+6)[2]))));

452

ELL_3V_LERP(g, alpha, sctx->grad + 3*(1+2*si), sctx->grad + 3*(1+2*siy))((g)[0] = (((alpha))*(((sctx->grad + 3*(1+2*siy))[0]) - ((
sctx->grad + 3*(1+2*si))[0])) + ((sctx->grad + 3*(1+2*si
))[0])), (g)[1] = (((alpha))*(((sctx->grad + 3*(1+2*siy))[
1]) - ((sctx->grad + 3*(1+2*si))[1])) + ((sctx->grad + 3
*(1+2*si))[1])), (g)[2] = (((alpha))*(((sctx->grad + 3*(1+
2*siy))[2]) - ((sctx->grad + 3*(1+2*si))[2])) + ((sctx->
grad + 3*(1+2*si))[2])));

453

ELL_3M_LERP(Tzm, alpha, sctx->t + 9*(0+2*si), sctx->t + 9*(0+2*siy))((((Tzm)+0)[0] = ((((alpha)))*((((sctx->t + 9*(0+2*siy))+0
)[0]) - (((sctx->t + 9*(0+2*si))+0)[0])) + (((sctx->t +
9*(0+2*si))+0)[0])), ((Tzm)+0)[1] = ((((alpha)))*((((sctx->
t + 9*(0+2*siy))+0)[1]) - (((sctx->t + 9*(0+2*si))+0)[1]))
+ (((sctx->t + 9*(0+2*si))+0)[1])), ((Tzm)+0)[2] = ((((alpha
)))*((((sctx->t + 9*(0+2*siy))+0)[2]) - (((sctx->t + 9*
(0+2*si))+0)[2])) + (((sctx->t + 9*(0+2*si))+0)[2]))), (((
Tzm)+3)[0] = ((((alpha)))*((((sctx->t + 9*(0+2*siy))+3)[0]
) - (((sctx->t + 9*(0+2*si))+3)[0])) + (((sctx->t + 9*(
0+2*si))+3)[0])), ((Tzm)+3)[1] = ((((alpha)))*((((sctx->t +
9*(0+2*siy))+3)[1]) - (((sctx->t + 9*(0+2*si))+3)[1])) + (
((sctx->t + 9*(0+2*si))+3)[1])), ((Tzm)+3)[2] = ((((alpha)
))*((((sctx->t + 9*(0+2*siy))+3)[2]) - (((sctx->t + 9*(
0+2*si))+3)[2])) + (((sctx->t + 9*(0+2*si))+3)[2]))), (((Tzm
)+6)[0] = ((((alpha)))*((((sctx->t + 9*(0+2*siy))+6)[0]) -
(((sctx->t + 9*(0+2*si))+6)[0])) + (((sctx->t + 9*(0+2
*si))+6)[0])), ((Tzm)+6)[1] = ((((alpha)))*((((sctx->t + 9
*(0+2*siy))+6)[1]) - (((sctx->t + 9*(0+2*si))+6)[1])) + ((
(sctx->t + 9*(0+2*si))+6)[1])), ((Tzm)+6)[2] = ((((alpha))
)*((((sctx->t + 9*(0+2*siy))+6)[2]) - (((sctx->t + 9*(0
+2*si))+6)[2])) + (((sctx->t + 9*(0+2*si))+6)[2]))));

454

ELL_3V_LERP(gzm, alpha, sctx->grad + 3*(0+2*si), sctx->grad + 3*(0+2*siy))((gzm)[0] = (((alpha))*(((sctx->grad + 3*(0+2*siy))[0]) - (
(sctx->grad + 3*(0+2*si))[0])) + ((sctx->grad + 3*(0+2*
si))[0])), (gzm)[1] = (((alpha))*(((sctx->grad + 3*(0+2*siy
))[1]) - ((sctx->grad + 3*(0+2*si))[1])) + ((sctx->grad
+ 3*(0+2*si))[1])), (gzm)[2] = (((alpha))*(((sctx->grad +
3*(0+2*siy))[2]) - ((sctx->grad + 3*(0+2*si))[2])) + ((sctx
->grad + 3*(0+2*si))[2])));

455

if (bag->zi==sz-2) {

456

457

} else {

458

ELL_3M_LERP(Tzp, alpha, sctx->tcontext + 9*(1+2*si),((((Tzp)+0)[0] = ((((alpha)))*((((sctx->tcontext + 9*(1+2*
siy))+0)[0]) - (((sctx->tcontext + 9*(1+2*si))+0)[0])) + (
((sctx->tcontext + 9*(1+2*si))+0)[0])), ((Tzp)+0)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(1+2*siy))+0)[1]) - (((sctx
->tcontext + 9*(1+2*si))+0)[1])) + (((sctx->tcontext + 9
*(1+2*si))+0)[1])), ((Tzp)+0)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(1+2*siy))+0)[2]) - (((sctx->tcontext + 9*(1+
2*si))+0)[2])) + (((sctx->tcontext + 9*(1+2*si))+0)[2]))),
(((Tzp)+3)[0] = ((((alpha)))*((((sctx->tcontext + 9*(1+2*
siy))+3)[0]) - (((sctx->tcontext + 9*(1+2*si))+3)[0])) + (
((sctx->tcontext + 9*(1+2*si))+3)[0])), ((Tzp)+3)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(1+2*siy))+3)[1]) - (((sctx
->tcontext + 9*(1+2*si))+3)[1])) + (((sctx->tcontext + 9
*(1+2*si))+3)[1])), ((Tzp)+3)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(1+2*siy))+3)[2]) - (((sctx->tcontext + 9*(1+
2*si))+3)[2])) + (((sctx->tcontext + 9*(1+2*si))+3)[2]))),
(((Tzp)+6)[0] = ((((alpha)))*((((sctx->tcontext + 9*(1+2*
siy))+6)[0]) - (((sctx->tcontext + 9*(1+2*si))+6)[0])) + (
((sctx->tcontext + 9*(1+2*si))+6)[0])), ((Tzp)+6)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(1+2*siy))+6)[1]) - (((sctx
->tcontext + 9*(1+2*si))+6)[1])) + (((sctx->tcontext + 9
*(1+2*si))+6)[1])), ((Tzp)+6)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(1+2*siy))+6)[2]) - (((sctx->tcontext + 9*(1+
2*si))+6)[2])) + (((sctx->tcontext + 9*(1+2*si))+6)[2]))))

459

sctx->tcontext + 9*(1+2*siy))((((Tzp)+0)[0] = ((((alpha)))*((((sctx->tcontext + 9*(1+2*
siy))+0)[0]) - (((sctx->tcontext + 9*(1+2*si))+0)[0])) + (
((sctx->tcontext + 9*(1+2*si))+0)[0])), ((Tzp)+0)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(1+2*siy))+0)[1]) - (((sctx
->tcontext + 9*(1+2*si))+0)[1])) + (((sctx->tcontext + 9
*(1+2*si))+0)[1])), ((Tzp)+0)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(1+2*siy))+0)[2]) - (((sctx->tcontext + 9*(1+
2*si))+0)[2])) + (((sctx->tcontext + 9*(1+2*si))+0)[2]))),
(((Tzp)+3)[0] = ((((alpha)))*((((sctx->tcontext + 9*(1+2*
siy))+3)[0]) - (((sctx->tcontext + 9*(1+2*si))+3)[0])) + (
((sctx->tcontext + 9*(1+2*si))+3)[0])), ((Tzp)+3)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(1+2*siy))+3)[1]) - (((sctx
->tcontext + 9*(1+2*si))+3)[1])) + (((sctx->tcontext + 9
*(1+2*si))+3)[1])), ((Tzp)+3)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(1+2*siy))+3)[2]) - (((sctx->tcontext + 9*(1+
2*si))+3)[2])) + (((sctx->tcontext + 9*(1+2*si))+3)[2]))),
(((Tzp)+6)[0] = ((((alpha)))*((((sctx->tcontext + 9*(1+2*
siy))+6)[0]) - (((sctx->tcontext + 9*(1+2*si))+6)[0])) + (
((sctx->tcontext + 9*(1+2*si))+6)[0])), ((Tzp)+6)[1] = (((
(alpha)))*((((sctx->tcontext + 9*(1+2*siy))+6)[1]) - (((sctx
->tcontext + 9*(1+2*si))+6)[1])) + (((sctx->tcontext + 9
*(1+2*si))+6)[1])), ((Tzp)+6)[2] = ((((alpha)))*((((sctx->
tcontext + 9*(1+2*siy))+6)[2]) - (((sctx->tcontext + 9*(1+
2*si))+6)[2])) + (((sctx->tcontext + 9*(1+2*si))+6)[2]))));

460

ELL_3V_LERP(gzp, alpha, sctx->gradcontext + 3*(1+2*si),((gzp)[0] = (((alpha))*(((sctx->gradcontext + 3*(1+2*siy))
[0]) - ((sctx->gradcontext + 3*(1+2*si))[0])) + ((sctx->
gradcontext + 3*(1+2*si))[0])), (gzp)[1] = (((alpha))*(((sctx
->gradcontext + 3*(1+2*siy))[1]) - ((sctx->gradcontext +
3*(1+2*si))[1])) + ((sctx->gradcontext + 3*(1+2*si))[1]))
, (gzp)[2] = (((alpha))*(((sctx->gradcontext + 3*(1+2*siy)
)[2]) - ((sctx->gradcontext + 3*(1+2*si))[2])) + ((sctx->
gradcontext + 3*(1+2*si))[2])))

461

sctx->gradcontext + 3*(1+2*siy))((gzp)[0] = (((alpha))*(((sctx->gradcontext + 3*(1+2*siy))
[0]) - ((sctx->gradcontext + 3*(1+2*si))[0])) + ((sctx->
gradcontext + 3*(1+2*si))[0])), (gzp)[1] = (((alpha))*(((sctx
->gradcontext + 3*(1+2*siy))[1]) - ((sctx->gradcontext +
3*(1+2*si))[1])) + ((sctx->gradcontext + 3*(1+2*si))[1]))
, (gzp)[2] = (((alpha))*(((sctx->gradcontext + 3*(1+2*siy)
)[2]) - ((sctx->gradcontext + 3*(1+2*si))[2])) + ((sctx->
gradcontext + 3*(1+2*si))[2])));

462

463

464

}

465

if (xi==0) {

466

467

} else {

468

ELL_3M_LERP(Txm, alpha, sctx->t + 9*(1+2*siX), sctx->t + 9*(1+2*siXy))((((Txm)+0)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*siXy))+
0)[0]) - (((sctx->t + 9*(1+2*siX))+0)[0])) + (((sctx->t
+ 9*(1+2*siX))+0)[0])), ((Txm)+0)[1] = ((((alpha)))*((((sctx
->t + 9*(1+2*siXy))+0)[1]) - (((sctx->t + 9*(1+2*siX))+
0)[1])) + (((sctx->t + 9*(1+2*siX))+0)[1])), ((Txm)+0)[2] =
((((alpha)))*((((sctx->t + 9*(1+2*siXy))+0)[2]) - (((sctx
->t + 9*(1+2*siX))+0)[2])) + (((sctx->t + 9*(1+2*siX))+
0)[2]))), (((Txm)+3)[0] = ((((alpha)))*((((sctx->t + 9*(1+
2*siXy))+3)[0]) - (((sctx->t + 9*(1+2*siX))+3)[0])) + (((sctx
->t + 9*(1+2*siX))+3)[0])), ((Txm)+3)[1] = ((((alpha)))*((
((sctx->t + 9*(1+2*siXy))+3)[1]) - (((sctx->t + 9*(1+2*
siX))+3)[1])) + (((sctx->t + 9*(1+2*siX))+3)[1])), ((Txm)+
3)[2] = ((((alpha)))*((((sctx->t + 9*(1+2*siXy))+3)[2]) - (
((sctx->t + 9*(1+2*siX))+3)[2])) + (((sctx->t + 9*(1+2*
siX))+3)[2]))), (((Txm)+6)[0] = ((((alpha)))*((((sctx->t +
9*(1+2*siXy))+6)[0]) - (((sctx->t + 9*(1+2*siX))+6)[0])) +
(((sctx->t + 9*(1+2*siX))+6)[0])), ((Txm)+6)[1] = ((((alpha
)))*((((sctx->t + 9*(1+2*siXy))+6)[1]) - (((sctx->t + 9
*(1+2*siX))+6)[1])) + (((sctx->t + 9*(1+2*siX))+6)[1])), (
(Txm)+6)[2] = ((((alpha)))*((((sctx->t + 9*(1+2*siXy))+6)[
2]) - (((sctx->t + 9*(1+2*siX))+6)[2])) + (((sctx->t + 9
*(1+2*siX))+6)[2]))));

469

ELL_3V_LERP(gxm, alpha, sctx->grad + 3*(1+2*siX),((gxm)[0] = (((alpha))*(((sctx->grad + 3*(1+2*siXy))[0]) -
((sctx->grad + 3*(1+2*siX))[0])) + ((sctx->grad + 3*(1
+2*siX))[0])), (gxm)[1] = (((alpha))*(((sctx->grad + 3*(1+
2*siXy))[1]) - ((sctx->grad + 3*(1+2*siX))[1])) + ((sctx->
grad + 3*(1+2*siX))[1])), (gxm)[2] = (((alpha))*(((sctx->grad
+ 3*(1+2*siXy))[2]) - ((sctx->grad + 3*(1+2*siX))[2])) + (
(sctx->grad + 3*(1+2*siX))[2])))

470

sctx->grad + 3*(1+2*siXy))((gxm)[0] = (((alpha))*(((sctx->grad + 3*(1+2*siXy))[0]) -
((sctx->grad + 3*(1+2*siX))[0])) + ((sctx->grad + 3*(1
+2*siX))[0])), (gxm)[1] = (((alpha))*(((sctx->grad + 3*(1+
2*siXy))[1]) - ((sctx->grad + 3*(1+2*siX))[1])) + ((sctx->
grad + 3*(1+2*siX))[1])), (gxm)[2] = (((alpha))*(((sctx->grad
+ 3*(1+2*siXy))[2]) - ((sctx->grad + 3*(1+2*siX))[2])) + (
(sctx->grad + 3*(1+2*siX))[2])));

471

}

472

if (xi==sx-1) {

473

ELL_3M_COPY(Txp, T)((((Txp)+0)[0] = ((T)+0)[0], ((Txp)+0)[1] = ((T)+0)[1], ((Txp
)+0)[2] = ((T)+0)[2]), (((Txp)+3)[0] = ((T)+3)[0], ((Txp)+3)[
1] = ((T)+3)[1], ((Txp)+3)[2] = ((T)+3)[2]), (((Txp)+6)[0] = (
(T)+6)[0], ((Txp)+6)[1] = ((T)+6)[1], ((Txp)+6)[2] = ((T)+6)[
2])); ELL_3V_COPY(gxp, g)((gxp)[0] = (g)[0], (gxp)[1] = (g)[1], (gxp)[2] = (g)[2]);

474

} else {

475

ELL_3M_LERP(Txp, alpha, sctx->t + 9*(1+2*six), sctx->t + 9*(1+2*sixy))((((Txp)+0)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*sixy))+
0)[0]) - (((sctx->t + 9*(1+2*six))+0)[0])) + (((sctx->t
+ 9*(1+2*six))+0)[0])), ((Txp)+0)[1] = ((((alpha)))*((((sctx
->t + 9*(1+2*sixy))+0)[1]) - (((sctx->t + 9*(1+2*six))+
0)[1])) + (((sctx->t + 9*(1+2*six))+0)[1])), ((Txp)+0)[2] =
((((alpha)))*((((sctx->t + 9*(1+2*sixy))+0)[2]) - (((sctx
->t + 9*(1+2*six))+0)[2])) + (((sctx->t + 9*(1+2*six))+
0)[2]))), (((Txp)+3)[0] = ((((alpha)))*((((sctx->t + 9*(1+
2*sixy))+3)[0]) - (((sctx->t + 9*(1+2*six))+3)[0])) + (((sctx
->t + 9*(1+2*six))+3)[0])), ((Txp)+3)[1] = ((((alpha)))*((
((sctx->t + 9*(1+2*sixy))+3)[1]) - (((sctx->t + 9*(1+2*
six))+3)[1])) + (((sctx->t + 9*(1+2*six))+3)[1])), ((Txp)+
3)[2] = ((((alpha)))*((((sctx->t + 9*(1+2*sixy))+3)[2]) - (
((sctx->t + 9*(1+2*six))+3)[2])) + (((sctx->t + 9*(1+2*
six))+3)[2]))), (((Txp)+6)[0] = ((((alpha)))*((((sctx->t +
9*(1+2*sixy))+6)[0]) - (((sctx->t + 9*(1+2*six))+6)[0])) +
(((sctx->t + 9*(1+2*six))+6)[0])), ((Txp)+6)[1] = ((((alpha
)))*((((sctx->t + 9*(1+2*sixy))+6)[1]) - (((sctx->t + 9
*(1+2*six))+6)[1])) + (((sctx->t + 9*(1+2*six))+6)[1])), (
(Txp)+6)[2] = ((((alpha)))*((((sctx->t + 9*(1+2*sixy))+6)[
2]) - (((sctx->t + 9*(1+2*six))+6)[2])) + (((sctx->t + 9
*(1+2*six))+6)[2]))));

476

ELL_3V_LERP(gxp, alpha, sctx->grad + 3*(1+2*six),((gxp)[0] = (((alpha))*(((sctx->grad + 3*(1+2*sixy))[0]) -
((sctx->grad + 3*(1+2*six))[0])) + ((sctx->grad + 3*(1
+2*six))[0])), (gxp)[1] = (((alpha))*(((sctx->grad + 3*(1+
2*sixy))[1]) - ((sctx->grad + 3*(1+2*six))[1])) + ((sctx->
grad + 3*(1+2*six))[1])), (gxp)[2] = (((alpha))*(((sctx->grad
+ 3*(1+2*sixy))[2]) - ((sctx->grad + 3*(1+2*six))[2])) + (
(sctx->grad + 3*(1+2*six))[2])))

477

sctx->grad + 3*(1+2*sixy))((gxp)[0] = (((alpha))*(((sctx->grad + 3*(1+2*sixy))[0]) -
((sctx->grad + 3*(1+2*six))[0])) + ((sctx->grad + 3*(1
+2*six))[0])), (gxp)[1] = (((alpha))*(((sctx->grad + 3*(1+
2*sixy))[1]) - ((sctx->grad + 3*(1+2*six))[1])) + ((sctx->
grad + 3*(1+2*six))[1])), (gxp)[2] = (((alpha))*(((sctx->grad
+ 3*(1+2*sixy))[2]) - ((sctx->grad + 3*(1+2*six))[2])) + (
(sctx->grad + 3*(1+2*six))[2])));

478

}

479

if (xi!=0 && xi!=sx-1) {

480

481

482

}

483

if (yi>0 && yi<sy-2) {

484

unsigned int siyy = xi + sx*(yi+2);

485

ELL_3M_LERP(Tym, alpha, sctx->t + 9*(1+2*siY), sctx->t + 9*(1+2*si))((((Tym)+0)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*si))+0)
[0]) - (((sctx->t + 9*(1+2*siY))+0)[0])) + (((sctx->t +
9*(1+2*siY))+0)[0])), ((Tym)+0)[1] = ((((alpha)))*((((sctx->
t + 9*(1+2*si))+0)[1]) - (((sctx->t + 9*(1+2*siY))+0)[1]))
+ (((sctx->t + 9*(1+2*siY))+0)[1])), ((Tym)+0)[2] = ((((alpha
)))*((((sctx->t + 9*(1+2*si))+0)[2]) - (((sctx->t + 9*(
1+2*siY))+0)[2])) + (((sctx->t + 9*(1+2*siY))+0)[2]))), ((
(Tym)+3)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*si))+3)[0]
) - (((sctx->t + 9*(1+2*siY))+3)[0])) + (((sctx->t + 9*
(1+2*siY))+3)[0])), ((Tym)+3)[1] = ((((alpha)))*((((sctx->
t + 9*(1+2*si))+3)[1]) - (((sctx->t + 9*(1+2*siY))+3)[1]))
+ (((sctx->t + 9*(1+2*siY))+3)[1])), ((Tym)+3)[2] = ((((alpha
)))*((((sctx->t + 9*(1+2*si))+3)[2]) - (((sctx->t + 9*(
1+2*siY))+3)[2])) + (((sctx->t + 9*(1+2*siY))+3)[2]))), ((
(Tym)+6)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*si))+6)[0]
) - (((sctx->t + 9*(1+2*siY))+6)[0])) + (((sctx->t + 9*
(1+2*siY))+6)[0])), ((Tym)+6)[1] = ((((alpha)))*((((sctx->
t + 9*(1+2*si))+6)[1]) - (((sctx->t + 9*(1+2*siY))+6)[1]))
+ (((sctx->t + 9*(1+2*siY))+6)[1])), ((Tym)+6)[2] = ((((alpha
)))*((((sctx->t + 9*(1+2*si))+6)[2]) - (((sctx->t + 9*(
1+2*siY))+6)[2])) + (((sctx->t + 9*(1+2*siY))+6)[2]))));

486

ELL_3V_LERP(gym, alpha, sctx->grad + 3*(1+2*siY),((gym)[0] = (((alpha))*(((sctx->grad + 3*(1+2*si))[0]) - (
(sctx->grad + 3*(1+2*siY))[0])) + ((sctx->grad + 3*(1+2
*siY))[0])), (gym)[1] = (((alpha))*(((sctx->grad + 3*(1+2*
si))[1]) - ((sctx->grad + 3*(1+2*siY))[1])) + ((sctx->grad
+ 3*(1+2*siY))[1])), (gym)[2] = (((alpha))*(((sctx->grad +
3*(1+2*si))[2]) - ((sctx->grad + 3*(1+2*siY))[2])) + ((sctx
->grad + 3*(1+2*siY))[2])))

487

sctx->grad + 3*(1+2*si))((gym)[0] = (((alpha))*(((sctx->grad + 3*(1+2*si))[0]) - (
(sctx->grad + 3*(1+2*siY))[0])) + ((sctx->grad + 3*(1+2
*siY))[0])), (gym)[1] = (((alpha))*(((sctx->grad + 3*(1+2*
si))[1]) - ((sctx->grad + 3*(1+2*siY))[1])) + ((sctx->grad
+ 3*(1+2*siY))[1])), (gym)[2] = (((alpha))*(((sctx->grad +
3*(1+2*si))[2]) - ((sctx->grad + 3*(1+2*siY))[2])) + ((sctx
->grad + 3*(1+2*siY))[2])));

488

ELL_3M_LERP(Typ, alpha, sctx->t + 9*(1+2*siy), sctx->t + 9*(1+2*siyy))((((Typ)+0)[0] = ((((alpha)))*((((sctx->t + 9*(1+2*siyy))+
0)[0]) - (((sctx->t + 9*(1+2*siy))+0)[0])) + (((sctx->t
+ 9*(1+2*siy))+0)[0])), ((Typ)+0)[1] = ((((alpha)))*((((sctx
->t + 9*(1+2*siyy))+0)[1]) - (((sctx->t + 9*(1+2*siy))+
0)[1])) + (((sctx->t + 9*(1+2*siy))+0)[1])), ((Typ)+0)[2] =
((((alpha)))*((((sctx->t + 9*(1+2*siyy))+0)[2]) - (((sctx
->t + 9*(1+2*siy))+0)[2])) + (((sctx->t + 9*(1+2*siy))+
0)[2]))), (((Typ)+3)[0] = ((((alpha)))*((((sctx->t + 9*(1+
2*siyy))+3)[0]) - (((sctx->t + 9*(1+2*siy))+3)[0])) + (((sctx
->t + 9*(1+2*siy))+3)[0])), ((Typ)+3)[1] = ((((alpha)))*((
((sctx->t + 9*(1+2*siyy))+3)[1]) - (((sctx->t + 9*(1+2*
siy))+3)[1])) + (((sctx->t + 9*(1+2*siy))+3)[1])), ((Typ)+
3)[2] = ((((alpha)))*((((sctx->t + 9*(1+2*siyy))+3)[2]) - (
((sctx->t + 9*(1+2*siy))+3)[2])) + (((sctx->t + 9*(1+2*
siy))+3)[2]))), (((Typ)+6)[0] = ((((alpha)))*((((sctx->t +
9*(1+2*siyy))+6)[0]) - (((sctx->t + 9*(1+2*siy))+6)[0])) +
(((sctx->t + 9*(1+2*siy))+6)[0])), ((Typ)+6)[1] = ((((alpha
)))*((((sctx->t + 9*(1+2*siyy))+6)[1]) - (((sctx->t + 9
*(1+2*siy))+6)[1])) + (((sctx->t + 9*(1+2*siy))+6)[1])), (
(Typ)+6)[2] = ((((alpha)))*((((sctx->t + 9*(1+2*siyy))+6)[
2]) - (((sctx->t + 9*(1+2*siy))+6)[2])) + (((sctx->t + 9
*(1+2*siy))+6)[2]))));

489

ELL_3V_LERP(gyp, alpha, sctx->grad + 3*(1+2*siy),((gyp)[0] = (((alpha))*(((sctx->grad + 3*(1+2*siyy))[0]) -
((sctx->grad + 3*(1+2*siy))[0])) + ((sctx->grad + 3*(1
+2*siy))[0])), (gyp)[1] = (((alpha))*(((sctx->grad + 3*(1+
2*siyy))[1]) - ((sctx->grad + 3*(1+2*siy))[1])) + ((sctx->
grad + 3*(1+2*siy))[1])), (gyp)[2] = (((alpha))*(((sctx->grad
+ 3*(1+2*siyy))[2]) - ((sctx->grad + 3*(1+2*siy))[2])) + (
(sctx->grad + 3*(1+2*siy))[2])))

490

sctx->grad + 3*(1+2*siyy))((gyp)[0] = (((alpha))*(((sctx->grad + 3*(1+2*siyy))[0]) -
((sctx->grad + 3*(1+2*siy))[0])) + ((sctx->grad + 3*(1
+2*siy))[0])), (gyp)[1] = (((alpha))*(((sctx->grad + 3*(1+
2*siyy))[1]) - ((sctx->grad + 3*(1+2*siy))[1])) + ((sctx->
grad + 3*(1+2*siy))[1])), (gyp)[2] = (((alpha))*(((sctx->grad
+ 3*(1+2*siyy))[2]) - ((sctx->grad + 3*(1+2*siy))[2])) + (
(sctx->grad + 3*(1+2*siy))[2])));

491

492

493

} else {

494

ELL_3M_COPY(Tym, sctx->t + 9*(1+2*si))((((Tym)+0)[0] = ((sctx->t + 9*(1+2*si))+0)[0], ((Tym)+0)[
1] = ((sctx->t + 9*(1+2*si))+0)[1], ((Tym)+0)[2] = ((sctx->
t + 9*(1+2*si))+0)[2]), (((Tym)+3)[0] = ((sctx->t + 9*(1+2
*si))+3)[0], ((Tym)+3)[1] = ((sctx->t + 9*(1+2*si))+3)[1],
((Tym)+3)[2] = ((sctx->t + 9*(1+2*si))+3)[2]), (((Tym)+6)
[0] = ((sctx->t + 9*(1+2*si))+6)[0], ((Tym)+6)[1] = ((sctx
->t + 9*(1+2*si))+6)[1], ((Tym)+6)[2] = ((sctx->t + 9*(
1+2*si))+6)[2]));

495

ELL_3V_COPY(gym, sctx->grad + 3*(1+2*si))((gym)[0] = (sctx->grad + 3*(1+2*si))[0], (gym)[1] = (sctx
->grad + 3*(1+2*si))[1], (gym)[2] = (sctx->grad + 3*(1+
2*si))[2]);

496

ELL_3M_COPY(Typ, sctx->t + 9*(1+2*six))((((Typ)+0)[0] = ((sctx->t + 9*(1+2*six))+0)[0], ((Typ)+0)
[1] = ((sctx->t + 9*(1+2*six))+0)[1], ((Typ)+0)[2] = ((sctx
->t + 9*(1+2*six))+0)[2]), (((Typ)+3)[0] = ((sctx->t + 9
*(1+2*six))+3)[0], ((Typ)+3)[1] = ((sctx->t + 9*(1+2*six))
+3)[1], ((Typ)+3)[2] = ((sctx->t + 9*(1+2*six))+3)[2]), ((
(Typ)+6)[0] = ((sctx->t + 9*(1+2*six))+6)[0], ((Typ)+6)[1]
= ((sctx->t + 9*(1+2*six))+6)[1], ((Typ)+6)[2] = ((sctx->
t + 9*(1+2*six))+6)[2]));

497

ELL_3V_COPY(gyp, sctx->grad + 3*(1+2*six))((gyp)[0] = (sctx->grad + 3*(1+2*six))[0], (gyp)[1] = (sctx
->grad + 3*(1+2*six))[1], (gyp)[2] = (sctx->grad + 3*(1
+2*six))[2]);

498

}

499

computeGradientLin(res, T, g,

500

Txm, gxm, Txp, gxp,

501

Tym, gym, Typ, gyp,

502

Tzm, gzm, Tzp, gzp);

503

break;

504

}

505

}

506

507

/* Given a unique face ID and coordinates, compute the crease surface

508

* normal at the specified degenerate point */

509

static void

510

computeFaceGradient(seekContext *sctx, double *res,

511

unsigned int xi, unsigned int yi,

512

char faceid, double *coords) {

513

double T[9], Txm[9], Txp[9], Tym[9], Typ[9], Tzm[9], Tzp[9],

514

g[3], gxm[3], gxp[3], gym[3], gyp[3], gzm[3], gzp[3];

515

unsigned int sx = AIR_CAST(unsigned int, sctx->sx)((unsigned int)(sctx->sx));

516

unsigned int sy = AIR_CAST(unsigned int, sctx->sy)((unsigned int)(sctx->sy));

517

unsigned int si = xi + sx*yi;

518

unsigned int six = xi + 1 + sx*yi, siX = xi - 1 + sx*yi;

519

unsigned int siy = xi + sx*(yi+1), siY = xi + sx*(yi-1);

520

unsigned int sixy = xi + 1 + sx*(yi+1), sixY = xi + 1 + sx*(yi-1),

521

siXy = xi - 1 + sx*(yi+1);

522

523

/* Again, lots of special cases to fill Txm, gxm, etc. */

524

switch (faceid) {

Control jumps to 'case 2:' at line 611

→

525

case 0:

526

/* bilinearly interpolate Tzp/gzp first */

527

ELL_3M_LERP(Txm, coords[1], sctx->t + 9*(1+2*si), sctx->t + 9*(1+2*siy))((((Txm)+0)[0] = ((((coords[1])))*((((sctx->t + 9*(1+2*siy
))+0)[0]) - (((sctx->t + 9*(1+2*si))+0)[0])) + (((sctx->
t + 9*(1+2*si))+0)[0])), ((Txm)+0)[1] = ((((coords[1])))*((((
sctx->t + 9*(1+2*siy))+0)[1]) - (((sctx->t + 9*(1+2*si)
)+0)[1])) + (((sctx->t + 9*(1+2*si))+0)[1])), ((Txm)+0)[2]
= ((((coords[1])))*((((sctx->t + 9*(1+2*siy))+0)[2]) - ((
(sctx->t + 9*(1+2*si))+0)[2])) + (((sctx->t + 9*(1+2*si
))+0)[2]))), (((Txm)+3)[0] = ((((coords[1])))*((((sctx->t +
9*(1+2*siy))+3)[0]) - (((sctx->t + 9*(1+2*si))+3)[0])) + (
((sctx->t + 9*(1+2*si))+3)[0])), ((Txm)+3)[1] = ((((coords
[1])))*((((sctx->t + 9*(1+2*siy))+3)[1]) - (((sctx->t +
9*(1+2*si))+3)[1])) + (((sctx->t + 9*(1+2*si))+3)[1])), (
(Txm)+3)[2] = ((((coords[1])))*((((sctx->t + 9*(1+2*siy))+
3)[2]) - (((sctx->t + 9*(1+2*si))+3)[2])) + (((sctx->t +
9*(1+2*si))+3)[2]))), (((Txm)+6)[0] = ((((coords[1])))*((((sctx
->t + 9*(1+2*siy))+6)[0]) - (((sctx->t + 9*(1+2*si))+6)
[0])) + (((sctx->t + 9*(1+2*si))+6)[0])), ((Txm)+6)[1] = (
(((coords[1])))*((((sctx->t + 9*(1+2*siy))+6)[1]) - (((sctx
->t + 9*(1+2*si))+6)[1])) + (((sctx->t + 9*(1+2*si))+6)
[1])), ((Txm)+6)[2] = ((((coords[1])))*((((sctx->t + 9*(1+
2*siy))+6)[2]) - (((sctx->t + 9*(1+2*si))+6)[2])) + (((sctx
->t + 9*(1+2*si))+6)[2]))));

528

ELL_3V_LERP(gxm, coords[1], sctx->grad + 3*(1+2*si),((gxm)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*siy))[0]
) - ((sctx->grad + 3*(1+2*si))[0])) + ((sctx->grad + 3*
(1+2*si))[0])), (gxm)[1] = (((coords[1]))*(((sctx->grad + 3
*(1+2*siy))[1]) - ((sctx->grad + 3*(1+2*si))[1])) + ((sctx
->grad + 3*(1+2*si))[1])), (gxm)[2] = (((coords[1]))*(((sctx
->grad + 3*(1+2*siy))[2]) - ((sctx->grad + 3*(1+2*si))[
2])) + ((sctx->grad + 3*(1+2*si))[2])))

529

sctx->grad + 3*(1+2*siy))((gxm)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*siy))[0]
) - ((sctx->grad + 3*(1+2*si))[0])) + ((sctx->grad + 3*
(1+2*si))[0])), (gxm)[1] = (((coords[1]))*(((sctx->grad + 3
*(1+2*siy))[1]) - ((sctx->grad + 3*(1+2*si))[1])) + ((sctx
->grad + 3*(1+2*si))[1])), (gxm)[2] = (((coords[1]))*(((sctx
->grad + 3*(1+2*siy))[2]) - ((sctx->grad + 3*(1+2*si))[
2])) + ((sctx->grad + 3*(1+2*si))[2])));

530

ELL_3M_LERP(Txp, coords[1], sctx->t + 9*(1+2*six), sctx->t + 9*(1+2*sixy))((((Txp)+0)[0] = ((((coords[1])))*((((sctx->t + 9*(1+2*sixy
))+0)[0]) - (((sctx->t + 9*(1+2*six))+0)[0])) + (((sctx->
t + 9*(1+2*six))+0)[0])), ((Txp)+0)[1] = ((((coords[1])))*(((
(sctx->t + 9*(1+2*sixy))+0)[1]) - (((sctx->t + 9*(1+2*six
))+0)[1])) + (((sctx->t + 9*(1+2*six))+0)[1])), ((Txp)+0)[
2] = ((((coords[1])))*((((sctx->t + 9*(1+2*sixy))+0)[2]) -
(((sctx->t + 9*(1+2*six))+0)[2])) + (((sctx->t + 9*(1+
2*six))+0)[2]))), (((Txp)+3)[0] = ((((coords[1])))*((((sctx->
t + 9*(1+2*sixy))+3)[0]) - (((sctx->t + 9*(1+2*six))+3)[0]
)) + (((sctx->t + 9*(1+2*six))+3)[0])), ((Txp)+3)[1] = (((
(coords[1])))*((((sctx->t + 9*(1+2*sixy))+3)[1]) - (((sctx
->t + 9*(1+2*six))+3)[1])) + (((sctx->t + 9*(1+2*six))+
3)[1])), ((Txp)+3)[2] = ((((coords[1])))*((((sctx->t + 9*(
1+2*sixy))+3)[2]) - (((sctx->t + 9*(1+2*six))+3)[2])) + ((
(sctx->t + 9*(1+2*six))+3)[2]))), (((Txp)+6)[0] = ((((coords
[1])))*((((sctx->t + 9*(1+2*sixy))+6)[0]) - (((sctx->t +
9*(1+2*six))+6)[0])) + (((sctx->t + 9*(1+2*six))+6)[0])),
((Txp)+6)[1] = ((((coords[1])))*((((sctx->t + 9*(1+2*sixy
))+6)[1]) - (((sctx->t + 9*(1+2*six))+6)[1])) + (((sctx->
t + 9*(1+2*six))+6)[1])), ((Txp)+6)[2] = ((((coords[1])))*(((
(sctx->t + 9*(1+2*sixy))+6)[2]) - (((sctx->t + 9*(1+2*six
))+6)[2])) + (((sctx->t + 9*(1+2*six))+6)[2]))));

531

ELL_3V_LERP(gxp, coords[1], sctx->grad + 3*(1+2*six),((gxp)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*sixy))[0
]) - ((sctx->grad + 3*(1+2*six))[0])) + ((sctx->grad + 3
*(1+2*six))[0])), (gxp)[1] = (((coords[1]))*(((sctx->grad +
3*(1+2*sixy))[1]) - ((sctx->grad + 3*(1+2*six))[1])) + ((
sctx->grad + 3*(1+2*six))[1])), (gxp)[2] = (((coords[1]))*
(((sctx->grad + 3*(1+2*sixy))[2]) - ((sctx->grad + 3*(1
+2*six))[2])) + ((sctx->grad + 3*(1+2*six))[2])))

532

sctx->grad + 3*(1+2*sixy))((gxp)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*sixy))[0
]) - ((sctx->grad + 3*(1+2*six))[0])) + ((sctx->grad + 3
*(1+2*six))[0])), (gxp)[1] = (((coords[1]))*(((sctx->grad +
3*(1+2*sixy))[1]) - ((sctx->grad + 3*(1+2*six))[1])) + ((
sctx->grad + 3*(1+2*six))[1])), (gxp)[2] = (((coords[1]))*
(((sctx->grad + 3*(1+2*sixy))[2]) - ((sctx->grad + 3*(1
+2*six))[2])) + ((sctx->grad + 3*(1+2*six))[2])));

533

ELL_3M_LERP(Tzp, coords[0], Txm, Txp)((((Tzp)+0)[0] = ((((coords[0])))*((((Txp)+0)[0]) - (((Txm)+0
)[0])) + (((Txm)+0)[0])), ((Tzp)+0)[1] = ((((coords[0])))*(((
(Txp)+0)[1]) - (((Txm)+0)[1])) + (((Txm)+0)[1])), ((Tzp)+0)[2
] = ((((coords[0])))*((((Txp)+0)[2]) - (((Txm)+0)[2])) + (((Txm
)+0)[2]))), (((Tzp)+3)[0] = ((((coords[0])))*((((Txp)+3)[0]) -
(((Txm)+3)[0])) + (((Txm)+3)[0])), ((Tzp)+3)[1] = ((((coords
[0])))*((((Txp)+3)[1]) - (((Txm)+3)[1])) + (((Txm)+3)[1])), (
(Tzp)+3)[2] = ((((coords[0])))*((((Txp)+3)[2]) - (((Txm)+3)[2
])) + (((Txm)+3)[2]))), (((Tzp)+6)[0] = ((((coords[0])))*((((
Txp)+6)[0]) - (((Txm)+6)[0])) + (((Txm)+6)[0])), ((Tzp)+6)[1]
= ((((coords[0])))*((((Txp)+6)[1]) - (((Txm)+6)[1])) + (((Txm
)+6)[1])), ((Tzp)+6)[2] = ((((coords[0])))*((((Txp)+6)[2]) - (
((Txm)+6)[2])) + (((Txm)+6)[2]))));

534

ELL_3V_LERP(gzp, coords[0], gxm, gxp)((gzp)[0] = (((coords[0]))*(((gxp)[0]) - ((gxm)[0])) + ((gxm)
[0])), (gzp)[1] = (((coords[0]))*(((gxp)[1]) - ((gxm)[1])) + (
(gxm)[1])), (gzp)[2] = (((coords[0]))*(((gxp)[2]) - ((gxm)[2]
)) + ((gxm)[2])));

535

/* now, compute all required points on the bottom face */

536

ELL_3M_LERP(Txm, coords[1], sctx->t + 9*(0+2*si), sctx->t + 9*(0+2*siy))((((Txm)+0)[0] = ((((coords[1])))*((((sctx->t + 9*(0+2*siy
))+0)[0]) - (((sctx->t + 9*(0+2*si))+0)[0])) + (((sctx->
t + 9*(0+2*si))+0)[0])), ((Txm)+0)[1] = ((((coords[1])))*((((
sctx->t + 9*(0+2*siy))+0)[1]) - (((sctx->t + 9*(0+2*si)
)+0)[1])) + (((sctx->t + 9*(0+2*si))+0)[1])), ((Txm)+0)[2]
= ((((coords[1])))*((((sctx->t + 9*(0+2*siy))+0)[2]) - ((
(sctx->t + 9*(0+2*si))+0)[2])) + (((sctx->t + 9*(0+2*si
))+0)[2]))), (((Txm)+3)[0] = ((((coords[1])))*((((sctx->t +
9*(0+2*siy))+3)[0]) - (((sctx->t + 9*(0+2*si))+3)[0])) + (
((sctx->t + 9*(0+2*si))+3)[0])), ((Txm)+3)[1] = ((((coords
[1])))*((((sctx->t + 9*(0+2*siy))+3)[1]) - (((sctx->t +
9*(0+2*si))+3)[1])) + (((sctx->t + 9*(0+2*si))+3)[1])), (
(Txm)+3)[2] = ((((coords[1])))*((((sctx->t + 9*(0+2*siy))+
3)[2]) - (((sctx->t + 9*(0+2*si))+3)[2])) + (((sctx->t +
9*(0+2*si))+3)[2]))), (((Txm)+6)[0] = ((((coords[1])))*((((sctx
->t + 9*(0+2*siy))+6)[0]) - (((sctx->t + 9*(0+2*si))+6)
[0])) + (((sctx->t + 9*(0+2*si))+6)[0])), ((Txm)+6)[1] = (
(((coords[1])))*((((sctx->t + 9*(0+2*siy))+6)[1]) - (((sctx
->t + 9*(0+2*si))+6)[1])) + (((sctx->t + 9*(0+2*si))+6)
[1])), ((Txm)+6)[2] = ((((coords[1])))*((((sctx->t + 9*(0+
2*siy))+6)[2]) - (((sctx->t + 9*(0+2*si))+6)[2])) + (((sctx
->t + 9*(0+2*si))+6)[2]))));

537

ELL_3V_LERP(gxm, coords[1], sctx->grad + 3*(0+2*si),((gxm)[0] = (((coords[1]))*(((sctx->grad + 3*(0+2*siy))[0]
) - ((sctx->grad + 3*(0+2*si))[0])) + ((sctx->grad + 3*
(0+2*si))[0])), (gxm)[1] = (((coords[1]))*(((sctx->grad + 3
*(0+2*siy))[1]) - ((sctx->grad + 3*(0+2*si))[1])) + ((sctx
->grad + 3*(0+2*si))[1])), (gxm)[2] = (((coords[1]))*(((sctx
->grad + 3*(0+2*siy))[2]) - ((sctx->grad + 3*(0+2*si))[
2])) + ((sctx->grad + 3*(0+2*si))[2])))

538

sctx->grad + 3*(0+2*siy))((gxm)[0] = (((coords[1]))*(((sctx->grad + 3*(0+2*siy))[0]
) - ((sctx->grad + 3*(0+2*si))[0])) + ((sctx->grad + 3*
(0+2*si))[0])), (gxm)[1] = (((coords[1]))*(((sctx->grad + 3
*(0+2*siy))[1]) - ((sctx->grad + 3*(0+2*si))[1])) + ((sctx
->grad + 3*(0+2*si))[1])), (gxm)[2] = (((coords[1]))*(((sctx
->grad + 3*(0+2*siy))[2]) - ((sctx->grad + 3*(0+2*si))[
2])) + ((sctx->grad + 3*(0+2*si))[2])));

539

ELL_3M_LERP(Txp, coords[1], sctx->t + 9*(0+2*six), sctx->t + 9*(0+2*sixy))((((Txp)+0)[0] = ((((coords[1])))*((((sctx->t + 9*(0+2*sixy
))+0)[0]) - (((sctx->t + 9*(0+2*six))+0)[0])) + (((sctx->
t + 9*(0+2*six))+0)[0])), ((Txp)+0)[1] = ((((coords[1])))*(((
(sctx->t + 9*(0+2*sixy))+0)[1]) - (((sctx->t + 9*(0+2*six
))+0)[1])) + (((sctx->t + 9*(0+2*six))+0)[1])), ((Txp)+0)[
2] = ((((coords[1])))*((((sctx->t + 9*(0+2*sixy))+0)[2]) -
(((sctx->t + 9*(0+2*six))+0)[2])) + (((sctx->t + 9*(0+
2*six))+0)[2]))), (((Txp)+3)[0] = ((((coords[1])))*((((sctx->
t + 9*(0+2*sixy))+3)[0]) - (((sctx->t + 9*(0+2*six))+3)[0]
)) + (((sctx->t + 9*(0+2*six))+3)[0])), ((Txp)+3)[1] = (((
(coords[1])))*((((sctx->t + 9*(0+2*sixy))+3)[1]) - (((sctx
->t + 9*(0+2*six))+3)[1])) + (((sctx->t + 9*(0+2*six))+
3)[1])), ((Txp)+3)[2] = ((((coords[1])))*((((sctx->t + 9*(
0+2*sixy))+3)[2]) - (((sctx->t + 9*(0+2*six))+3)[2])) + ((
(sctx->t + 9*(0+2*six))+3)[2]))), (((Txp)+6)[0] = ((((coords
[1])))*((((sctx->t + 9*(0+2*sixy))+6)[0]) - (((sctx->t +
9*(0+2*six))+6)[0])) + (((sctx->t + 9*(0+2*six))+6)[0])),
((Txp)+6)[1] = ((((coords[1])))*((((sctx->t + 9*(0+2*sixy
))+6)[1]) - (((sctx->t + 9*(0+2*six))+6)[1])) + (((sctx->
t + 9*(0+2*six))+6)[1])), ((Txp)+6)[2] = ((((coords[1])))*(((
(sctx->t + 9*(0+2*sixy))+6)[2]) - (((sctx->t + 9*(0+2*six
))+6)[2])) + (((sctx->t + 9*(0+2*six))+6)[2]))));

540

ELL_3V_LERP(gxp, coords[1], sctx->grad + 3*(0+2*six),((gxp)[0] = (((coords[1]))*(((sctx->grad + 3*(0+2*sixy))[0
]) - ((sctx->grad + 3*(0+2*six))[0])) + ((sctx->grad + 3
*(0+2*six))[0])), (gxp)[1] = (((coords[1]))*(((sctx->grad +
3*(0+2*sixy))[1]) - ((sctx->grad + 3*(0+2*six))[1])) + ((
sctx->grad + 3*(0+2*six))[1])), (gxp)[2] = (((coords[1]))*
(((sctx->grad + 3*(0+2*sixy))[2]) - ((sctx->grad + 3*(0
+2*six))[2])) + ((sctx->grad + 3*(0+2*six))[2])))

541

sctx->grad + 3*(0+2*sixy))((gxp)[0] = (((coords[1]))*(((sctx->grad + 3*(0+2*sixy))[0
]) - ((sctx->grad + 3*(0+2*six))[0])) + ((sctx->grad + 3
*(0+2*six))[0])), (gxp)[1] = (((coords[1]))*(((sctx->grad +
3*(0+2*sixy))[1]) - ((sctx->grad + 3*(0+2*six))[1])) + ((
sctx->grad + 3*(0+2*six))[1])), (gxp)[2] = (((coords[1]))*
(((sctx->grad + 3*(0+2*sixy))[2]) - ((sctx->grad + 3*(0
+2*six))[2])) + ((sctx->grad + 3*(0+2*six))[2])));

542

543

ELL_3M_LERP(Tym, coords[0], sctx->t + 9*(0+2*si), sctx->t + 9*(0+2*six))((((Tym)+0)[0] = ((((coords[0])))*((((sctx->t + 9*(0+2*six
))+0)[0]) - (((sctx->t + 9*(0+2*si))+0)[0])) + (((sctx->
t + 9*(0+2*si))+0)[0])), ((Tym)+0)[1] = ((((coords[0])))*((((
sctx->t + 9*(0+2*six))+0)[1]) - (((sctx->t + 9*(0+2*si)
)+0)[1])) + (((sctx->t + 9*(0+2*si))+0)[1])), ((Tym)+0)[2]
= ((((coords[0])))*((((sctx->t + 9*(0+2*six))+0)[2]) - ((
(sctx->t + 9*(0+2*si))+0)[2])) + (((sctx->t + 9*(0+2*si
))+0)[2]))), (((Tym)+3)[0] = ((((coords[0])))*((((sctx->t +
9*(0+2*six))+3)[0]) - (((sctx->t + 9*(0+2*si))+3)[0])) + (
((sctx->t + 9*(0+2*si))+3)[0])), ((Tym)+3)[1] = ((((coords
[0])))*((((sctx->t + 9*(0+2*six))+3)[1]) - (((sctx->t +
9*(0+2*si))+3)[1])) + (((sctx->t + 9*(0+2*si))+3)[1])), (
(Tym)+3)[2] = ((((coords[0])))*((((sctx->t + 9*(0+2*six))+
3)[2]) - (((sctx->t + 9*(0+2*si))+3)[2])) + (((sctx->t +
9*(0+2*si))+3)[2]))), (((Tym)+6)[0] = ((((coords[0])))*((((sctx
->t + 9*(0+2*six))+6)[0]) - (((sctx->t + 9*(0+2*si))+6)
[0])) + (((sctx->t + 9*(0+2*si))+6)[0])), ((Tym)+6)[1] = (
(((coords[0])))*((((sctx->t + 9*(0+2*six))+6)[1]) - (((sctx
->t + 9*(0+2*si))+6)[1])) + (((sctx->t + 9*(0+2*si))+6)
[1])), ((Tym)+6)[2] = ((((coords[0])))*((((sctx->t + 9*(0+
2*six))+6)[2]) - (((sctx->t + 9*(0+2*si))+6)[2])) + (((sctx
->t + 9*(0+2*si))+6)[2]))));

544

ELL_3V_LERP(gym, coords[0], sctx->grad + 3*(0+2*si),((gym)[0] = (((coords[0]))*(((sctx->grad + 3*(0+2*six))[0]
) - ((sctx->grad + 3*(0+2*si))[0])) + ((sctx->grad + 3*
(0+2*si))[0])), (gym)[1] = (((coords[0]))*(((sctx->grad + 3
*(0+2*six))[1]) - ((sctx->grad + 3*(0+2*si))[1])) + ((sctx
->grad + 3*(0+2*si))[1])), (gym)[2] = (((coords[0]))*(((sctx
->grad + 3*(0+2*six))[2]) - ((sctx->grad + 3*(0+2*si))[
2])) + ((sctx->grad + 3*(0+2*si))[2])))

545

sctx->grad + 3*(0+2*six))((gym)[0] = (((coords[0]))*(((sctx->grad + 3*(0+2*six))[0]
) - ((sctx->grad + 3*(0+2*si))[0])) + ((sctx->grad + 3*
(0+2*si))[0])), (gym)[1] = (((coords[0]))*(((sctx->grad + 3
*(0+2*six))[1]) - ((sctx->grad + 3*(0+2*si))[1])) + ((sctx
->grad + 3*(0+2*si))[1])), (gym)[2] = (((coords[0]))*(((sctx
->grad + 3*(0+2*six))[2]) - ((sctx->grad + 3*(0+2*si))[
2])) + ((sctx->grad + 3*(0+2*si))[2])));

546

ELL_3M_LERP(Typ, coords[0], sctx->t + 9*(0+2*siy), sctx->t + 9*(0+2*sixy))((((Typ)+0)[0] = ((((coords[0])))*((((sctx->t + 9*(0+2*sixy
))+0)[0]) - (((sctx->t + 9*(0+2*siy))+0)[0])) + (((sctx->
t + 9*(0+2*siy))+0)[0])), ((Typ)+0)[1] = ((((coords[0])))*(((
(sctx->t + 9*(0+2*sixy))+0)[1]) - (((sctx->t + 9*(0+2*siy
))+0)[1])) + (((sctx->t + 9*(0+2*siy))+0)[1])), ((Typ)+0)[
2] = ((((coords[0])))*((((sctx->t + 9*(0+2*sixy))+0)[2]) -
(((sctx->t + 9*(0+2*siy))+0)[2])) + (((sctx->t + 9*(0+
2*siy))+0)[2]))), (((Typ)+3)[0] = ((((coords[0])))*((((sctx->
t + 9*(0+2*sixy))+3)[0]) - (((sctx->t + 9*(0+2*siy))+3)[0]
)) + (((sctx->t + 9*(0+2*siy))+3)[0])), ((Typ)+3)[1] = (((
(coords[0])))*((((sctx->t + 9*(0+2*sixy))+3)[1]) - (((sctx
->t + 9*(0+2*siy))+3)[1])) + (((sctx->t + 9*(0+2*siy))+
3)[1])), ((Typ)+3)[2] = ((((coords[0])))*((((sctx->t + 9*(
0+2*sixy))+3)[2]) - (((sctx->t + 9*(0+2*siy))+3)[2])) + ((
(sctx->t + 9*(0+2*siy))+3)[2]))), (((Typ)+6)[0] = ((((coords
[0])))*((((sctx->t + 9*(0+2*sixy))+6)[0]) - (((sctx->t +
9*(0+2*siy))+6)[0])) + (((sctx->t + 9*(0+2*siy))+6)[0])),
((Typ)+6)[1] = ((((coords[0])))*((((sctx->t + 9*(0+2*sixy
))+6)[1]) - (((sctx->t + 9*(0+2*siy))+6)[1])) + (((sctx->
t + 9*(0+2*siy))+6)[1])), ((Typ)+6)[2] = ((((coords[0])))*(((
(sctx->t + 9*(0+2*sixy))+6)[2]) - (((sctx->t + 9*(0+2*siy
))+6)[2])) + (((sctx->t + 9*(0+2*siy))+6)[2]))));

547

ELL_3V_LERP(gyp, coords[0], sctx->grad + 3*(0+2*siy),((gyp)[0] = (((coords[0]))*(((sctx->grad + 3*(0+2*sixy))[0
]) - ((sctx->grad + 3*(0+2*siy))[0])) + ((sctx->grad + 3
*(0+2*siy))[0])), (gyp)[1] = (((coords[0]))*(((sctx->grad +
3*(0+2*sixy))[1]) - ((sctx->grad + 3*(0+2*siy))[1])) + ((
sctx->grad + 3*(0+2*siy))[1])), (gyp)[2] = (((coords[0]))*
(((sctx->grad + 3*(0+2*sixy))[2]) - ((sctx->grad + 3*(0
+2*siy))[2])) + ((sctx->grad + 3*(0+2*siy))[2])))

548

sctx->grad + 3*(0+2*sixy))((gyp)[0] = (((coords[0]))*(((sctx->grad + 3*(0+2*sixy))[0
]) - ((sctx->grad + 3*(0+2*siy))[0])) + ((sctx->grad + 3
*(0+2*siy))[0])), (gyp)[1] = (((coords[0]))*(((sctx->grad +
3*(0+2*sixy))[1]) - ((sctx->grad + 3*(0+2*siy))[1])) + ((
sctx->grad + 3*(0+2*siy))[1])), (gyp)[2] = (((coords[0]))*
(((sctx->grad + 3*(0+2*sixy))[2]) - ((sctx->grad + 3*(0
+2*siy))[2])) + ((sctx->grad + 3*(0+2*siy))[2])));

549

550

ELL_3M_LERP(T, coords[0], Txm, Txp)((((T)+0)[0] = ((((coords[0])))*((((Txp)+0)[0]) - (((Txm)+0)[
0])) + (((Txm)+0)[0])), ((T)+0)[1] = ((((coords[0])))*((((Txp
)+0)[1]) - (((Txm)+0)[1])) + (((Txm)+0)[1])), ((T)+0)[2] = ((
((coords[0])))*((((Txp)+0)[2]) - (((Txm)+0)[2])) + (((Txm)+0)
[2]))), (((T)+3)[0] = ((((coords[0])))*((((Txp)+3)[0]) - (((Txm
)+3)[0])) + (((Txm)+3)[0])), ((T)+3)[1] = ((((coords[0])))*((
((Txp)+3)[1]) - (((Txm)+3)[1])) + (((Txm)+3)[1])), ((T)+3)[2]
= ((((coords[0])))*((((Txp)+3)[2]) - (((Txm)+3)[2])) + (((Txm
)+3)[2]))), (((T)+6)[0] = ((((coords[0])))*((((Txp)+6)[0]) - (
((Txm)+6)[0])) + (((Txm)+6)[0])), ((T)+6)[1] = ((((coords[0])
))*((((Txp)+6)[1]) - (((Txm)+6)[1])) + (((Txm)+6)[1])), ((T)+
6)[2] = ((((coords[0])))*((((Txp)+6)[2]) - (((Txm)+6)[2])) + (
((Txm)+6)[2]))));

551

ELL_3V_LERP(g, coords[0], gxm, gxp)((g)[0] = (((coords[0]))*(((gxp)[0]) - ((gxm)[0])) + ((gxm)[0
])), (g)[1] = (((coords[0]))*(((gxp)[1]) - ((gxm)[1])) + ((gxm
)[1])), (g)[2] = (((coords[0]))*(((gxp)[2]) - ((gxm)[2])) + (
(gxm)[2])));

552

553

computeGradientLin(sctx->facenorm+3*(faceid+4*si), T, g,

554

Txm, gxm, Txp, gxp,

555

Tym, gym, Typ, gyp,

556

T, g, Tzp, gzp);

557

break;

558

case 1:

559

/* bilinearly interpolate Typ/gyp first */

560

if (yi!=sy-1) {

561

ELL_3M_LERP(Txm, coords[1], sctx->t + 9*(0+2*siy), sctx->t + 9*(1+2*siy))((((Txm)+0)[0] = ((((coords[1])))*((((sctx->t + 9*(1+2*siy
))+0)[0]) - (((sctx->t + 9*(0+2*siy))+0)[0])) + (((sctx->
t + 9*(0+2*siy))+0)[0])), ((Txm)+0)[1] = ((((coords[1])))*(((
(sctx->t + 9*(1+2*siy))+0)[1]) - (((sctx->t + 9*(0+2*siy
))+0)[1])) + (((sctx->t + 9*(0+2*siy))+0)[1])), ((Txm)+0)[
2] = ((((coords[1])))*((((sctx->t + 9*(1+2*siy))+0)[2]) - (
((sctx->t + 9*(0+2*siy))+0)[2])) + (((sctx->t + 9*(0+2*
siy))+0)[2]))), (((Txm)+3)[0] = ((((coords[1])))*((((sctx->
t + 9*(1+2*siy))+3)[0]) - (((sctx->t + 9*(0+2*siy))+3)[0])
) + (((sctx->t + 9*(0+2*siy))+3)[0])), ((Txm)+3)[1] = ((((
coords[1])))*((((sctx->t + 9*(1+2*siy))+3)[1]) - (((sctx->
t + 9*(0+2*siy))+3)[1])) + (((sctx->t + 9*(0+2*siy))+3)[1]
)), ((Txm)+3)[2] = ((((coords[1])))*((((sctx->t + 9*(1+2*siy
))+3)[2]) - (((sctx->t + 9*(0+2*siy))+3)[2])) + (((sctx->
t + 9*(0+2*siy))+3)[2]))), (((Txm)+6)[0] = ((((coords[1])))*(
(((sctx->t + 9*(1+2*siy))+6)[0]) - (((sctx->t + 9*(0+2*
siy))+6)[0])) + (((sctx->t + 9*(0+2*siy))+6)[0])), ((Txm)+
6)[1] = ((((coords[1])))*((((sctx->t + 9*(1+2*siy))+6)[1])
- (((sctx->t + 9*(0+2*siy))+6)[1])) + (((sctx->t + 9*(
0+2*siy))+6)[1])), ((Txm)+6)[2] = ((((coords[1])))*((((sctx->
t + 9*(1+2*siy))+6)[2]) - (((sctx->t + 9*(0+2*siy))+6)[2])
) + (((sctx->t + 9*(0+2*siy))+6)[2]))));

562

ELL_3V_LERP(gxm, coords[1], sctx->grad + 3*(0+2*siy),((gxm)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*siy))[0]
) - ((sctx->grad + 3*(0+2*siy))[0])) + ((sctx->grad + 3
*(0+2*siy))[0])), (gxm)[1] = (((coords[1]))*(((sctx->grad +
3*(1+2*siy))[1]) - ((sctx->grad + 3*(0+2*siy))[1])) + ((sctx
->grad + 3*(0+2*siy))[1])), (gxm)[2] = (((coords[1]))*(((sctx
->grad + 3*(1+2*siy))[2]) - ((sctx->grad + 3*(0+2*siy))
[2])) + ((sctx->grad + 3*(0+2*siy))[2])))

563

sctx->grad + 3*(1+2*siy))((gxm)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*siy))[0]
) - ((sctx->grad + 3*(0+2*siy))[0])) + ((sctx->grad + 3
*(0+2*siy))[0])), (gxm)[1] = (((coords[1]))*(((sctx->grad +
3*(1+2*siy))[1]) - ((sctx->grad + 3*(0+2*siy))[1])) + ((sctx
->grad + 3*(0+2*siy))[1])), (gxm)[2] = (((coords[1]))*(((sctx
->grad + 3*(1+2*siy))[2]) - ((sctx->grad + 3*(0+2*siy))
[2])) + ((sctx->grad + 3*(0+2*siy))[2])));

564

ELL_3M_LERP(Txp, coords[1], sctx->t + 9*(0+2*sixy),((((Txp)+0)[0] = ((((coords[1])))*((((sctx->t + 9*(1+2*sixy
))+0)[0]) - (((sctx->t + 9*(0+2*sixy))+0)[0])) + (((sctx->
t + 9*(0+2*sixy))+0)[0])), ((Txp)+0)[1] = ((((coords[1])))*((
((sctx->t + 9*(1+2*sixy))+0)[1]) - (((sctx->t + 9*(0+2*
sixy))+0)[1])) + (((sctx->t + 9*(0+2*sixy))+0)[1])), ((Txp
)+0)[2] = ((((coords[1])))*((((sctx->t + 9*(1+2*sixy))+0)[
2]) - (((sctx->t + 9*(0+2*sixy))+0)[2])) + (((sctx->t +
9*(0+2*sixy))+0)[2]))), (((Txp)+3)[0] = ((((coords[1])))*(((
(sctx->t + 9*(1+2*sixy))+3)[0]) - (((sctx->t + 9*(0+2*sixy
))+3)[0])) + (((sctx->t + 9*(0+2*sixy))+3)[0])), ((Txp)+3)
[1] = ((((coords[1])))*((((sctx->t + 9*(1+2*sixy))+3)[1]) -
(((sctx->t + 9*(0+2*sixy))+3)[1])) + (((sctx->t + 9*(0
+2*sixy))+3)[1])), ((Txp)+3)[2] = ((((coords[1])))*((((sctx->
t + 9*(1+2*sixy))+3)[2]) - (((sctx->t + 9*(0+2*sixy))+3)[2
])) + (((sctx->t + 9*(0+2*sixy))+3)[2]))), (((Txp)+6)[0] =
((((coords[1])))*((((sctx->t + 9*(1+2*sixy))+6)[0]) - (((
sctx->t + 9*(0+2*sixy))+6)[0])) + (((sctx->t + 9*(0+2*sixy
))+6)[0])), ((Txp)+6)[1] = ((((coords[1])))*((((sctx->t + 9
*(1+2*sixy))+6)[1]) - (((sctx->t + 9*(0+2*sixy))+6)[1])) +
(((sctx->t + 9*(0+2*sixy))+6)[1])), ((Txp)+6)[2] = ((((coords
[1])))*((((sctx->t + 9*(1+2*sixy))+6)[2]) - (((sctx->t +
9*(0+2*sixy))+6)[2])) + (((sctx->t + 9*(0+2*sixy))+6)[2])
)))

565

sctx->t + 9*(1+2*sixy))((((Txp)+0)[0] = ((((coords[1])))*((((sctx->t + 9*(1+2*sixy
))+0)[0]) - (((sctx->t + 9*(0+2*sixy))+0)[0])) + (((sctx->
t + 9*(0+2*sixy))+0)[0])), ((Txp)+0)[1] = ((((coords[1])))*((
((sctx->t + 9*(1+2*sixy))+0)[1]) - (((sctx->t + 9*(0+2*
sixy))+0)[1])) + (((sctx->t + 9*(0+2*sixy))+0)[1])), ((Txp
)+0)[2] = ((((coords[1])))*((((sctx->t + 9*(1+2*sixy))+0)[
2]) - (((sctx->t + 9*(0+2*sixy))+0)[2])) + (((sctx->t +
9*(0+2*sixy))+0)[2]))), (((Txp)+3)[0] = ((((coords[1])))*(((
(sctx->t + 9*(1+2*sixy))+3)[0]) - (((sctx->t + 9*(0+2*sixy
))+3)[0])) + (((sctx->t + 9*(0+2*sixy))+3)[0])), ((Txp)+3)
[1] = ((((coords[1])))*((((sctx->t + 9*(1+2*sixy))+3)[1]) -
(((sctx->t + 9*(0+2*sixy))+3)[1])) + (((sctx->t + 9*(0
+2*sixy))+3)[1])), ((Txp)+3)[2] = ((((coords[1])))*((((sctx->
t + 9*(1+2*sixy))+3)[2]) - (((sctx->t + 9*(0+2*sixy))+3)[2
])) + (((sctx->t + 9*(0+2*sixy))+3)[2]))), (((Txp)+6)[0] =
((((coords[1])))*((((sctx->t + 9*(1+2*sixy))+6)[0]) - (((
sctx->t + 9*(0+2*sixy))+6)[0])) + (((sctx->t + 9*(0+2*sixy
))+6)[0])), ((Txp)+6)[1] = ((((coords[1])))*((((sctx->t + 9
*(1+2*sixy))+6)[1]) - (((sctx->t + 9*(0+2*sixy))+6)[1])) +
(((sctx->t + 9*(0+2*sixy))+6)[1])), ((Txp)+6)[2] = ((((coords
[1])))*((((sctx->t + 9*(1+2*sixy))+6)[2]) - (((sctx->t +
9*(0+2*sixy))+6)[2])) + (((sctx->t + 9*(0+2*sixy))+6)[2])
)));

566

ELL_3V_LERP(gxp, coords[1], sctx->grad + 3*(0+2*sixy),((gxp)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*sixy))[0
]) - ((sctx->grad + 3*(0+2*sixy))[0])) + ((sctx->grad +
3*(0+2*sixy))[0])), (gxp)[1] = (((coords[1]))*(((sctx->grad
+ 3*(1+2*sixy))[1]) - ((sctx->grad + 3*(0+2*sixy))[1])) +
((sctx->grad + 3*(0+2*sixy))[1])), (gxp)[2] = (((coords[1
]))*(((sctx->grad + 3*(1+2*sixy))[2]) - ((sctx->grad + 3
*(0+2*sixy))[2])) + ((sctx->grad + 3*(0+2*sixy))[2])))

567

sctx->grad + 3*(1+2*sixy))((gxp)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*sixy))[0
]) - ((sctx->grad + 3*(0+2*sixy))[0])) + ((sctx->grad +
3*(0+2*sixy))[0])), (gxp)[1] = (((coords[1]))*(((sctx->grad
+ 3*(1+2*sixy))[1]) - ((sctx->grad + 3*(0+2*sixy))[1])) +
((sctx->grad + 3*(0+2*sixy))[1])), (gxp)[2] = (((coords[1
]))*(((sctx->grad + 3*(1+2*sixy))[2]) - ((sctx->grad + 3
*(0+2*sixy))[2])) + ((sctx->grad + 3*(0+2*sixy))[2])));

568

ELL_3M_LERP(Typ, coords[0], Txm, Txp)((((Typ)+0)[0] = ((((coords[0])))*((((Txp)+0)[0]) - (((Txm)+0
)[0])) + (((Txm)+0)[0])), ((Typ)+0)[1] = ((((coords[0])))*(((
(Txp)+0)[1]) - (((Txm)+0)[1])) + (((Txm)+0)[1])), ((Typ)+0)[2
] = ((((coords[0])))*((((Txp)+0)[2]) - (((Txm)+0)[2])) + (((Txm
)+0)[2]))), (((Typ)+3)[0] = ((((coords[0])))*((((Txp)+3)[0]) -
(((Txm)+3)[0])) + (((Txm)+3)[0])), ((Typ)+3)[1] = ((((coords
[0])))*((((Txp)+3)[1]) - (((Txm)+3)[1])) + (((Txm)+3)[1])), (
(Typ)+3)[2] = ((((coords[0])))*((((Txp)+3)[2]) - (((Txm)+3)[2
])) + (((Txm)+3)[2]))), (((Typ)+6)[0] = ((((coords[0])))*((((
Txp)+6)[0]) - (((Txm)+6)[0])) + (((Txm)+6)[0])), ((Typ)+6)[1]
= ((((coords[0])))*((((Txp)+6)[1]) - (((Txm)+6)[1])) + (((Txm
)+6)[1])), ((Typ)+6)[2] = ((((coords[0])))*((((Txp)+6)[2]) - (
((Txm)+6)[2])) + (((Txm)+6)[2]))));

569

ELL_3V_LERP(gyp, coords[0], gxm, gxp)((gyp)[0] = (((coords[0]))*(((gxp)[0]) - ((gxm)[0])) + ((gxm)
[0])), (gyp)[1] = (((coords[0]))*(((gxp)[1]) - ((gxm)[1])) + (
(gxm)[1])), (gyp)[2] = (((coords[0]))*(((gxp)[2]) - ((gxm)[2]
)) + ((gxm)[2])));

570

} else {

571

ELL_3M_LERP(Txm, coords[1], sctx->t + 9*(0+2*siY), sctx->t + 9*(1+2*siY))((((Txm)+0)[0] = ((((coords[1])))*((((sctx->t + 9*(1+2*siY
))+0)[0]) - (((sctx->t + 9*(0+2*siY))+0)[0])) + (((sctx->
t + 9*(0+2*siY))+0)[0])), ((Txm)+0)[1] = ((((coords[1])))*(((
(sctx->t + 9*(1+2*siY))+0)[1]) - (((sctx->t + 9*(0+2*siY
))+0)[1])) + (((sctx->t + 9*(0+2*siY))+0)[1])), ((Txm)+0)[
2] = ((((coords[1])))*((((sctx->t + 9*(1+2*siY))+0)[2]) - (
((sctx->t + 9*(0+2*siY))+0)[2])) + (((sctx->t + 9*(0+2*
siY))+0)[2]))), (((Txm)+3)[0] = ((((coords[1])))*((((sctx->
t + 9*(1+2*siY))+3)[0]) - (((sctx->t + 9*(0+2*siY))+3)[0])
) + (((sctx->t + 9*(0+2*siY))+3)[0])), ((Txm)+3)[1] = ((((
coords[1])))*((((sctx->t + 9*(1+2*siY))+3)[1]) - (((sctx->
t + 9*(0+2*siY))+3)[1])) + (((sctx->t + 9*(0+2*siY))+3)[1]
)), ((Txm)+3)[2] = ((((coords[1])))*((((sctx->t + 9*(1+2*siY
))+3)[2]) - (((sctx->t + 9*(0+2*siY))+3)[2])) + (((sctx->
t + 9*(0+2*siY))+3)[2]))), (((Txm)+6)[0] = ((((coords[1])))*(
(((sctx->t + 9*(1+2*siY))+6)[0]) - (((sctx->t + 9*(0+2*
siY))+6)[0])) + (((sctx->t + 9*(0+2*siY))+6)[0])), ((Txm)+
6)[1] = ((((coords[1])))*((((sctx->t + 9*(1+2*siY))+6)[1])
- (((sctx->t + 9*(0+2*siY))+6)[1])) + (((sctx->t + 9*(
0+2*siY))+6)[1])), ((Txm)+6)[2] = ((((coords[1])))*((((sctx->
t + 9*(1+2*siY))+6)[2]) - (((sctx->t + 9*(0+2*siY))+6)[2])
) + (((sctx->t + 9*(0+2*siY))+6)[2]))));

572

ELL_3V_LERP(gxm, coords[1], sctx->grad + 3*(0+2*siY),((gxm)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*siY))[0]
) - ((sctx->grad + 3*(0+2*siY))[0])) + ((sctx->grad + 3
*(0+2*siY))[0])), (gxm)[1] = (((coords[1]))*(((sctx->grad +
3*(1+2*siY))[1]) - ((sctx->grad + 3*(0+2*siY))[1])) + ((sctx
->grad + 3*(0+2*siY))[1])), (gxm)[2] = (((coords[1]))*(((sctx
->grad + 3*(1+2*siY))[2]) - ((sctx->grad + 3*(0+2*siY))
[2])) + ((sctx->grad + 3*(0+2*siY))[2])))

573

sctx->grad + 3*(1+2*siY))((gxm)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*siY))[0]
) - ((sctx->grad + 3*(0+2*siY))[0])) + ((sctx->grad + 3
*(0+2*siY))[0])), (gxm)[1] = (((coords[1]))*(((sctx->grad +
3*(1+2*siY))[1]) - ((sctx->grad + 3*(0+2*siY))[1])) + ((sctx
->grad + 3*(0+2*siY))[1])), (gxm)[2] = (((coords[1]))*(((sctx
->grad + 3*(1+2*siY))[2]) - ((sctx->grad + 3*(0+2*siY))
[2])) + ((sctx->grad + 3*(0+2*siY))[2])));

574

ELL_3M_LERP(Txp, coords[1], sctx->t + 9*(0+2*sixY),((((Txp)+0)[0] = ((((coords[1])))*((((sctx->t + 9*(1+2*sixY
))+0)[0]) - (((sctx->t + 9*(0+2*sixY))+0)[0])) + (((sctx->
t + 9*(0+2*sixY))+0)[0])), ((Txp)+0)[1] = ((((coords[1])))*((
((sctx->t + 9*(1+2*sixY))+0)[1]) - (((sctx->t + 9*(0+2*
sixY))+0)[1])) + (((sctx->t + 9*(0+2*sixY))+0)[1])), ((Txp
)+0)[2] = ((((coords[1])))*((((sctx->t + 9*(1+2*sixY))+0)[
2]) - (((sctx->t + 9*(0+2*sixY))+0)[2])) + (((sctx->t +
9*(0+2*sixY))+0)[2]))), (((Txp)+3)[0] = ((((coords[1])))*(((
(sctx->t + 9*(1+2*sixY))+3)[0]) - (((sctx->t + 9*(0+2*sixY
))+3)[0])) + (((sctx->t + 9*(0+2*sixY))+3)[0])), ((Txp)+3)
[1] = ((((coords[1])))*((((sctx->t + 9*(1+2*sixY))+3)[1]) -
(((sctx->t + 9*(0+2*sixY))+3)[1])) + (((sctx->t + 9*(0
+2*sixY))+3)[1])), ((Txp)+3)[2] = ((((coords[1])))*((((sctx->
t + 9*(1+2*sixY))+3)[2]) - (((sctx->t + 9*(0+2*sixY))+3)[2
])) + (((sctx->t + 9*(0+2*sixY))+3)[2]))), (((Txp)+6)[0] =
((((coords[1])))*((((sctx->t + 9*(1+2*sixY))+6)[0]) - (((
sctx->t + 9*(0+2*sixY))+6)[0])) + (((sctx->t + 9*(0+2*sixY
))+6)[0])), ((Txp)+6)[1] = ((((coords[1])))*((((sctx->t + 9
*(1+2*sixY))+6)[1]) - (((sctx->t + 9*(0+2*sixY))+6)[1])) +
(((sctx->t + 9*(0+2*sixY))+6)[1])), ((Txp)+6)[2] = ((((coords
[1])))*((((sctx->t + 9*(1+2*sixY))+6)[2]) - (((sctx->t +
9*(0+2*sixY))+6)[2])) + (((sctx->t + 9*(0+2*sixY))+6)[2])
)))

575

sctx->t + 9*(1+2*sixY))((((Txp)+0)[0] = ((((coords[1])))*((((sctx->t + 9*(1+2*sixY
))+0)[0]) - (((sctx->t + 9*(0+2*sixY))+0)[0])) + (((sctx->
t + 9*(0+2*sixY))+0)[0])), ((Txp)+0)[1] = ((((coords[1])))*((
((sctx->t + 9*(1+2*sixY))+0)[1]) - (((sctx->t + 9*(0+2*
sixY))+0)[1])) + (((sctx->t + 9*(0+2*sixY))+0)[1])), ((Txp
)+0)[2] = ((((coords[1])))*((((sctx->t + 9*(1+2*sixY))+0)[
2]) - (((sctx->t + 9*(0+2*sixY))+0)[2])) + (((sctx->t +
9*(0+2*sixY))+0)[2]))), (((Txp)+3)[0] = ((((coords[1])))*(((
(sctx->t + 9*(1+2*sixY))+3)[0]) - (((sctx->t + 9*(0+2*sixY
))+3)[0])) + (((sctx->t + 9*(0+2*sixY))+3)[0])), ((Txp)+3)
[1] = ((((coords[1])))*((((sctx->t + 9*(1+2*sixY))+3)[1]) -
(((sctx->t + 9*(0+2*sixY))+3)[1])) + (((sctx->t + 9*(0
+2*sixY))+3)[1])), ((Txp)+3)[2] = ((((coords[1])))*((((sctx->
t + 9*(1+2*sixY))+3)[2]) - (((sctx->t + 9*(0+2*sixY))+3)[2
])) + (((sctx->t + 9*(0+2*sixY))+3)[2]))), (((Txp)+6)[0] =
((((coords[1])))*((((sctx->t + 9*(1+2*sixY))+6)[0]) - (((
sctx->t + 9*(0+2*sixY))+6)[0])) + (((sctx->t + 9*(0+2*sixY
))+6)[0])), ((Txp)+6)[1] = ((((coords[1])))*((((sctx->t + 9
*(1+2*sixY))+6)[1]) - (((sctx->t + 9*(0+2*sixY))+6)[1])) +
(((sctx->t + 9*(0+2*sixY))+6)[1])), ((Txp)+6)[2] = ((((coords
[1])))*((((sctx->t + 9*(1+2*sixY))+6)[2]) - (((sctx->t +
9*(0+2*sixY))+6)[2])) + (((sctx->t + 9*(0+2*sixY))+6)[2])
)));

576

ELL_3V_LERP(gxp, coords[1], sctx->grad + 3*(0+2*sixY),((gxp)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*sixY))[0
]) - ((sctx->grad + 3*(0+2*sixY))[0])) + ((sctx->grad +
3*(0+2*sixY))[0])), (gxp)[1] = (((coords[1]))*(((sctx->grad
+ 3*(1+2*sixY))[1]) - ((sctx->grad + 3*(0+2*sixY))[1])) +
((sctx->grad + 3*(0+2*sixY))[1])), (gxp)[2] = (((coords[1
]))*(((sctx->grad + 3*(1+2*sixY))[2]) - ((sctx->grad + 3
*(0+2*sixY))[2])) + ((sctx->grad + 3*(0+2*sixY))[2])))

577

sctx->grad + 3*(1+2*sixY))((gxp)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*sixY))[0
]) - ((sctx->grad + 3*(0+2*sixY))[0])) + ((sctx->grad +
3*(0+2*sixY))[0])), (gxp)[1] = (((coords[1]))*(((sctx->grad
+ 3*(1+2*sixY))[1]) - ((sctx->grad + 3*(0+2*sixY))[1])) +
((sctx->grad + 3*(0+2*sixY))[1])), (gxp)[2] = (((coords[1
]))*(((sctx->grad + 3*(1+2*sixY))[2]) - ((sctx->grad + 3
*(0+2*sixY))[2])) + ((sctx->grad + 3*(0+2*sixY))[2])));

578

ELL_3M_LERP(Tym, coords[0], Txm, Txp)((((Tym)+0)[0] = ((((coords[0])))*((((Txp)+0)[0]) - (((Txm)+0
)[0])) + (((Txm)+0)[0])), ((Tym)+0)[1] = ((((coords[0])))*(((
(Txp)+0)[1]) - (((Txm)+0)[1])) + (((Txm)+0)[1])), ((Tym)+0)[2
] = ((((coords[0])))*((((Txp)+0)[2]) - (((Txm)+0)[2])) + (((Txm
)+0)[2]))), (((Tym)+3)[0] = ((((coords[0])))*((((Txp)+3)[0]) -
(((Txm)+3)[0])) + (((Txm)+3)[0])), ((Tym)+3)[1] = ((((coords
[0])))*((((Txp)+3)[1]) - (((Txm)+3)[1])) + (((Txm)+3)[1])), (
(Tym)+3)[2] = ((((coords[0])))*((((Txp)+3)[2]) - (((Txm)+3)[2
])) + (((Txm)+3)[2]))), (((Tym)+6)[0] = ((((coords[0])))*((((
Txp)+6)[0]) - (((Txm)+6)[0])) + (((Txm)+6)[0])), ((Tym)+6)[1]
= ((((coords[0])))*((((Txp)+6)[1]) - (((Txm)+6)[1])) + (((Txm
)+6)[1])), ((Tym)+6)[2] = ((((coords[0])))*((((Txp)+6)[2]) - (
((Txm)+6)[2])) + (((Txm)+6)[2]))));

579

ELL_3V_LERP(gym, coords[0], gxm, gxp)((gym)[0] = (((coords[0]))*(((gxp)[0]) - ((gxm)[0])) + ((gxm)
[0])), (gym)[1] = (((coords[0]))*(((gxp)[1]) - ((gxm)[1])) + (
(gxm)[1])), (gym)[2] = (((coords[0]))*(((gxp)[2]) - ((gxm)[2]
)) + ((gxm)[2])));

580

}

581

/* now, compute remaining points */

582

ELL_3M_LERP(Txm, coords[1], sctx->t + 9*(0+2*si), sctx->t + 9*(1+2*si))((((Txm)+0)[0] = ((((coords[1])))*((((sctx->t + 9*(1+2*si)
)+0)[0]) - (((sctx->t + 9*(0+2*si))+0)[0])) + (((sctx->
t + 9*(0+2*si))+0)[0])), ((Txm)+0)[1] = ((((coords[1])))*((((
sctx->t + 9*(1+2*si))+0)[1]) - (((sctx->t + 9*(0+2*si))
+0)[1])) + (((sctx->t + 9*(0+2*si))+0)[1])), ((Txm)+0)[2] =
((((coords[1])))*((((sctx->t + 9*(1+2*si))+0)[2]) - (((sctx
->t + 9*(0+2*si))+0)[2])) + (((sctx->t + 9*(0+2*si))+0)
[2]))), (((Txm)+3)[0] = ((((coords[1])))*((((sctx->t + 9*(
1+2*si))+3)[0]) - (((sctx->t + 9*(0+2*si))+3)[0])) + (((sctx
->t + 9*(0+2*si))+3)[0])), ((Txm)+3)[1] = ((((coords[1])))
*((((sctx->t + 9*(1+2*si))+3)[1]) - (((sctx->t + 9*(0+2
*si))+3)[1])) + (((sctx->t + 9*(0+2*si))+3)[1])), ((Txm)+3
)[2] = ((((coords[1])))*((((sctx->t + 9*(1+2*si))+3)[2]) -
(((sctx->t + 9*(0+2*si))+3)[2])) + (((sctx->t + 9*(0+2
*si))+3)[2]))), (((Txm)+6)[0] = ((((coords[1])))*((((sctx->
t + 9*(1+2*si))+6)[0]) - (((sctx->t + 9*(0+2*si))+6)[0])) +
(((sctx->t + 9*(0+2*si))+6)[0])), ((Txm)+6)[1] = ((((coords
[1])))*((((sctx->t + 9*(1+2*si))+6)[1]) - (((sctx->t + 9
*(0+2*si))+6)[1])) + (((sctx->t + 9*(0+2*si))+6)[1])), ((Txm
)+6)[2] = ((((coords[1])))*((((sctx->t + 9*(1+2*si))+6)[2]
) - (((sctx->t + 9*(0+2*si))+6)[2])) + (((sctx->t + 9*(
0+2*si))+6)[2]))));

583

ELL_3V_LERP(gxm, coords[1], sctx->grad + 3*(0+2*si),((gxm)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*si))[0])
- ((sctx->grad + 3*(0+2*si))[0])) + ((sctx->grad + 3*(
0+2*si))[0])), (gxm)[1] = (((coords[1]))*(((sctx->grad + 3
*(1+2*si))[1]) - ((sctx->grad + 3*(0+2*si))[1])) + ((sctx->
grad + 3*(0+2*si))[1])), (gxm)[2] = (((coords[1]))*(((sctx->
grad + 3*(1+2*si))[2]) - ((sctx->grad + 3*(0+2*si))[2])) +
((sctx->grad + 3*(0+2*si))[2])))

584

sctx->grad + 3*(1+2*si))((gxm)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*si))[0])
- ((sctx->grad + 3*(0+2*si))[0])) + ((sctx->grad + 3*(
0+2*si))[0])), (gxm)[1] = (((coords[1]))*(((sctx->grad + 3
*(1+2*si))[1]) - ((sctx->grad + 3*(0+2*si))[1])) + ((sctx->
grad + 3*(0+2*si))[1])), (gxm)[2] = (((coords[1]))*(((sctx->
grad + 3*(1+2*si))[2]) - ((sctx->grad + 3*(0+2*si))[2])) +
((sctx->grad + 3*(0+2*si))[2])));

585

ELL_3M_LERP(Txp, coords[1], sctx->t + 9*(0+2*six), sctx->t + 9*(1+2*six))((((Txp)+0)[0] = ((((coords[1])))*((((sctx->t + 9*(1+2*six
))+0)[0]) - (((sctx->t + 9*(0+2*six))+0)[0])) + (((sctx->
t + 9*(0+2*six))+0)[0])), ((Txp)+0)[1] = ((((coords[1])))*(((
(sctx->t + 9*(1+2*six))+0)[1]) - (((sctx->t + 9*(0+2*six
))+0)[1])) + (((sctx->t + 9*(0+2*six))+0)[1])), ((Txp)+0)[
2] = ((((coords[1])))*((((sctx->t + 9*(1+2*six))+0)[2]) - (
((sctx->t + 9*(0+2*six))+0)[2])) + (((sctx->t + 9*(0+2*
six))+0)[2]))), (((Txp)+3)[0] = ((((coords[1])))*((((sctx->
t + 9*(1+2*six))+3)[0]) - (((sctx->t + 9*(0+2*six))+3)[0])
) + (((sctx->t + 9*(0+2*six))+3)[0])), ((Txp)+3)[1] = ((((
coords[1])))*((((sctx->t + 9*(1+2*six))+3)[1]) - (((sctx->
t + 9*(0+2*six))+3)[1])) + (((sctx->t + 9*(0+2*six))+3)[1]
)), ((Txp)+3)[2] = ((((coords[1])))*((((sctx->t + 9*(1+2*six
))+3)[2]) - (((sctx->t + 9*(0+2*six))+3)[2])) + (((sctx->
t + 9*(0+2*six))+3)[2]))), (((Txp)+6)[0] = ((((coords[1])))*(
(((sctx->t + 9*(1+2*six))+6)[0]) - (((sctx->t + 9*(0+2*
six))+6)[0])) + (((sctx->t + 9*(0+2*six))+6)[0])), ((Txp)+
6)[1] = ((((coords[1])))*((((sctx->t + 9*(1+2*six))+6)[1])
- (((sctx->t + 9*(0+2*six))+6)[1])) + (((sctx->t + 9*(
0+2*six))+6)[1])), ((Txp)+6)[2] = ((((coords[1])))*((((sctx->
t + 9*(1+2*six))+6)[2]) - (((sctx->t + 9*(0+2*six))+6)[2])
) + (((sctx->t + 9*(0+2*six))+6)[2]))));

586

ELL_3V_LERP(gxp, coords[1], sctx->grad + 3*(0+2*six),((gxp)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*six))[0]
) - ((sctx->grad + 3*(0+2*six))[0])) + ((sctx->grad + 3
*(0+2*six))[0])), (gxp)[1] = (((coords[1]))*(((sctx->grad +
3*(1+2*six))[1]) - ((sctx->grad + 3*(0+2*six))[1])) + ((sctx
->grad + 3*(0+2*six))[1])), (gxp)[2] = (((coords[1]))*(((sctx
->grad + 3*(1+2*six))[2]) - ((sctx->grad + 3*(0+2*six))
[2])) + ((sctx->grad + 3*(0+2*six))[2])))

587

sctx->grad + 3*(1+2*six))((gxp)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*six))[0]
) - ((sctx->grad + 3*(0+2*six))[0])) + ((sctx->grad + 3
*(0+2*six))[0])), (gxp)[1] = (((coords[1]))*(((sctx->grad +
3*(1+2*six))[1]) - ((sctx->grad + 3*(0+2*six))[1])) + ((sctx
->grad + 3*(0+2*six))[1])), (gxp)[2] = (((coords[1]))*(((sctx
->grad + 3*(1+2*six))[2]) - ((sctx->grad + 3*(0+2*six))
[2])) + ((sctx->grad + 3*(0+2*six))[2])));

588

589

ELL_3M_LERP(Tzm, coords[0], sctx->t + 9*(0+2*si), sctx->t + 9*(0+2*six))((((Tzm)+0)[0] = ((((coords[0])))*((((sctx->t + 9*(0+2*six
))+0)[0]) - (((sctx->t + 9*(0+2*si))+0)[0])) + (((sctx->
t + 9*(0+2*si))+0)[0])), ((Tzm)+0)[1] = ((((coords[0])))*((((
sctx->t + 9*(0+2*six))+0)[1]) - (((sctx->t + 9*(0+2*si)
)+0)[1])) + (((sctx->t + 9*(0+2*si))+0)[1])), ((Tzm)+0)[2]
= ((((coords[0])))*((((sctx->t + 9*(0+2*six))+0)[2]) - ((
(sctx->t + 9*(0+2*si))+0)[2])) + (((sctx->t + 9*(0+2*si
))+0)[2]))), (((Tzm)+3)[0] = ((((coords[0])))*((((sctx->t +
9*(0+2*six))+3)[0]) - (((sctx->t + 9*(0+2*si))+3)[0])) + (
((sctx->t + 9*(0+2*si))+3)[0])), ((Tzm)+3)[1] = ((((coords
[0])))*((((sctx->t + 9*(0+2*six))+3)[1]) - (((sctx->t +
9*(0+2*si))+3)[1])) + (((sctx->t + 9*(0+2*si))+3)[1])), (
(Tzm)+3)[2] = ((((coords[0])))*((((sctx->t + 9*(0+2*six))+
3)[2]) - (((sctx->t + 9*(0+2*si))+3)[2])) + (((sctx->t +
9*(0+2*si))+3)[2]))), (((Tzm)+6)[0] = ((((coords[0])))*((((sctx
->t + 9*(0+2*six))+6)[0]) - (((sctx->t + 9*(0+2*si))+6)
[0])) + (((sctx->t + 9*(0+2*si))+6)[0])), ((Tzm)+6)[1] = (
(((coords[0])))*((((sctx->t + 9*(0+2*six))+6)[1]) - (((sctx
->t + 9*(0+2*si))+6)[1])) + (((sctx->t + 9*(0+2*si))+6)
[1])), ((Tzm)+6)[2] = ((((coords[0])))*((((sctx->t + 9*(0+
2*six))+6)[2]) - (((sctx->t + 9*(0+2*si))+6)[2])) + (((sctx
->t + 9*(0+2*si))+6)[2]))));

590

ELL_3V_LERP(gzm, coords[0], sctx->grad + 3*(0+2*si),((gzm)[0] = (((coords[0]))*(((sctx->grad + 3*(0+2*six))[0]
) - ((sctx->grad + 3*(0+2*si))[0])) + ((sctx->grad + 3*
(0+2*si))[0])), (gzm)[1] = (((coords[0]))*(((sctx->grad + 3
*(0+2*six))[1]) - ((sctx->grad + 3*(0+2*si))[1])) + ((sctx
->grad + 3*(0+2*si))[1])), (gzm)[2] = (((coords[0]))*(((sctx
->grad + 3*(0+2*six))[2]) - ((sctx->grad + 3*(0+2*si))[
2])) + ((sctx->grad + 3*(0+2*si))[2])))

591

sctx->grad + 3*(0+2*six))((gzm)[0] = (((coords[0]))*(((sctx->grad + 3*(0+2*six))[0]
) - ((sctx->grad + 3*(0+2*si))[0])) + ((sctx->grad + 3*
(0+2*si))[0])), (gzm)[1] = (((coords[0]))*(((sctx->grad + 3
*(0+2*six))[1]) - ((sctx->grad + 3*(0+2*si))[1])) + ((sctx
->grad + 3*(0+2*si))[1])), (gzm)[2] = (((coords[0]))*(((sctx
->grad + 3*(0+2*six))[2]) - ((sctx->grad + 3*(0+2*si))[
2])) + ((sctx->grad + 3*(0+2*si))[2])));

592

ELL_3M_LERP(Tzp, coords[0], sctx->t + 9*(1+2*si), sctx->t + 9*(1+2*six))((((Tzp)+0)[0] = ((((coords[0])))*((((sctx->t + 9*(1+2*six
))+0)[0]) - (((sctx->t + 9*(1+2*si))+0)[0])) + (((sctx->
t + 9*(1+2*si))+0)[0])), ((Tzp)+0)[1] = ((((coords[0])))*((((
sctx->t + 9*(1+2*six))+0)[1]) - (((sctx->t + 9*(1+2*si)
)+0)[1])) + (((sctx->t + 9*(1+2*si))+0)[1])), ((Tzp)+0)[2]
= ((((coords[0])))*((((sctx->t + 9*(1+2*six))+0)[2]) - ((
(sctx->t + 9*(1+2*si))+0)[2])) + (((sctx->t + 9*(1+2*si
))+0)[2]))), (((Tzp)+3)[0] = ((((coords[0])))*((((sctx->t +
9*(1+2*six))+3)[0]) - (((sctx->t + 9*(1+2*si))+3)[0])) + (
((sctx->t + 9*(1+2*si))+3)[0])), ((Tzp)+3)[1] = ((((coords
[0])))*((((sctx->t + 9*(1+2*six))+3)[1]) - (((sctx->t +
9*(1+2*si))+3)[1])) + (((sctx->t + 9*(1+2*si))+3)[1])), (
(Tzp)+3)[2] = ((((coords[0])))*((((sctx->t + 9*(1+2*six))+
3)[2]) - (((sctx->t + 9*(1+2*si))+3)[2])) + (((sctx->t +
9*(1+2*si))+3)[2]))), (((Tzp)+6)[0] = ((((coords[0])))*((((sctx
->t + 9*(1+2*six))+6)[0]) - (((sctx->t + 9*(1+2*si))+6)
[0])) + (((sctx->t + 9*(1+2*si))+6)[0])), ((Tzp)+6)[1] = (
(((coords[0])))*((((sctx->t + 9*(1+2*six))+6)[1]) - (((sctx
->t + 9*(1+2*si))+6)[1])) + (((sctx->t + 9*(1+2*si))+6)
[1])), ((Tzp)+6)[2] = ((((coords[0])))*((((sctx->t + 9*(1+
2*six))+6)[2]) - (((sctx->t + 9*(1+2*si))+6)[2])) + (((sctx
->t + 9*(1+2*si))+6)[2]))));

593

ELL_3V_LERP(gzp, coords[0], sctx->grad + 3*(1+2*si),((gzp)[0] = (((coords[0]))*(((sctx->grad + 3*(1+2*six))[0]
) - ((sctx->grad + 3*(1+2*si))[0])) + ((sctx->grad + 3*
(1+2*si))[0])), (gzp)[1] = (((coords[0]))*(((sctx->grad + 3
*(1+2*six))[1]) - ((sctx->grad + 3*(1+2*si))[1])) + ((sctx
->grad + 3*(1+2*si))[1])), (gzp)[2] = (((coords[0]))*(((sctx
->grad + 3*(1+2*six))[2]) - ((sctx->grad + 3*(1+2*si))[
2])) + ((sctx->grad + 3*(1+2*si))[2])))

594

sctx->grad + 3*(1+2*six))((gzp)[0] = (((coords[0]))*(((sctx->grad + 3*(1+2*six))[0]
) - ((sctx->grad + 3*(1+2*si))[0])) + ((sctx->grad + 3*
(1+2*si))[0])), (gzp)[1] = (((coords[0]))*(((sctx->grad + 3
*(1+2*six))[1]) - ((sctx->grad + 3*(1+2*si))[1])) + ((sctx
->grad + 3*(1+2*si))[1])), (gzp)[2] = (((coords[0]))*(((sctx
->grad + 3*(1+2*six))[2]) - ((sctx->grad + 3*(1+2*si))[
2])) + ((sctx->grad + 3*(1+2*si))[2])));

595

596

597

598

599

if (yi!=sy-1) {

600

computeGradientLin(sctx->facenorm+3*(faceid+4*si), T, g,

601

Txm, gxm, Txp, gxp,

602

T, g, Typ, gyp,

603

Tzm, gzm, Tzp, gzp);

604

} else {

605

computeGradientLin(sctx->facenorm+3*(faceid+4*si), T, g,

606

Txm, gxm, Txp, gxp,

607

Tym, gym, T, g,

608

Tzm, gzm, Tzp, gzp);

609

}

610

break;

611

case 2:

612

/* bilinearly interpolate Txp/gxp first */

613

if (xi!=sx-1) {

←

Taking false branch

→

614

ELL_3M_LERP(Tym, coords[1], sctx->t + 9*(0+2*six), sctx->t + 9*(1+2*six))((((Tym)+0)[0] = ((((coords[1])))*((((sctx->t + 9*(1+2*six
))+0)[0]) - (((sctx->t + 9*(0+2*six))+0)[0])) + (((sctx->
t + 9*(0+2*six))+0)[0])), ((Tym)+0)[1] = ((((coords[1])))*(((
(sctx->t + 9*(1+2*six))+0)[1]) - (((sctx->t + 9*(0+2*six
))+0)[1])) + (((sctx->t + 9*(0+2*six))+0)[1])), ((Tym)+0)[
2] = ((((coords[1])))*((((sctx->t + 9*(1+2*six))+0)[2]) - (
((sctx->t + 9*(0+2*six))+0)[2])) + (((sctx->t + 9*(0+2*
six))+0)[2]))), (((Tym)+3)[0] = ((((coords[1])))*((((sctx->
t + 9*(1+2*six))+3)[0]) - (((sctx->t + 9*(0+2*six))+3)[0])
) + (((sctx->t + 9*(0+2*six))+3)[0])), ((Tym)+3)[1] = ((((
coords[1])))*((((sctx->t + 9*(1+2*six))+3)[1]) - (((sctx->
t + 9*(0+2*six))+3)[1])) + (((sctx->t + 9*(0+2*six))+3)[1]
)), ((Tym)+3)[2] = ((((coords[1])))*((((sctx->t + 9*(1+2*six
))+3)[2]) - (((sctx->t + 9*(0+2*six))+3)[2])) + (((sctx->
t + 9*(0+2*six))+3)[2]))), (((Tym)+6)[0] = ((((coords[1])))*(
(((sctx->t + 9*(1+2*six))+6)[0]) - (((sctx->t + 9*(0+2*
six))+6)[0])) + (((sctx->t + 9*(0+2*six))+6)[0])), ((Tym)+
6)[1] = ((((coords[1])))*((((sctx->t + 9*(1+2*six))+6)[1])
- (((sctx->t + 9*(0+2*six))+6)[1])) + (((sctx->t + 9*(
0+2*six))+6)[1])), ((Tym)+6)[2] = ((((coords[1])))*((((sctx->
t + 9*(1+2*six))+6)[2]) - (((sctx->t + 9*(0+2*six))+6)[2])
) + (((sctx->t + 9*(0+2*six))+6)[2]))));

615

ELL_3V_LERP(gym, coords[1], sctx->grad + 3*(0+2*six),((gym)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*six))[0]
) - ((sctx->grad + 3*(0+2*six))[0])) + ((sctx->grad + 3
*(0+2*six))[0])), (gym)[1] = (((coords[1]))*(((sctx->grad +
3*(1+2*six))[1]) - ((sctx->grad + 3*(0+2*six))[1])) + ((sctx
->grad + 3*(0+2*six))[1])), (gym)[2] = (((coords[1]))*(((sctx
->grad + 3*(1+2*six))[2]) - ((sctx->grad + 3*(0+2*six))
[2])) + ((sctx->grad + 3*(0+2*six))[2])))

616

sctx->grad + 3*(1+2*six))((gym)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*six))[0]
) - ((sctx->grad + 3*(0+2*six))[0])) + ((sctx->grad + 3
*(0+2*six))[0])), (gym)[1] = (((coords[1]))*(((sctx->grad +
3*(1+2*six))[1]) - ((sctx->grad + 3*(0+2*six))[1])) + ((sctx
->grad + 3*(0+2*six))[1])), (gym)[2] = (((coords[1]))*(((sctx
->grad + 3*(1+2*six))[2]) - ((sctx->grad + 3*(0+2*six))
[2])) + ((sctx->grad + 3*(0+2*six))[2])));

617

ELL_3M_LERP(Typ, coords[1], sctx->t + 9*(0+2*sixy),((((Typ)+0)[0] = ((((coords[1])))*((((sctx->t + 9*(1+2*sixy
))+0)[0]) - (((sctx->t + 9*(0+2*sixy))+0)[0])) + (((sctx->
t + 9*(0+2*sixy))+0)[0])), ((Typ)+0)[1] = ((((coords[1])))*((
((sctx->t + 9*(1+2*sixy))+0)[1]) - (((sctx->t + 9*(0+2*
sixy))+0)[1])) + (((sctx->t + 9*(0+2*sixy))+0)[1])), ((Typ
)+0)[2] = ((((coords[1])))*((((sctx->t + 9*(1+2*sixy))+0)[
2]) - (((sctx->t + 9*(0+2*sixy))+0)[2])) + (((sctx->t +
9*(0+2*sixy))+0)[2]))), (((Typ)+3)[0] = ((((coords[1])))*(((
(sctx->t + 9*(1+2*sixy))+3)[0]) - (((sctx->t + 9*(0+2*sixy
))+3)[0])) + (((sctx->t + 9*(0+2*sixy))+3)[0])), ((Typ)+3)
[1] = ((((coords[1])))*((((sctx->t + 9*(1+2*sixy))+3)[1]) -
(((sctx->t + 9*(0+2*sixy))+3)[1])) + (((sctx->t + 9*(0
+2*sixy))+3)[1])), ((Typ)+3)[2] = ((((coords[1])))*((((sctx->
t + 9*(1+2*sixy))+3)[2]) - (((sctx->t + 9*(0+2*sixy))+3)[2
])) + (((sctx->t + 9*(0+2*sixy))+3)[2]))), (((Typ)+6)[0] =
((((coords[1])))*((((sctx->t + 9*(1+2*sixy))+6)[0]) - (((
sctx->t + 9*(0+2*sixy))+6)[0])) + (((sctx->t + 9*(0+2*sixy
))+6)[0])), ((Typ)+6)[1] = ((((coords[1])))*((((sctx->t + 9
*(1+2*sixy))+6)[1]) - (((sctx->t + 9*(0+2*sixy))+6)[1])) +
(((sctx->t + 9*(0+2*sixy))+6)[1])), ((Typ)+6)[2] = ((((coords
[1])))*((((sctx->t + 9*(1+2*sixy))+6)[2]) - (((sctx->t +
9*(0+2*sixy))+6)[2])) + (((sctx->t + 9*(0+2*sixy))+6)[2])
)))

618

sctx->t + 9*(1+2*sixy))((((Typ)+0)[0] = ((((coords[1])))*((((sctx->t + 9*(1+2*sixy
))+0)[0]) - (((sctx->t + 9*(0+2*sixy))+0)[0])) + (((sctx->
t + 9*(0+2*sixy))+0)[0])), ((Typ)+0)[1] = ((((coords[1])))*((
((sctx->t + 9*(1+2*sixy))+0)[1]) - (((sctx->t + 9*(0+2*
sixy))+0)[1])) + (((sctx->t + 9*(0+2*sixy))+0)[1])), ((Typ
)+0)[2] = ((((coords[1])))*((((sctx->t + 9*(1+2*sixy))+0)[
2]) - (((sctx->t + 9*(0+2*sixy))+0)[2])) + (((sctx->t +
9*(0+2*sixy))+0)[2]))), (((Typ)+3)[0] = ((((coords[1])))*(((
(sctx->t + 9*(1+2*sixy))+3)[0]) - (((sctx->t + 9*(0+2*sixy
))+3)[0])) + (((sctx->t + 9*(0+2*sixy))+3)[0])), ((Typ)+3)
[1] = ((((coords[1])))*((((sctx->t + 9*(1+2*sixy))+3)[1]) -
(((sctx->t + 9*(0+2*sixy))+3)[1])) + (((sctx->t + 9*(0
+2*sixy))+3)[1])), ((Typ)+3)[2] = ((((coords[1])))*((((sctx->
t + 9*(1+2*sixy))+3)[2]) - (((sctx->t + 9*(0+2*sixy))+3)[2
])) + (((sctx->t + 9*(0+2*sixy))+3)[2]))), (((Typ)+6)[0] =
((((coords[1])))*((((sctx->t + 9*(1+2*sixy))+6)[0]) - (((
sctx->t + 9*(0+2*sixy))+6)[0])) + (((sctx->t + 9*(0+2*sixy
))+6)[0])), ((Typ)+6)[1] = ((((coords[1])))*((((sctx->t + 9
*(1+2*sixy))+6)[1]) - (((sctx->t + 9*(0+2*sixy))+6)[1])) +
(((sctx->t + 9*(0+2*sixy))+6)[1])), ((Typ)+6)[2] = ((((coords
[1])))*((((sctx->t + 9*(1+2*sixy))+6)[2]) - (((sctx->t +
9*(0+2*sixy))+6)[2])) + (((sctx->t + 9*(0+2*sixy))+6)[2])
)));

619

ELL_3V_LERP(gyp, coords[1], sctx->grad + 3*(0+2*sixy),((gyp)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*sixy))[0
]) - ((sctx->grad + 3*(0+2*sixy))[0])) + ((sctx->grad +
3*(0+2*sixy))[0])), (gyp)[1] = (((coords[1]))*(((sctx->grad
+ 3*(1+2*sixy))[1]) - ((sctx->grad + 3*(0+2*sixy))[1])) +
((sctx->grad + 3*(0+2*sixy))[1])), (gyp)[2] = (((coords[1
]))*(((sctx->grad + 3*(1+2*sixy))[2]) - ((sctx->grad + 3
*(0+2*sixy))[2])) + ((sctx->grad + 3*(0+2*sixy))[2])))

620

sctx->grad + 3*(1+2*sixy))((gyp)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*sixy))[0
]) - ((sctx->grad + 3*(0+2*sixy))[0])) + ((sctx->grad +
3*(0+2*sixy))[0])), (gyp)[1] = (((coords[1]))*(((sctx->grad
+ 3*(1+2*sixy))[1]) - ((sctx->grad + 3*(0+2*sixy))[1])) +
((sctx->grad + 3*(0+2*sixy))[1])), (gyp)[2] = (((coords[1
]))*(((sctx->grad + 3*(1+2*sixy))[2]) - ((sctx->grad + 3
*(0+2*sixy))[2])) + ((sctx->grad + 3*(0+2*sixy))[2])));

621

ELL_3M_LERP(Txp, coords[0], Tym, Typ)((((Txp)+0)[0] = ((((coords[0])))*((((Typ)+0)[0]) - (((Tym)+0
)[0])) + (((Tym)+0)[0])), ((Txp)+0)[1] = ((((coords[0])))*(((
(Typ)+0)[1]) - (((Tym)+0)[1])) + (((Tym)+0)[1])), ((Txp)+0)[2
] = ((((coords[0])))*((((Typ)+0)[2]) - (((Tym)+0)[2])) + (((Tym
)+0)[2]))), (((Txp)+3)[0] = ((((coords[0])))*((((Typ)+3)[0]) -
(((Tym)+3)[0])) + (((Tym)+3)[0])), ((Txp)+3)[1] = ((((coords
[0])))*((((Typ)+3)[1]) - (((Tym)+3)[1])) + (((Tym)+3)[1])), (
(Txp)+3)[2] = ((((coords[0])))*((((Typ)+3)[2]) - (((Tym)+3)[2
])) + (((Tym)+3)[2]))), (((Txp)+6)[0] = ((((coords[0])))*((((
Typ)+6)[0]) - (((Tym)+6)[0])) + (((Tym)+6)[0])), ((Txp)+6)[1]
= ((((coords[0])))*((((Typ)+6)[1]) - (((Tym)+6)[1])) + (((Tym
)+6)[1])), ((Txp)+6)[2] = ((((coords[0])))*((((Typ)+6)[2]) - (
((Tym)+6)[2])) + (((Tym)+6)[2]))));

622

ELL_3V_LERP(gxp, coords[0], gym, gyp)((gxp)[0] = (((coords[0]))*(((gyp)[0]) - ((gym)[0])) + ((gym)
[0])), (gxp)[1] = (((coords[0]))*(((gyp)[1]) - ((gym)[1])) + (
(gym)[1])), (gxp)[2] = (((coords[0]))*(((gyp)[2]) - ((gym)[2]
)) + ((gym)[2])));

623

} else {

624

ELL_3M_LERP(Tym, coords[1], sctx->t + 9*(0+2*siX), sctx->t + 9*(1+2*siX))((((Tym)+0)[0] = ((((coords[1])))*((((sctx->t + 9*(1+2*siX
))+0)[0]) - (((sctx->t + 9*(0+2*siX))+0)[0])) + (((sctx->
t + 9*(0+2*siX))+0)[0])), ((Tym)+0)[1] = ((((coords[1])))*(((
(sctx->t + 9*(1+2*siX))+0)[1]) - (((sctx->t + 9*(0+2*siX
))+0)[1])) + (((sctx->t + 9*(0+2*siX))+0)[1])), ((Tym)+0)[
2] = ((((coords[1])))*((((sctx->t + 9*(1+2*siX))+0)[2]) - (
((sctx->t + 9*(0+2*siX))+0)[2])) + (((sctx->t + 9*(0+2*
siX))+0)[2]))), (((Tym)+3)[0] = ((((coords[1])))*((((sctx->
t + 9*(1+2*siX))+3)[0]) - (((sctx->t + 9*(0+2*siX))+3)[0])
) + (((sctx->t + 9*(0+2*siX))+3)[0])), ((Tym)+3)[1] = ((((
coords[1])))*((((sctx->t + 9*(1+2*siX))+3)[1]) - (((sctx->
t + 9*(0+2*siX))+3)[1])) + (((sctx->t + 9*(0+2*siX))+3)[1]
)), ((Tym)+3)[2] = ((((coords[1])))*((((sctx->t + 9*(1+2*siX
))+3)[2]) - (((sctx->t + 9*(0+2*siX))+3)[2])) + (((sctx->
t + 9*(0+2*siX))+3)[2]))), (((Tym)+6)[0] = ((((coords[1])))*(
(((sctx->t + 9*(1+2*siX))+6)[0]) - (((sctx->t + 9*(0+2*
siX))+6)[0])) + (((sctx->t + 9*(0+2*siX))+6)[0])), ((Tym)+
6)[1] = ((((coords[1])))*((((sctx->t + 9*(1+2*siX))+6)[1])
- (((sctx->t + 9*(0+2*siX))+6)[1])) + (((sctx->t + 9*(
0+2*siX))+6)[1])), ((Tym)+6)[2] = ((((coords[1])))*((((sctx->
t + 9*(1+2*siX))+6)[2]) - (((sctx->t + 9*(0+2*siX))+6)[2])
) + (((sctx->t + 9*(0+2*siX))+6)[2]))));

625

ELL_3V_LERP(gym, coords[1], sctx->grad + 3*(0+2*siX),((gym)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*siX))[0]
) - ((sctx->grad + 3*(0+2*siX))[0])) + ((sctx->grad + 3
*(0+2*siX))[0])), (gym)[1] = (((coords[1]))*(((sctx->grad +
3*(1+2*siX))[1]) - ((sctx->grad + 3*(0+2*siX))[1])) + ((sctx
->grad + 3*(0+2*siX))[1])), (gym)[2] = (((coords[1]))*(((sctx
->grad + 3*(1+2*siX))[2]) - ((sctx->grad + 3*(0+2*siX))
[2])) + ((sctx->grad + 3*(0+2*siX))[2])))

626

sctx->grad + 3*(1+2*siX))((gym)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*siX))[0]
) - ((sctx->grad + 3*(0+2*siX))[0])) + ((sctx->grad + 3
*(0+2*siX))[0])), (gym)[1] = (((coords[1]))*(((sctx->grad +
3*(1+2*siX))[1]) - ((sctx->grad + 3*(0+2*siX))[1])) + ((sctx
->grad + 3*(0+2*siX))[1])), (gym)[2] = (((coords[1]))*(((sctx
->grad + 3*(1+2*siX))[2]) - ((sctx->grad + 3*(0+2*siX))
[2])) + ((sctx->grad + 3*(0+2*siX))[2])));

627

ELL_3M_LERP(Typ, coords[1], sctx->t + 9*(0+2*siXy),((((Typ)+0)[0] = ((((coords[1])))*((((sctx->t + 9*(1+2*siXy
))+0)[0]) - (((sctx->t + 9*(0+2*siXy))+0)[0])) + (((sctx->
t + 9*(0+2*siXy))+0)[0])), ((Typ)+0)[1] = ((((coords[1])))*((
((sctx->t + 9*(1+2*siXy))+0)[1]) - (((sctx->t + 9*(0+2*
siXy))+0)[1])) + (((sctx->t + 9*(0+2*siXy))+0)[1])), ((Typ
)+0)[2] = ((((coords[1])))*((((sctx->t + 9*(1+2*siXy))+0)[
2]) - (((sctx->t + 9*(0+2*siXy))+0)[2])) + (((sctx->t +
9*(0+2*siXy))+0)[2]))), (((Typ)+3)[0] = ((((coords[1])))*(((
(sctx->t + 9*(1+2*siXy))+3)[0]) - (((sctx->t + 9*(0+2*siXy
))+3)[0])) + (((sctx->t + 9*(0+2*siXy))+3)[0])), ((Typ)+3)
[1] = ((((coords[1])))*((((sctx->t + 9*(1+2*siXy))+3)[1]) -
(((sctx->t + 9*(0+2*siXy))+3)[1])) + (((sctx->t + 9*(0
+2*siXy))+3)[1])), ((Typ)+3)[2] = ((((coords[1])))*((((sctx->
t + 9*(1+2*siXy))+3)[2]) - (((sctx->t + 9*(0+2*siXy))+3)[2
])) + (((sctx->t + 9*(0+2*siXy))+3)[2]))), (((Typ)+6)[0] =
((((coords[1])))*((((sctx->t + 9*(1+2*siXy))+6)[0]) - (((
sctx->t + 9*(0+2*siXy))+6)[0])) + (((sctx->t + 9*(0+2*siXy
))+6)[0])), ((Typ)+6)[1] = ((((coords[1])))*((((sctx->t + 9
*(1+2*siXy))+6)[1]) - (((sctx->t + 9*(0+2*siXy))+6)[1])) +
(((sctx->t + 9*(0+2*siXy))+6)[1])), ((Typ)+6)[2] = ((((coords
[1])))*((((sctx->t + 9*(1+2*siXy))+6)[2]) - (((sctx->t +
9*(0+2*siXy))+6)[2])) + (((sctx->t + 9*(0+2*siXy))+6)[2])
)))

628

sctx->t + 9*(1+2*siXy))((((Typ)+0)[0] = ((((coords[1])))*((((sctx->t + 9*(1+2*siXy
))+0)[0]) - (((sctx->t + 9*(0+2*siXy))+0)[0])) + (((sctx->
t + 9*(0+2*siXy))+0)[0])), ((Typ)+0)[1] = ((((coords[1])))*((
((sctx->t + 9*(1+2*siXy))+0)[1]) - (((sctx->t + 9*(0+2*
siXy))+0)[1])) + (((sctx->t + 9*(0+2*siXy))+0)[1])), ((Typ
)+0)[2] = ((((coords[1])))*((((sctx->t + 9*(1+2*siXy))+0)[
2]) - (((sctx->t + 9*(0+2*siXy))+0)[2])) + (((sctx->t +
9*(0+2*siXy))+0)[2]))), (((Typ)+3)[0] = ((((coords[1])))*(((
(sctx->t + 9*(1+2*siXy))+3)[0]) - (((sctx->t + 9*(0+2*siXy
))+3)[0])) + (((sctx->t + 9*(0+2*siXy))+3)[0])), ((Typ)+3)
[1] = ((((coords[1])))*((((sctx->t + 9*(1+2*siXy))+3)[1]) -
(((sctx->t + 9*(0+2*siXy))+3)[1])) + (((sctx->t + 9*(0
+2*siXy))+3)[1])), ((Typ)+3)[2] = ((((coords[1])))*((((sctx->
t + 9*(1+2*siXy))+3)[2]) - (((sctx->t + 9*(0+2*siXy))+3)[2
])) + (((sctx->t + 9*(0+2*siXy))+3)[2]))), (((Typ)+6)[0] =
((((coords[1])))*((((sctx->t + 9*(1+2*siXy))+6)[0]) - (((
sctx->t + 9*(0+2*siXy))+6)[0])) + (((sctx->t + 9*(0+2*siXy
))+6)[0])), ((Typ)+6)[1] = ((((coords[1])))*((((sctx->t + 9
*(1+2*siXy))+6)[1]) - (((sctx->t + 9*(0+2*siXy))+6)[1])) +
(((sctx->t + 9*(0+2*siXy))+6)[1])), ((Typ)+6)[2] = ((((coords
[1])))*((((sctx->t + 9*(1+2*siXy))+6)[2]) - (((sctx->t +
9*(0+2*siXy))+6)[2])) + (((sctx->t + 9*(0+2*siXy))+6)[2])
)));

629

ELL_3V_LERP(gyp, coords[1], sctx->grad + 3*(0+2*siXy),((gyp)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*siXy))[0
]) - ((sctx->grad + 3*(0+2*siXy))[0])) + ((sctx->grad +
3*(0+2*siXy))[0])), (gyp)[1] = (((coords[1]))*(((sctx->grad
+ 3*(1+2*siXy))[1]) - ((sctx->grad + 3*(0+2*siXy))[1])) +
((sctx->grad + 3*(0+2*siXy))[1])), (gyp)[2] = (((coords[1
]))*(((sctx->grad + 3*(1+2*siXy))[2]) - ((sctx->grad + 3
*(0+2*siXy))[2])) + ((sctx->grad + 3*(0+2*siXy))[2])))

630

sctx->grad + 3*(1+2*siXy))((gyp)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*siXy))[0
]) - ((sctx->grad + 3*(0+2*siXy))[0])) + ((sctx->grad +
3*(0+2*siXy))[0])), (gyp)[1] = (((coords[1]))*(((sctx->grad
+ 3*(1+2*siXy))[1]) - ((sctx->grad + 3*(0+2*siXy))[1])) +
((sctx->grad + 3*(0+2*siXy))[1])), (gyp)[2] = (((coords[1
]))*(((sctx->grad + 3*(1+2*siXy))[2]) - ((sctx->grad + 3
*(0+2*siXy))[2])) + ((sctx->grad + 3*(0+2*siXy))[2])));

631

ELL_3M_LERP(Txm, coords[0], Tym, Typ)((((Txm)+0)[0] = ((((coords[0])))*((((Typ)+0)[0]) - (((Tym)+0
)[0])) + (((Tym)+0)[0])), ((Txm)+0)[1] = ((((coords[0])))*(((
(Typ)+0)[1]) - (((Tym)+0)[1])) + (((Tym)+0)[1])), ((Txm)+0)[2
] = ((((coords[0])))*((((Typ)+0)[2]) - (((Tym)+0)[2])) + (((Tym
)+0)[2]))), (((Txm)+3)[0] = ((((coords[0])))*((((Typ)+3)[0]) -
(((Tym)+3)[0])) + (((Tym)+3)[0])), ((Txm)+3)[1] = ((((coords
[0])))*((((Typ)+3)[1]) - (((Tym)+3)[1])) + (((Tym)+3)[1])), (
(Txm)+3)[2] = ((((coords[0])))*((((Typ)+3)[2]) - (((Tym)+3)[2
])) + (((Tym)+3)[2]))), (((Txm)+6)[0] = ((((coords[0])))*((((
Typ)+6)[0]) - (((Tym)+6)[0])) + (((Tym)+6)[0])), ((Txm)+6)[1]
= ((((coords[0])))*((((Typ)+6)[1]) - (((Tym)+6)[1])) + (((Tym
)+6)[1])), ((Txm)+6)[2] = ((((coords[0])))*((((Typ)+6)[2]) - (
((Tym)+6)[2])) + (((Tym)+6)[2]))));

632

ELL_3V_LERP(gxm, coords[0], gym, gyp)((gxm)[0] = (((coords[0]))*(((gyp)[0]) - ((gym)[0])) + ((gym)
[0])), (gxm)[1] = (((coords[0]))*(((gyp)[1]) - ((gym)[1])) + (
(gym)[1])), (gxm)[2] = (((coords[0]))*(((gyp)[2]) - ((gym)[2]
)) + ((gym)[2])));

633

}

634

/* now, compute remaining points */

635

ELL_3M_LERP(Tym, coords[1], sctx->t + 9*(0+2*si), sctx->t + 9*(1+2*si))((((Tym)+0)[0] = ((((coords[1])))*((((sctx->t + 9*(1+2*si)
)+0)[0]) - (((sctx->t + 9*(0+2*si))+0)[0])) + (((sctx->
t + 9*(0+2*si))+0)[0])), ((Tym)+0)[1] = ((((coords[1])))*((((
sctx->t + 9*(1+2*si))+0)[1]) - (((sctx->t + 9*(0+2*si))
+0)[1])) + (((sctx->t + 9*(0+2*si))+0)[1])), ((Tym)+0)[2] =
((((coords[1])))*((((sctx->t + 9*(1+2*si))+0)[2]) - (((sctx
->t + 9*(0+2*si))+0)[2])) + (((sctx->t + 9*(0+2*si))+0)
[2]))), (((Tym)+3)[0] = ((((coords[1])))*((((sctx->t + 9*(
1+2*si))+3)[0]) - (((sctx->t + 9*(0+2*si))+3)[0])) + (((sctx
->t + 9*(0+2*si))+3)[0])), ((Tym)+3)[1] = ((((coords[1])))
*((((sctx->t + 9*(1+2*si))+3)[1]) - (((sctx->t + 9*(0+2
*si))+3)[1])) + (((sctx->t + 9*(0+2*si))+3)[1])), ((Tym)+3
)[2] = ((((coords[1])))*((((sctx->t + 9*(1+2*si))+3)[2]) -
(((sctx->t + 9*(0+2*si))+3)[2])) + (((sctx->t + 9*(0+2
*si))+3)[2]))), (((Tym)+6)[0] = ((((coords[1])))*((((sctx->
t + 9*(1+2*si))+6)[0]) - (((sctx->t + 9*(0+2*si))+6)[0])) +
(((sctx->t + 9*(0+2*si))+6)[0])), ((Tym)+6)[1] = ((((coords
[1])))*((((sctx->t + 9*(1+2*si))+6)[1]) - (((sctx->t + 9
*(0+2*si))+6)[1])) + (((sctx->t + 9*(0+2*si))+6)[1])), ((Tym
)+6)[2] = ((((coords[1])))*((((sctx->t + 9*(1+2*si))+6)[2]
) - (((sctx->t + 9*(0+2*si))+6)[2])) + (((sctx->t + 9*(
0+2*si))+6)[2]))));

636

ELL_3V_LERP(gym, coords[1], sctx->grad + 3*(0+2*si),((gym)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*si))[0])
- ((sctx->grad + 3*(0+2*si))[0])) + ((sctx->grad + 3*(
0+2*si))[0])), (gym)[1] = (((coords[1]))*(((sctx->grad + 3
*(1+2*si))[1]) - ((sctx->grad + 3*(0+2*si))[1])) + ((sctx->
grad + 3*(0+2*si))[1])), (gym)[2] = (((coords[1]))*(((sctx->
grad + 3*(1+2*si))[2]) - ((sctx->grad + 3*(0+2*si))[2])) +
((sctx->grad + 3*(0+2*si))[2])))

637

sctx->grad + 3*(1+2*si))((gym)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*si))[0])
- ((sctx->grad + 3*(0+2*si))[0])) + ((sctx->grad + 3*(
0+2*si))[0])), (gym)[1] = (((coords[1]))*(((sctx->grad + 3
*(1+2*si))[1]) - ((sctx->grad + 3*(0+2*si))[1])) + ((sctx->
grad + 3*(0+2*si))[1])), (gym)[2] = (((coords[1]))*(((sctx->
grad + 3*(1+2*si))[2]) - ((sctx->grad + 3*(0+2*si))[2])) +
((sctx->grad + 3*(0+2*si))[2])));

638

ELL_3M_LERP(Typ, coords[1], sctx->t + 9*(0+2*siy), sctx->t + 9*(1+2*siy))((((Typ)+0)[0] = ((((coords[1])))*((((sctx->t + 9*(1+2*siy
))+0)[0]) - (((sctx->t + 9*(0+2*siy))+0)[0])) + (((sctx->
t + 9*(0+2*siy))+0)[0])), ((Typ)+0)[1] = ((((coords[1])))*(((
(sctx->t + 9*(1+2*siy))+0)[1]) - (((sctx->t + 9*(0+2*siy
))+0)[1])) + (((sctx->t + 9*(0+2*siy))+0)[1])), ((Typ)+0)[
2] = ((((coords[1])))*((((sctx->t + 9*(1+2*siy))+0)[2]) - (
((sctx->t + 9*(0+2*siy))+0)[2])) + (((sctx->t + 9*(0+2*
siy))+0)[2]))), (((Typ)+3)[0] = ((((coords[1])))*((((sctx->
t + 9*(1+2*siy))+3)[0]) - (((sctx->t + 9*(0+2*siy))+3)[0])
) + (((sctx->t + 9*(0+2*siy))+3)[0])), ((Typ)+3)[1] = ((((
coords[1])))*((((sctx->t + 9*(1+2*siy))+3)[1]) - (((sctx->
t + 9*(0+2*siy))+3)[1])) + (((sctx->t + 9*(0+2*siy))+3)[1]
)), ((Typ)+3)[2] = ((((coords[1])))*((((sctx->t + 9*(1+2*siy
))+3)[2]) - (((sctx->t + 9*(0+2*siy))+3)[2])) + (((sctx->
t + 9*(0+2*siy))+3)[2]))), (((Typ)+6)[0] = ((((coords[1])))*(
(((sctx->t + 9*(1+2*siy))+6)[0]) - (((sctx->t + 9*(0+2*
siy))+6)[0])) + (((sctx->t + 9*(0+2*siy))+6)[0])), ((Typ)+
6)[1] = ((((coords[1])))*((((sctx->t + 9*(1+2*siy))+6)[1])
- (((sctx->t + 9*(0+2*siy))+6)[1])) + (((sctx->t + 9*(
0+2*siy))+6)[1])), ((Typ)+6)[2] = ((((coords[1])))*((((sctx->
t + 9*(1+2*siy))+6)[2]) - (((sctx->t + 9*(0+2*siy))+6)[2])
) + (((sctx->t + 9*(0+2*siy))+6)[2]))));

639

ELL_3V_LERP(gyp, coords[1], sctx->grad + 3*(0+2*siy),((gyp)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*siy))[0]
) - ((sctx->grad + 3*(0+2*siy))[0])) + ((sctx->grad + 3
*(0+2*siy))[0])), (gyp)[1] = (((coords[1]))*(((sctx->grad +
3*(1+2*siy))[1]) - ((sctx->grad + 3*(0+2*siy))[1])) + ((sctx
->grad + 3*(0+2*siy))[1])), (gyp)[2] = (((coords[1]))*(((sctx
->grad + 3*(1+2*siy))[2]) - ((sctx->grad + 3*(0+2*siy))
[2])) + ((sctx->grad + 3*(0+2*siy))[2])))

640

sctx->grad + 3*(1+2*siy))((gyp)[0] = (((coords[1]))*(((sctx->grad + 3*(1+2*siy))[0]
) - ((sctx->grad + 3*(0+2*siy))[0])) + ((sctx->grad + 3
*(0+2*siy))[0])), (gyp)[1] = (((coords[1]))*(((sctx->grad +
3*(1+2*siy))[1]) - ((sctx->grad + 3*(0+2*siy))[1])) + ((sctx
->grad + 3*(0+2*siy))[1])), (gyp)[2] = (((coords[1]))*(((sctx
->grad + 3*(1+2*siy))[2]) - ((sctx->grad + 3*(0+2*siy))
[2])) + ((sctx->grad + 3*(0+2*siy))[2])));

641

642

ELL_3M_LERP(Tzm, coords[0], sctx->t + 9*(0+2*si), sctx->t + 9*(0+2*siy))((((Tzm)+0)[0] = ((((coords[0])))*((((sctx->t + 9*(0+2*siy
))+0)[0]) - (((sctx->t + 9*(0+2*si))+0)[0])) + (((sctx->
t + 9*(0+2*si))+0)[0])), ((Tzm)+0)[1] = ((((coords[0])))*((((
sctx->t + 9*(0+2*siy))+0)[1]) - (((sctx->t + 9*(0+2*si)
)+0)[1])) + (((sctx->t + 9*(0+2*si))+0)[1])), ((Tzm)+0)[2]
= ((((coords[0])))*((((sctx->t + 9*(0+2*siy))+0)[2]) - ((
(sctx->t + 9*(0+2*si))+0)[2])) + (((sctx->t + 9*(0+2*si
))+0)[2]))), (((Tzm)+3)[0] = ((((coords[0])))*((((sctx->t +
9*(0+2*siy))+3)[0]) - (((sctx->t + 9*(0+2*si))+3)[0])) + (
((sctx->t + 9*(0+2*si))+3)[0])), ((Tzm)+3)[1] = ((((coords
[0])))*((((sctx->t + 9*(0+2*siy))+3)[1]) - (((sctx->t +
9*(0+2*si))+3)[1])) + (((sctx->t + 9*(0+2*si))+3)[1])), (
(Tzm)+3)[2] = ((((coords[0])))*((((sctx->t + 9*(0+2*siy))+
3)[2]) - (((sctx->t + 9*(0+2*si))+3)[2])) + (((sctx->t +
9*(0+2*si))+3)[2]))), (((Tzm)+6)[0] = ((((coords[0])))*((((sctx
->t + 9*(0+2*siy))+6)[0]) - (((sctx->t + 9*(0+2*si))+6)
[0])) + (((sctx->t + 9*(0+2*si))+6)[0])), ((Tzm)+6)[1] = (
(((coords[0])))*((((sctx->t + 9*(0+2*siy))+6)[1]) - (((sctx
->t + 9*(0+2*si))+6)[1])) + (((sctx->t + 9*(0+2*si))+6)
[1])), ((Tzm)+6)[2] = ((((coords[0])))*((((sctx->t + 9*(0+
2*siy))+6)[2]) - (((sctx->t + 9*(0+2*si))+6)[2])) + (((sctx
->t + 9*(0+2*si))+6)[2]))));

643

ELL_3V_LERP(gzm, coords[0], sctx->grad + 3*(0+2*si),((gzm)[0] = (((coords[0]))*(((sctx->grad + 3*(0+2*siy))[0]
) - ((sctx->grad + 3*(0+2*si))[0])) + ((sctx->grad + 3*
(0+2*si))[0])), (gzm)[1] = (((coords[0]))*(((sctx->grad + 3
*(0+2*siy))[1]) - ((sctx->grad + 3*(0+2*si))[1])) + ((sctx
->grad + 3*(0+2*si))[1])), (gzm)[2] = (((coords[0]))*(((sctx
->grad + 3*(0+2*siy))[2]) - ((sctx->grad + 3*(0+2*si))[
2])) + ((sctx->grad + 3*(0+2*si))[2])))

644

sctx->grad + 3*(0+2*siy))((gzm)[0] = (((coords[0]))*(((sctx->grad + 3*(0+2*siy))[0]
) - ((sctx->grad + 3*(0+2*si))[0])) + ((sctx->grad + 3*
(0+2*si))[0])), (gzm)[1] = (((coords[0]))*(((sctx->grad + 3
*(0+2*siy))[1]) - ((sctx->grad + 3*(0+2*si))[1])) + ((sctx
->grad + 3*(0+2*si))[1])), (gzm)[2] = (((coords[0]))*(((sctx
->grad + 3*(0+2*siy))[2]) - ((sctx->grad + 3*(0+2*si))[
2])) + ((sctx->grad + 3*(0+2*si))[2])));

645

ELL_3M_LERP(Tzp, coords[0], sctx->t + 9*(1+2*si), sctx->t + 9*(1+2*siy))((((Tzp)+0)[0] = ((((coords[0])))*((((sctx->t + 9*(1+2*siy
))+0)[0]) - (((sctx->t + 9*(1+2*si))+0)[0])) + (((sctx->
t + 9*(1+2*si))+0)[0])), ((Tzp)+0)[1] = ((((coords[0])))*((((
sctx->t + 9*(1+2*siy))+0)[1]) - (((sctx->t + 9*(1+2*si)
)+0)[1])) + (((sctx->t + 9*(1+2*si))+0)[1])), ((Tzp)+0)[2]
= ((((coords[0])))*((((sctx->t + 9*(1+2*siy))+0)[2]) - ((
(sctx->t + 9*(1+2*si))+0)[2])) + (((sctx->t + 9*(1+2*si
))+0)[2]))), (((Tzp)+3)[0] = ((((coords[0])))*((((sctx->t +
9*(1+2*siy))+3)[0]) - (((sctx->t + 9*(1+2*si))+3)[0])) + (
((sctx->t + 9*(1+2*si))+3)[0])), ((Tzp)+3)[1] = ((((coords
[0])))*((((sctx->t + 9*(1+2*siy))+3)[1]) - (((sctx->t +
9*(1+2*si))+3)[1])) + (((sctx->t + 9*(1+2*si))+3)[1])), (
(Tzp)+3)[2] = ((((coords[0])))*((((sctx->t + 9*(1+2*siy))+
3)[2]) - (((sctx->t + 9*(1+2*si))+3)[2])) + (((sctx->t +
9*(1+2*si))+3)[2]))), (((Tzp)+6)[0] = ((((coords[0])))*((((sctx
->t + 9*(1+2*siy))+6)[0]) - (((sctx->t + 9*(1+2*si))+6)
[0])) + (((sctx->t + 9*(1+2*si))+6)[0])), ((Tzp)+6)[1] = (
(((coords[0])))*((((sctx->t + 9*(1+2*siy))+6)[1]) - (((sctx
->t + 9*(1+2*si))+6)[1])) + (((sctx->t + 9*(1+2*si))+6)
[1])), ((Tzp)+6)[2] = ((((coords[0])))*((((sctx->t + 9*(1+
2*siy))+6)[2]) - (((sctx->t + 9*(1+2*si))+6)[2])) + (((sctx
->t + 9*(1+2*si))+6)[2]))));

646

ELL_3V_LERP(gzp, coords[0], sctx->grad + 3*(1+2*si),((gzp)[0] = (((coords[0]))*(((sctx->grad + 3*(1+2*siy))[0]
) - ((sctx->grad + 3*(1+2*si))[0])) + ((sctx->grad + 3*
(1+2*si))[0])), (gzp)[1] = (((coords[0]))*(((sctx->grad + 3
*(1+2*siy))[1]) - ((sctx->grad + 3*(1+2*si))[1])) + ((sctx
->grad + 3*(1+2*si))[1])), (gzp)[2] = (((coords[0]))*(((sctx
->grad + 3*(1+2*siy))[2]) - ((sctx->grad + 3*(1+2*si))[
2])) + ((sctx->grad + 3*(1+2*si))[2])))

647

sctx->grad + 3*(1+2*siy))((gzp)[0] = (((coords[0]))*(((sctx->grad + 3*(1+2*siy))[0]
) - ((sctx->grad + 3*(1+2*si))[0])) + ((sctx->grad + 3*
(1+2*si))[0])), (gzp)[1] = (((coords[0]))*(((sctx->grad + 3
*(1+2*siy))[1]) - ((sctx->grad + 3*(1+2*si))[1])) + ((sctx
->grad + 3*(1+2*si))[1])), (gzp)[2] = (((coords[0]))*(((sctx
->grad + 3*(1+2*siy))[2]) - ((sctx->grad + 3*(1+2*si))[
2])) + ((sctx->grad + 3*(1+2*si))[2])));

648

649

ELL_3M_LERP(T, coords[0], Tym, Typ)((((T)+0)[0] = ((((coords[0])))*((((Typ)+0)[0]) - (((Tym)+0)[
0])) + (((Tym)+0)[0])), ((T)+0)[1] = ((((coords[0])))*((((Typ
)+0)[1]) - (((Tym)+0)[1])) + (((Tym)+0)[1])), ((T)+0)[2] = ((
((coords[0])))*((((Typ)+0)[2]) - (((Tym)+0)[2])) + (((Tym)+0)
[2]))), (((T)+3)[0] = ((((coords[0])))*((((Typ)+3)[0]) - (((Tym
)+3)[0])) + (((Tym)+3)[0])), ((T)+3)[1] = ((((coords[0])))*((
((Typ)+3)[1]) - (((Tym)+3)[1])) + (((Tym)+3)[1])), ((T)+3)[2]
= ((((coords[0])))*((((Typ)+3)[2]) - (((Tym)+3)[2])) + (((Tym
)+3)[2]))), (((T)+6)[0] = ((((coords[0])))*((((Typ)+6)[0]) - (
((Tym)+6)[0])) + (((Tym)+6)[0])), ((T)+6)[1] = ((((coords[0])
))*((((Typ)+6)[1]) - (((Tym)+6)[1])) + (((Tym)+6)[1])), ((T)+
6)[2] = ((((coords[0])))*((((Typ)+6)[2]) - (((Tym)+6)[2])) + (
((Tym)+6)[2]))));

650

ELL_3V_LERP(g, coords[0], gym, gyp)((g)[0] = (((coords[0]))*(((gyp)[0]) - ((gym)[0])) + ((gym)[0
])), (g)[1] = (((coords[0]))*(((gyp)[1]) - ((gym)[1])) + ((gym
)[1])), (g)[2] = (((coords[0]))*(((gyp)[2]) - ((gym)[2])) + (
(gym)[2])));

651

652

if (xi!=sx-1) {

←

Taking true branch

→

653

computeGradientLin(sctx->facenorm+3*(faceid+4*si), T, g,

←

Calling 'computeGradientLin'

→

654

T, g, Txp, gxp,

655

Tym, gym, Typ, gyp,

656

Tzm, gzm, Tzp, gzp);

657

} else {

658

computeGradientLin(sctx->facenorm+3*(faceid+4*si), T, g,

659

Txm, gxm, T, g,

660

Tym, gym, Typ, gyp,

661

Tzm, gzm, Tzp, gzp);

662

}

663

break;

664

case 3:

665

/* bilinearly interpolate Tzm/gzm first */

666

667

668

669

670

671

672

ELL_3M_LERP(Tzm, coords[0], Txm, Txp)((((Tzm)+0)[0] = ((((coords[0])))*((((Txp)+0)[0]) - (((Txm)+0
)[0])) + (((Txm)+0)[0])), ((Tzm)+0)[1] = ((((coords[0])))*(((
(Txp)+0)[1]) - (((Txm)+0)[1])) + (((Txm)+0)[1])), ((Tzm)+0)[2
] = ((((coords[0])))*((((Txp)+0)[2]) - (((Txm)+0)[2])) + (((Txm
)+0)[2]))), (((Tzm)+3)[0] = ((((coords[0])))*((((Txp)+3)[0]) -
(((Txm)+3)[0])) + (((Txm)+3)[0])), ((Tzm)+3)[1] = ((((coords
[0])))*((((Txp)+3)[1]) - (((Txm)+3)[1])) + (((Txm)+3)[1])), (
(Tzm)+3)[2] = ((((coords[0])))*((((Txp)+3)[2]) - (((Txm)+3)[2
])) + (((Txm)+3)[2]))), (((Tzm)+6)[0] = ((((coords[0])))*((((
Txp)+6)[0]) - (((Txm)+6)[0])) + (((Txm)+6)[0])), ((Tzm)+6)[1]
= ((((coords[0])))*((((Txp)+6)[1]) - (((Txm)+6)[1])) + (((Txm
)+6)[1])), ((Tzm)+6)[2] = ((((coords[0])))*((((Txp)+6)[2]) - (
((Txm)+6)[2])) + (((Txm)+6)[2]))));

673

ELL_3V_LERP(gzm, coords[0], gxm, gxp)((gzm)[0] = (((coords[0]))*(((gxp)[0]) - ((gxm)[0])) + ((gxm)
[0])), (gzm)[1] = (((coords[0]))*(((gxp)[1]) - ((gxm)[1])) + (
(gxm)[1])), (gzm)[2] = (((coords[0]))*(((gxp)[2]) - ((gxm)[2]
)) + ((gxm)[2])));

674

/* now, compute all required points on the top face */

675

676

677

678

679

680

681

682

ELL_3M_LERP(Tym, coords[0], sctx->t + 9*(1+2*si), sctx->t + 9*(1+2*six))((((Tym)+0)[0] = ((((coords[0])))*((((sctx->t + 9*(1+2*six
))+0)[0]) - (((sctx->t + 9*(1+2*si))+0)[0])) + (((sctx->
t + 9*(1+2*si))+0)[0])), ((Tym)+0)[1] = ((((coords[0])))*((((
sctx->t + 9*(1+2*six))+0)[1]) - (((sctx->t + 9*(1+2*si)
)+0)[1])) + (((sctx->t + 9*(1+2*si))+0)[1])), ((Tym)+0)[2]
= ((((coords[0])))*((((sctx->t + 9*(1+2*six))+0)[2]) - ((
(sctx->t + 9*(1+2*si))+0)[2])) + (((sctx->t + 9*(1+2*si
))+0)[2]))), (((Tym)+3)[0] = ((((coords[0])))*((((sctx->t +
9*(1+2*six))+3)[0]) - (((sctx->t + 9*(1+2*si))+3)[0])) + (
((sctx->t + 9*(1+2*si))+3)[0])), ((Tym)+3)[1] = ((((coords
[0])))*((((sctx->t + 9*(1+2*six))+3)[1]) - (((sctx->t +
9*(1+2*si))+3)[1])) + (((sctx->t + 9*(1+2*si))+3)[1])), (
(Tym)+3)[2] = ((((coords[0])))*((((sctx->t + 9*(1+2*six))+
3)[2]) - (((sctx->t + 9*(1+2*si))+3)[2])) + (((sctx->t +
9*(1+2*si))+3)[2]))), (((Tym)+6)[0] = ((((coords[0])))*((((sctx
->t + 9*(1+2*six))+6)[0]) - (((sctx->t + 9*(1+2*si))+6)
[0])) + (((sctx->t + 9*(1+2*si))+6)[0])), ((Tym)+6)[1] = (
(((coords[0])))*((((sctx->t + 9*(1+2*six))+6)[1]) - (((sctx
->t + 9*(1+2*si))+6)[1])) + (((sctx->t + 9*(1+2*si))+6)
[1])), ((Tym)+6)[2] = ((((coords[0])))*((((sctx->t + 9*(1+
2*six))+6)[2]) - (((sctx->t + 9*(1+2*si))+6)[2])) + (((sctx
->t + 9*(1+2*si))+6)[2]))));

683

ELL_3V_LERP(gym, coords[0], sctx->grad + 3*(1+2*si),((gym)[0] = (((coords[0]))*(((sctx->grad + 3*(1+2*six))[0]
) - ((sctx->grad + 3*(1+2*si))[0])) + ((sctx->grad + 3*
(1+2*si))[0])), (gym)[1] = (((coords[0]))*(((sctx->grad + 3
*(1+2*six))[1]) - ((sctx->grad + 3*(1+2*si))[1])) + ((sctx
->grad + 3*(1+2*si))[1])), (gym)[2] = (((coords[0]))*(((sctx
->grad + 3*(1+2*six))[2]) - ((sctx->grad + 3*(1+2*si))[
2])) + ((sctx->grad + 3*(1+2*si))[2])))

684

sctx->grad + 3*(1+2*six))((gym)[0] = (((coords[0]))*(((sctx->grad + 3*(1+2*six))[0]
) - ((sctx->grad + 3*(1+2*si))[0])) + ((sctx->grad + 3*
(1+2*si))[0])), (gym)[1] = (((coords[0]))*(((sctx->grad + 3
*(1+2*six))[1]) - ((sctx->grad + 3*(1+2*si))[1])) + ((sctx
->grad + 3*(1+2*si))[1])), (gym)[2] = (((coords[0]))*(((sctx
->grad + 3*(1+2*six))[2]) - ((sctx->grad + 3*(1+2*si))[
2])) + ((sctx->grad + 3*(1+2*si))[2])));

685

ELL_3M_LERP(Typ, coords[0], sctx->t + 9*(1+2*siy), sctx->t + 9*(1+2*sixy))((((Typ)+0)[0] = ((((coords[0])))*((((sctx->t + 9*(1+2*sixy
))+0)[0]) - (((sctx->t + 9*(1+2*siy))+0)[0])) + (((sctx->
t + 9*(1+2*siy))+0)[0])), ((Typ)+0)[1] = ((((coords[0])))*(((
(sctx->t + 9*(1+2*sixy))+0)[1]) - (((sctx->t + 9*(1+2*siy
))+0)[1])) + (((sctx->t + 9*(1+2*siy))+0)[1])), ((Typ)+0)[
2] = ((((coords[0])))*((((sctx->t + 9*(1+2*sixy))+0)[2]) -
(((sctx->t + 9*(1+2*siy))+0)[2])) + (((sctx->t + 9*(1+
2*siy))+0)[2]))), (((Typ)+3)[0] = ((((coords[0])))*((((sctx->
t + 9*(1+2*sixy))+3)[0]) - (((sctx->t + 9*(1+2*siy))+3)[0]
)) + (((sctx->t + 9*(1+2*siy))+3)[0])), ((Typ)+3)[1] = (((
(coords[0])))*((((sctx->t + 9*(1+2*sixy))+3)[1]) - (((sctx
->t + 9*(1+2*siy))+3)[1])) + (((sctx->t + 9*(1+2*siy))+
3)[1])), ((Typ)+3)[2] = ((((coords[0])))*((((sctx->t + 9*(
1+2*sixy))+3)[2]) - (((sctx->t + 9*(1+2*siy))+3)[2])) + ((
(sctx->t + 9*(1+2*siy))+3)[2]))), (((Typ)+6)[0] = ((((coords
[0])))*((((sctx->t + 9*(1+2*sixy))+6)[0]) - (((sctx->t +
9*(1+2*siy))+6)[0])) + (((sctx->t + 9*(1+2*siy))+6)[0])),
((Typ)+6)[1] = ((((coords[0])))*((((sctx->t + 9*(1+2*sixy
))+6)[1]) - (((sctx->t + 9*(1+2*siy))+6)[1])) + (((sctx->
t + 9*(1+2*siy))+6)[1])), ((Typ)+6)[2] = ((((coords[0])))*(((
(sctx->t + 9*(1+2*sixy))+6)[2]) - (((sctx->t + 9*(1+2*siy
))+6)[2])) + (((sctx->t + 9*(1+2*siy))+6)[2]))));

686

ELL_3V_LERP(gyp, coords[0], sctx->grad + 3*(1+2*siy),((gyp)[0] = (((coords[0]))*(((sctx->grad + 3*(1+2*sixy))[0
]) - ((sctx->grad + 3*(1+2*siy))[0])) + ((sctx->grad + 3
*(1+2*siy))[0])), (gyp)[1] = (((coords[0]))*(((sctx->grad +
3*(1+2*sixy))[1]) - ((sctx->grad + 3*(1+2*siy))[1])) + ((
sctx->grad + 3*(1+2*siy))[1])), (gyp)[2] = (((coords[0]))*
(((sctx->grad + 3*(1+2*sixy))[2]) - ((sctx->grad + 3*(1
+2*siy))[2])) + ((sctx->grad + 3*(1+2*siy))[2])))

687

sctx->grad + 3*(1+2*sixy))((gyp)[0] = (((coords[0]))*(((sctx->grad + 3*(1+2*sixy))[0
]) - ((sctx->grad + 3*(1+2*siy))[0])) + ((sctx->grad + 3
*(1+2*siy))[0])), (gyp)[1] = (((coords[0]))*(((sctx->grad +
3*(1+2*sixy))[1]) - ((sctx->grad + 3*(1+2*siy))[1])) + ((
sctx->grad + 3*(1+2*siy))[1])), (gyp)[2] = (((coords[0]))*
(((sctx->grad + 3*(1+2*sixy))[2]) - ((sctx->grad + 3*(1
+2*siy))[2])) + ((sctx->grad + 3*(1+2*siy))[2])));

688

689

690

691

692

computeGradientLin(sctx->facenorm+3*(faceid+4*si), T, g,

693

Txm, gxm, Txp, gxp,

694

Tym, gym, Typ, gyp,

695

Tzm, gzm, T, g);

696

break;

697

}

698

ELL_3V_COPY(res, sctx->facenorm+3*(faceid+4*si))((res)[0] = (sctx->facenorm+3*(faceid+4*si))[0], (res)[1] =
(sctx->facenorm+3*(faceid+4*si))[1], (res)[2] = (sctx->
facenorm+3*(faceid+4*si))[2]);

699

}

700

701

/* small helper routines: intersection tests */

702

703

/* check if a given 2D triangle is oriented clockwise (-1)

704

* or counter-clockwise (1).

705

* returns 0 if given points are collinear */

706

static int

707

checkTriOrientation (double *p1, double *p2, double *p3) {

708

double test = (((p2[0]-p1[0])*(p3[1]-p1[1])) - ((p3[0]-p1[0])*(p2[1]-p1[1])));

709

if (test > 0) return 1;

710

else if (test < 0) return -1;

711

else return 0;

712

}

713

714

/* check if two given 2D lines intersect */

715

static int

716

lineIntersectionTest (double *l1p1, double *l1p2, double *l2p1, double *l2p2) {

717

int or1 = checkTriOrientation(l1p1, l1p2, l2p1);

718

int or2 = checkTriOrientation(l1p1, l1p2, l2p2);

719

if (or1 != or2) {

720

or1 = checkTriOrientation(l2p1, l2p2, l1p1);

721

or2 = checkTriOrientation(l2p1, l2p2, l1p2);

722

if (or1 != or2)

723

return 1;

724

}

725

return 0;

726

}

727

728

/* check if two given 3D triangles intersect */

729

static int

730

triIntersectionTest (double *t1v1, double *t1v2, double *t1v3,

731

double *t2v1, double *t2v2, double *t2v3) {

732

double n1[3], n2[3], d1, d2;

733

double diff1[3], diff2[3];

734

double t2sd1, t2sd2, t2sd3;

735

ELL_3V_SUB(diff1, t1v2, t1v1)((diff1)[0] = (t1v2)[0] - (t1v1)[0], (diff1)[1] = (t1v2)[1] -
(t1v1)[1], (diff1)[2] = (t1v2)[2] - (t1v1)[2]);

736

ELL_3V_SUB(diff2, t1v3, t1v1)((diff2)[0] = (t1v3)[0] - (t1v1)[0], (diff2)[1] = (t1v3)[1] -
(t1v1)[1], (diff2)[2] = (t1v3)[2] - (t1v1)[2]);

737

ELL_3V_CROSS(n1,diff1,diff2)((n1)[0] = (diff1)[1]*(diff2)[2] - (diff1)[2]*(diff2)[1], (n1
)[1] = (diff1)[2]*(diff2)[0] - (diff1)[0]*(diff2)[2], (n1)[2]
= (diff1)[0]*(diff2)[1] - (diff1)[1]*(diff2)[0]);

738

d1=-ELL_3V_DOT(n1,t1v1)((n1)[0]*(t1v1)[0] + (n1)[1]*(t1v1)[1] + (n1)[2]*(t1v1)[2]);

739

740

/* compute scaled signed distances of t2 to plane of t1 */

741

t2sd1 = ELL_3V_DOT(n1, t2v1)((n1)[0]*(t2v1)[0] + (n1)[1]*(t2v1)[1] + (n1)[2]*(t2v1)[2])+d1;

742

t2sd2 = ELL_3V_DOT(n1, t2v2)((n1)[0]*(t2v2)[0] + (n1)[1]*(t2v2)[1] + (n1)[2]*(t2v2)[2])+d1;

743

t2sd3 = ELL_3V_DOT(n1, t2v3)((n1)[0]*(t2v3)[0] + (n1)[1]*(t2v3)[1] + (n1)[2]*(t2v3)[2])+d1;

744

745

if (t2sd1==0 && t2sd2==0 && t2sd3==0) {

746

/* coplanar case: handle in 2D */

747

double t1v12d[2], t1v22d[2], t1v32d[2], t2v12d[2], t2v22d[2], t2v32d[2];

748

if (fabs(n1[0])>=fabs(n1[1]) && fabs(n1[0])>=fabs(n1[2])) {

749

t1v12d[0]=t1v1[1]; t1v12d[1]=t1v1[2];

750

t1v22d[0]=t1v2[1]; t1v22d[1]=t1v2[2];

751

t1v32d[0]=t1v3[1]; t1v32d[1]=t1v3[2];

752

t2v12d[0]=t2v1[1]; t2v12d[1]=t2v1[2];

753

t2v22d[0]=t2v2[1]; t2v22d[1]=t2v2[2];

754

t2v32d[0]=t2v3[1]; t2v32d[1]=t2v3[2];

755

} else if (fabs(n1[1])>=fabs(n1[0]) && fabs(n1[1])>=fabs(n1[2])) {

756

t1v12d[0]=t1v1[0]; t1v12d[1]=t1v1[2];

757

t1v22d[0]=t1v2[0]; t1v22d[1]=t1v2[2];

758

t1v32d[0]=t1v3[0]; t1v32d[1]=t1v3[2];

759

t2v12d[0]=t2v1[0]; t2v12d[1]=t2v1[2];

760

t2v22d[0]=t2v2[0]; t2v22d[1]=t2v2[2];

761

t2v32d[0]=t2v3[0]; t2v32d[1]=t2v3[2];

762

} else {

763

t1v12d[0]=t1v1[0]; t1v12d[1]=t1v1[1];

764

t1v22d[0]=t1v2[0]; t1v22d[1]=t1v2[1];

765

t1v32d[0]=t1v3[0]; t1v32d[1]=t1v3[1];

766

t2v12d[0]=t2v1[0]; t2v12d[1]=t2v1[1];

767

t2v22d[0]=t2v2[0]; t2v22d[1]=t2v2[1];

768

t2v32d[0]=t2v3[0]; t2v32d[1]=t2v3[1];

769

}

770

/* we may assume that none of the triangles is fully contained

771

* within the other. Thus, it suffices to do a lot of 2D line-line

772

* intersections */

773

if (lineIntersectionTest(t1v12d, t1v22d, t2v12d, t2v22d) ||

774

lineIntersectionTest(t1v22d, t1v32d, t2v12d, t2v22d) ||

775

lineIntersectionTest(t1v32d, t1v12d, t2v12d, t2v22d) ||

776

lineIntersectionTest(t1v12d, t1v22d, t2v22d, t2v32d) ||

777

lineIntersectionTest(t1v22d, t1v32d, t2v22d, t2v32d) ||

778

lineIntersectionTest(t1v32d, t1v12d, t2v22d, t2v32d) ||

779

lineIntersectionTest(t1v12d, t1v22d, t2v32d, t2v12d) ||

780

lineIntersectionTest(t1v22d, t1v32d, t2v32d, t2v12d) ||

781

lineIntersectionTest(t1v32d, t1v12d, t2v32d, t2v12d))

782

return 1;

783

return 0;

784

} else {

785

/* pointers to the vertices on the same side / opposite side of plane */

786

double *t2s11, *t2s12, *t2s2, t2s11sd, t2s12sd, t2s2sd;

787

double t1sd1, t1sd2, t1sd3;

788

double *t1s11, *t1s12, *t1s2, t1s11sd, t1s12sd, t1s2sd;

789

double t1p11, t1p12, t1p2, t2p11, t2p12, t2p2;

790

double D[3]; /* direction vector of line */

791

double t1t1, t1t2, t2t1, t2t2;

792

if (t2sd1*t2sd2>=0 && t2sd1*t2sd3<=0) {

793

t2s11=t2v1; t2s12=t2v2; t2s2=t2v3; t2s11sd=t2sd1;

794

t2s12sd=t2sd2; t2s2sd=t2sd3;

795

} else if (t2sd1*t2sd3>=0 && t2sd1*t2sd2<=0) {

796

t2s11=t2v1; t2s12=t2v3; t2s2=t2v2; t2s11sd=t2sd1;

797

t2s12sd=t2sd3; t2s2sd=t2sd2;

798

} else if (t2sd2*t2sd3>=0 && t2sd1*t2sd2<=0) {

799

t2s11=t2v2; t2s12=t2v3; t2s2=t2v1; t2s11sd=t2sd2;

800

t2s12sd=t2sd3; t2s2sd=t2sd1;

801

} else

802

return 0; /* all on the same side; no intersection */

803

804

/* same game for triangle 2 */

805

ELL_3V_SUB(diff1, t2v2, t2v1)((diff1)[0] = (t2v2)[0] - (t2v1)[0], (diff1)[1] = (t2v2)[1] -
(t2v1)[1], (diff1)[2] = (t2v2)[2] - (t2v1)[2]);

806

ELL_3V_SUB(diff2, t2v3, t2v1)((diff2)[0] = (t2v3)[0] - (t2v1)[0], (diff2)[1] = (t2v3)[1] -
(t2v1)[1], (diff2)[2] = (t2v3)[2] - (t2v1)[2]);

807

ELL_3V_CROSS(n2, diff1, diff2)((n2)[0] = (diff1)[1]*(diff2)[2] - (diff1)[2]*(diff2)[1], (n2
)[1] = (diff1)[2]*(diff2)[0] - (diff1)[0]*(diff2)[2], (n2)[2]
= (diff1)[0]*(diff2)[1] - (diff1)[1]*(diff2)[0]);

808

d2=-ELL_3V_DOT(n2,t2v1)((n2)[0]*(t2v1)[0] + (n2)[1]*(t2v1)[1] + (n2)[2]*(t2v1)[2]);

809

t1sd1 = ELL_3V_DOT(n2, t1v1)((n2)[0]*(t1v1)[0] + (n2)[1]*(t1v1)[1] + (n2)[2]*(t1v1)[2])+d2;

810

t1sd2 = ELL_3V_DOT(n2, t1v2)((n2)[0]*(t1v2)[0] + (n2)[1]*(t1v2)[1] + (n2)[2]*(t1v2)[2])+d2;

811

t1sd3 = ELL_3V_DOT(n2, t1v3)((n2)[0]*(t1v3)[0] + (n2)[1]*(t1v3)[1] + (n2)[2]*(t1v3)[2])+d2;

812

if (t1sd1*t1sd2>=0 && t1sd1*t1sd3<=0) {

813

t1s11=t1v1; t1s12=t1v2; t1s2=t1v3; t1s11sd=t1sd1;

814

t1s12sd=t1sd2; t1s2sd=t1sd3;

815

} else if (t1sd1*t1sd3>=0 && t1sd1*t1sd2<=0) {

816

t1s11=t1v1; t1s12=t1v3; t1s2=t1v2; t1s11sd=t1sd1;

817

t1s12sd=t1sd3; t1s2sd=t1sd2;

818

} else if (t1sd2*t1sd3>=0 && t1sd1*t1sd2<=0) {

819

t1s11=t1v2; t1s12=t1v3; t1s2=t1v1; t1s11sd=t1sd2;

820

t1s12sd=t1sd3; t1s2sd=t1sd1;

821

} else

822

return 0; /* all on the same side; no intersection */

823

824

/* both planes intersect in a line; check if the intervals on that

825

* line intersect */

826

ELL_3V_CROSS(D,n1,n2)((D)[0] = (n1)[1]*(n2)[2] - (n1)[2]*(n2)[1], (D)[1] = (n1)[2]
*(n2)[0] - (n1)[0]*(n2)[2], (D)[2] = (n1)[0]*(n2)[1] - (n1)[1
]*(n2)[0]);

827

/* we are only interested in component magnitudes */

828

D[0]=fabs(D[0]); D[1]=fabs(D[1]); D[2]=fabs(D[2]);

829

if (D[0]>=D[1] && D[0]>=D[2]) {

830

t1p11=t1s11[0]; t1p12=t1s12[0]; t1p2=t1s2[0];

831

t2p11=t2s11[0]; t2p12=t2s12[0]; t2p2=t2s2[0];

832

} else if (D[1]>=D[0] && D[1]>=D[2]) {

833

t1p11=t1s11[1]; t1p12=t1s12[1]; t1p2=t1s2[1];

834

t2p11=t2s11[1]; t2p12=t2s12[1]; t2p2=t2s2[1];

835

} else {

836

t1p11=t1s11[2]; t1p12=t1s12[2]; t1p2=t1s2[2];

837

t2p11=t2s11[2]; t2p12=t2s12[2]; t2p2=t2s2[2];

838

}

839

/* compute interval boundaries */

840

t1t1=t1p11+(t1p2-t1p11)*t1s11sd/(t1s11sd-t1s2sd);

841

t1t2=t1p12+(t1p2-t1p12)*t1s12sd/(t1s12sd-t1s2sd);

842

if (t1t1>t1t2) {

843

double help=t1t1;

844

t1t1=t1t2;

845

t1t2=help;

846

}

847

t2t1=t2p11+(t2p2-t2p11)*t2s11sd/(t2s11sd-t2s2sd);

848

t2t2=t2p12+(t2p2-t2p12)*t2s12sd/(t2s12sd-t2s2sd);

849

if (t2t1>t2t2) {

850

double help=t2t1;

851

t2t1=t2t2;

852

t2t2=help;

853

}

854

/* test for interval intersection */

855

if (t2t1>t1t2 || t1t1>t2t2) return 0;

856

return 1;

857

}

858

}

859

860

/* Score possible local topologies based on the agreement of

861

* connecting lines with normal directions. Lower scores are

862

* better. */

863

864

/* Connections between degenerate points on cell faces; if only four

865

* degenerate points are present, set p31 to NULL */

866

static double

867

evaluateDegConnection(double *p11, double *p12, double *p13, double *p14,

868

double *p21, double *p22, double *p23, double *p24,

869

double *p31, double *p32, double *p33, double *p34,

870

double *n12, double *n13, double *n22, double *n23,

871

double *n32, double *n33) {

872

double diff1[3], diff2[3], diff3[3], ret;

873

/* first, perform intersection testing */

874

if (triIntersectionTest(p11, p12, p13, p21, p22, p23) ||

875

triIntersectionTest(p13, p14, p11, p21, p22, p23) ||

876

triIntersectionTest(p11, p12, p13, p23, p24, p21) ||

877

triIntersectionTest(p13, p14, p11, p23, p24, p21))

878

return 1e20;

879

if (p31 != NULL((void*)0)) { /* three pairs - some more to do */

880

if (triIntersectionTest(p11, p12, p13, p31, p32, p33) ||

881

triIntersectionTest(p11, p12, p13, p33, p34, p31) ||

882

triIntersectionTest(p13, p14, p11, p31, p32, p33) ||

883

triIntersectionTest(p13, p14, p11, p33, p34, p31) ||

884

triIntersectionTest(p21, p22, p23, p31, p32, p33) ||

885

triIntersectionTest(p21, p22, p23, p33, p34, p31) ||

886

triIntersectionTest(p23, p24, p21, p31, p32, p33) ||

887

triIntersectionTest(p23, p24, p21, p33, p34, p31))

888

return 1e20;

889

}

890

ELL_3V_SUB(diff1,p13,p12)((diff1)[0] = (p13)[0] - (p12)[0], (diff1)[1] = (p13)[1] - (p12
)[1], (diff1)[2] = (p13)[2] - (p12)[2]);

891

ELL_3V_SUB(diff2,p23,p22)((diff2)[0] = (p23)[0] - (p22)[0], (diff2)[1] = (p23)[1] - (p22
)[1], (diff2)[2] = (p23)[2] - (p22)[2]);

892

ret=fabs(ELL_3V_DOT(diff1,n12)((diff1)[0]*(n12)[0] + (diff1)[1]*(n12)[1] + (diff1)[2]*(n12)
[2]))+fabs(ELL_3V_DOT(diff1,n13)((diff1)[0]*(n13)[0] + (diff1)[1]*(n13)[1] + (diff1)[2]*(n13)
[2]))+

893

fabs(ELL_3V_DOT(diff2,n22)((diff2)[0]*(n22)[0] + (diff2)[1]*(n22)[1] + (diff2)[2]*(n22)
[2]))+fabs(ELL_3V_DOT(diff2,n23)((diff2)[0]*(n23)[0] + (diff2)[1]*(n23)[1] + (diff2)[2]*(n23)
[2]));

894

if (p31 != NULL((void*)0)) {

895

ELL_3V_SUB(diff3,p33,p32)((diff3)[0] = (p33)[0] - (p32)[0], (diff3)[1] = (p33)[1] - (p32
)[1], (diff3)[2] = (p33)[2] - (p32)[2]);

896

ret+=fabs(ELL_3V_DOT(diff3,n32)((diff3)[0]*(n32)[0] + (diff3)[1]*(n32)[1] + (diff3)[2]*(n32)
[2]))+fabs(ELL_3V_DOT(diff3,n33)((diff3)[0]*(n33)[0] + (diff3)[1]*(n33)[1] + (diff3)[2]*(n33)
[2]));

897

}

898

return ret;

899

}

900

901

/* suggests a connectivity for a non-trivial combination of

902

* intersection points in the plane.

903

* pairs is output (permutation of idcs)

904

* bestval is input/output (best value so far, start with something big)

905

* ct is the number of points (currently assumed even)

906

* idcs is input (idcs that still need to be permuted)

907

* fixedct is input (number of idcs that are already fixed at this depth)

908

* coords is an array of 2D coordinates

909

* norms is an array of 2D vectors */

910

static void

911

findConnectivity(signed char *pairs, double *bestval, int ct, char *idcs,

912

int fixedct, double *coords, double *norms) {

913

int i,j;

914

if (fixedct==ct) {

915

double weight=0;

916

for (i=0; i<ct-1; i+=2) {

917

double diff[2];

918

ELL_2V_SUB(diff,coords+2*idcs[i],coords+2*idcs[i+1])((diff)[0] = (coords+2*idcs[i])[0] - (coords+2*idcs[i+1])[0],
(diff)[1] = (coords+2*idcs[i])[1] - (coords+2*idcs[i+1])[1]);

919

weight+=fabs(ELL_2V_DOT(diff,norms+2*idcs[i])((diff)[0]*(norms+2*idcs[i])[0] + (diff)[1]*(norms+2*idcs[i])
[1]))+

920

fabs(ELL_2V_DOT(diff,norms+2*idcs[i+1])((diff)[0]*(norms+2*idcs[i+1])[0] + (diff)[1]*(norms+2*idcs[i
+1])[1]));

921

}

922

if (weight<*bestval) {

923

*bestval=weight;

924

memcpy(pairs,idcs,sizeof(char)*ct)__builtin___memcpy_chk (pairs, idcs, sizeof(char)*ct, __builtin_object_size
(pairs, 0));

925

}

926

return;

927

}

928

/* else: we need a recursion */

929

for (i=fixedct+1; i<ct; i++) {

930

int intersect=0;

931

char *idxnew;

932

if (NULL((void*)0) == (idxnew = (char*) malloc (sizeof(char)*ct)))

933

return;

934

memcpy(idxnew,idcs,sizeof(char)*ct)__builtin___memcpy_chk (idxnew, idcs, sizeof(char)*ct, __builtin_object_size
(idxnew, 0));

935

/* try any of the remaining indices as a pair */

936

idxnew[fixedct+1]=idcs[i];

937

idxnew[i]=idcs[fixedct+1];

938

/* check if the resulting line causes an intersection */

939

for (j=0;j<fixedct;j+=2) {

940

if (lineIntersectionTest(coords+2*idxnew[fixedct],

941

coords+2*idxnew[fixedct+1],

942

coords+2*idxnew[j],coords+2*idxnew[j+1])) {

943

intersect=1;

944

break;

945

}

946

}

947

if (!intersect) {

948

findConnectivity(pairs, bestval, ct, idxnew, fixedct+2, coords, norms);

949

}

950

free(idxnew);

951

}

952

}

953

954

#define _SEEK_TREATED_REQUEST0x01 0x01 /* this voxel has to be treated */

955

#define _SEEK_TREATED_EDGE00x02 0x02 /* unique edge 0 has been treated */

956

#define _SEEK_TREATED_EDGE10x04 0x04 /* unique edge 1 has been treated */

957

#define _SEEK_TREATED_EDGE20x08 0x08 /* unique edge 2 has been treated */

958

#define _SEEK_TREATED_EDGE30x10 0x10 /* unique edge 3 has been treated */

959

#define _SEEK_TREATED_EDGE40x20 0x20 /* unique edge 4 has been treated */

960

#define _SEEK_TREATED_FACE30x40 0x40 /* unique face 3 has been treated */

961

962

/* find deg. points, normals, and connectivity on a given (unique) face

963

* now refines the search if it couldn't find a degenerate point */

964

static void

965

connectFace(seekContext *sctx, baggage *bag,

966

unsigned int xi, unsigned int yi, unsigned char faceid) {

967

int edgeid[4][4]={{0, 2, 3, 1}, /* which edges belong to which unique face? */

968

{0, 5, 8, 4},

969

{1, 6, 9, 4},

970

{8,10,11, 9}};

971

unsigned int sx = AIR_CAST(unsigned int, sctx->sx)((unsigned int)(sctx->sx));

972

unsigned int si = xi + sx*yi;

973

unsigned int six = xi + 1 + sx*yi;

974

unsigned int siy = xi + sx*(yi+1);

975

unsigned int sixy = xi + 1 + sx*(yi+1);

976

char inter[12]; /* indices of intersections */

977

int pass; /* allow multiple refined passes */

978

int i;

979

/* voxel in which treated information is stored for local edge i */

980

/* which vertices form which unique face? */

981

int verti[4][4];

982

int voxel[4][4];

983

/* mask for treated information in the above voxel */

984

char mask[4][4]={{_SEEK_TREATED_EDGE00x02, _SEEK_TREATED_EDGE10x04,

985

_SEEK_TREATED_EDGE00x02, _SEEK_TREATED_EDGE10x04},

986

{_SEEK_TREATED_EDGE00x02, _SEEK_TREATED_EDGE20x08,

987

_SEEK_TREATED_EDGE30x10, _SEEK_TREATED_EDGE20x08},

988

{_SEEK_TREATED_EDGE10x04, _SEEK_TREATED_EDGE20x08,

989

_SEEK_TREATED_EDGE40x20, _SEEK_TREATED_EDGE20x08},

990

{_SEEK_TREATED_EDGE30x10, _SEEK_TREATED_EDGE40x20,

991

_SEEK_TREATED_EDGE30x10, _SEEK_TREATED_EDGE40x20}};

992

/* start- and endpoints of the edges */

993

int verts[4][4], verte[4][4];

994

char treat[4]={0,0,0,0};

995

double dpthresh[3]={0.7,0.8,0.9};

996

/* candidates for degenerate points */

997

double candidates[18]={0.5,0.5, 0.25,0.25, 0.25,0.75,

998

0.75,0.25, 0.75,0.75, 0.5,0.25,

999

0.25,0.5, 0.75,0.5, 0.6,0.75};

1000

int cand_idx[4]={0, 1, 5, 9};

1001

int interct;

1002

1003

/* apparently, some C compilers cannot make these initializations in-place */

1004

ELL_4V_SET(verti[0], 0+2*si, 0+2*six, 0+2*siy, 0+2*sixy)((verti[0])[0] = (0+2*si), (verti[0])[1] = (0+2*six), (verti[
0])[2] = (0+2*siy), (verti[0])[3] = (0+2*sixy));

1005

ELL_4V_SET(verti[1], 0+2*si, 0+2*six, 1+2*si, 1+2*six)((verti[1])[0] = (0+2*si), (verti[1])[1] = (0+2*six), (verti[
1])[2] = (1+2*si), (verti[1])[3] = (1+2*six));

1006

ELL_4V_SET(verti[2], 0+2*si, 0+2*siy, 1+2*si, 1+2*siy)((verti[2])[0] = (0+2*si), (verti[2])[1] = (0+2*siy), (verti[
2])[2] = (1+2*si), (verti[2])[3] = (1+2*siy));

1007

ELL_4V_SET(verti[3], 1+2*si, 1+2*six, 1+2*siy, 1+2*sixy)((verti[3])[0] = (1+2*si), (verti[3])[1] = (1+2*six), (verti[
3])[2] = (1+2*siy), (verti[3])[3] = (1+2*sixy));

1008

ELL_4V_SET(voxel[0], si, six, siy, si)((voxel[0])[0] = (si), (voxel[0])[1] = (six), (voxel[0])[2] =
(siy), (voxel[0])[3] = (si));

1009

ELL_4V_SET(voxel[1], si, six, si, si)((voxel[1])[0] = (si), (voxel[1])[1] = (six), (voxel[1])[2] =
(si), (voxel[1])[3] = (si));

1010

ELL_4V_SET(voxel[2], si, siy, si, si)((voxel[2])[0] = (si), (voxel[2])[1] = (siy), (voxel[2])[2] =
(si), (voxel[2])[3] = (si));

1011

ELL_4V_SET(voxel[3], si, six, siy, si)((voxel[3])[0] = (si), (voxel[3])[1] = (six), (voxel[3])[2] =
(siy), (voxel[3])[3] = (si));

1012

ELL_4V_SET(verts[0], 0+2*si, 0+2*six, 0+2*siy, 0+2*si)((verts[0])[0] = (0+2*si), (verts[0])[1] = (0+2*six), (verts[
0])[2] = (0+2*siy), (verts[0])[3] = (0+2*si));

1013

ELL_4V_SET(verts[1], 0+2*si, 0+2*six, 1+2*si, 0+2*si)((verts[1])[0] = (0+2*si), (verts[1])[1] = (0+2*six), (verts[
1])[2] = (1+2*si), (verts[1])[3] = (0+2*si));

1014

ELL_4V_SET(verts[2], 0+2*si, 0+2*siy, 1+2*si, 0+2*si)((verts[2])[0] = (0+2*si), (verts[2])[1] = (0+2*siy), (verts[
2])[2] = (1+2*si), (verts[2])[3] = (0+2*si));

1015

ELL_4V_SET(verts[3], 1+2*si, 1+2*six, 1+2*siy, 1+2*si)((verts[3])[0] = (1+2*si), (verts[3])[1] = (1+2*six), (verts[
3])[2] = (1+2*siy), (verts[3])[3] = (1+2*si));

1016

ELL_4V_SET(verte[0], 0+2*six, 0+2*sixy, 0+2*sixy, 0+2*siy)((verte[0])[0] = (0+2*six), (verte[0])[1] = (0+2*sixy), (verte
[0])[2] = (0+2*sixy), (verte[0])[3] = (0+2*siy));

1017

ELL_4V_SET(verte[1], 0+2*six, 1+2*six, 1+2*six, 1+2*si)((verte[1])[0] = (0+2*six), (verte[1])[1] = (1+2*six), (verte
[1])[2] = (1+2*six), (verte[1])[3] = (1+2*si));

1018

ELL_4V_SET(verte[2], 0+2*siy, 1+2*siy, 1+2*siy, 1+2*si)((verte[2])[0] = (0+2*siy), (verte[2])[1] = (1+2*siy), (verte
[2])[2] = (1+2*siy), (verte[2])[3] = (1+2*si));

1019

ELL_4V_SET(verte[3], 1+2*six, 1+2*sixy, 1+2*sixy, 1+2*siy)((verte[3])[0] = (1+2*six), (verte[3])[1] = (1+2*sixy), (verte
[3])[2] = (1+2*sixy), (verte[3])[3] = (1+2*siy));

1020

1021

/* find out which edges have not yet been treated */

1022

for (i=0; i<4; i++) {

1023

if (!(sctx->treated[voxel[faceid][i]]&mask[faceid][i])) {

1024

treat[i]=1; /* we need to treat this */

1025

sctx->treated[voxel[faceid][i]] |= mask[faceid][i];

1026

}

1027

}

1028

1029

for (pass=0; pass<3; pass++) {

1030

/* first, find intersections for edges that need treatment */

1031

int j;

1032

for (j=0; j<4; j++) {

1033

double interpos[8];

1034

if (!treat[j]) continue;

1035

interct=findFeatureIntersection(interpos,

1036

sctx->t + 9*verts[faceid][j],

1037

sctx->hess + 9*verts[faceid][j],

1038

sctx->grad + 3*verts[faceid][j],

1039

sctx->t + 9*verte[faceid][j],

1040

sctx->hess + 9*verte[faceid][j],

1041

sctx->grad + 3*verte[faceid][j],

1042

0.0, 1.0, bag->esIdx==2,

1043

sctx->evalDiffThresh,

1044

dpthresh[pass]);

1045

if (interct>3) interct=3;

1046

for (i=0; i<interct; i++) {

1047

double x=0, y=0, z=0; unsigned int xb=0, yb=0, idb=0;

1048

sctx->edgealpha[3*(bag->evti[edgeid[faceid][j]]+5*si)+i] = interpos[i];

1049

switch (edgeid[faceid][j]) {

1050

case 0: x=xi+interpos[i]; y=yi; z=bag->zi;

1051

xb=xi; yb=yi; idb=0; break;

1052

case 1: x=xi; y=yi+interpos[i]; z=bag->zi;

1053

xb=xi; yb=yi; idb=1; break;

1054

case 2: x=xi+1; y=yi+interpos[i]; z=bag->zi;

1055

xb=xi+1; yb=yi; idb=1; break;

1056

case 3: x=xi+interpos[i]; y=yi+1; z=bag->zi;

1057

xb=xi; yb=yi+1; idb=0; break;

1058

case 4: x=xi; y=yi; z=bag->zi+interpos[i];

1059

xb=xi; yb=yi; idb=2; break;

1060

case 5: x=xi+1; y=yi; z=bag->zi+interpos[i];

1061

xb=xi+1; yb=yi; idb=2; break;

1062

case 6: x=xi; y=yi+1; z=bag->zi+interpos[i];

1063

xb=xi; yb=yi+1; idb=2; break;

1064

case 7: x=xi+1; y=yi+1; z=bag->zi+interpos[i];

1065

xb=xi+1; yb=yi+1; idb=2; break;

1066

case 8: x=xi+interpos[i]; y=yi; z=bag->zi+1;

1067

xb=xi; yb=yi; idb=3; break;

1068

case 9: x=xi; y=yi+interpos[i]; z=bag->zi+1;

1069

xb=xi; yb=yi; idb=4; break;

1070

case 10: x=xi+1; y=yi+interpos[i]; z=bag->zi+1;

1071

xb=xi+1; yb=yi; idb=4; break;

1072

case 11: x=xi+interpos[i]; y=yi+1; z=bag->zi+1;

1073

xb=xi; yb=yi+1; idb=3; break;

1074

}

1075

ELL_3V_SET(sctx->edgeicoord+9*(bag->evti[edgeid[faceid][j]]+5*si)+3*i,((sctx->edgeicoord+9*(bag->evti[edgeid[faceid][j]]+5*si
)+3*i)[0] = (x), (sctx->edgeicoord+9*(bag->evti[edgeid[
faceid][j]]+5*si)+3*i)[1] = (y), (sctx->edgeicoord+9*(bag->
evti[edgeid[faceid][j]]+5*si)+3*i)[2] = (z))

1076

x, y, z)((sctx->edgeicoord+9*(bag->evti[edgeid[faceid][j]]+5*si
)+3*i)[0] = (x), (sctx->edgeicoord+9*(bag->evti[edgeid[
faceid][j]]+5*si)+3*i)[1] = (y), (sctx->edgeicoord+9*(bag->
evti[edgeid[faceid][j]]+5*si)+3*i)[2] = (z));

1077

computeEdgeGradient(sctx, bag, sctx->edgenorm+

1078

9*(bag->evti[edgeid[faceid][j]]+5*si)+3*i,

1079

xb, yb, idb, interpos[i]);

1080

}

1081

}

1082

1083

interct=0; /* number of feature intersections */

1084

for (i=0; i<3; i++) {

1085

if (sctx->edgealpha[3*(bag->evti[edgeid[faceid][0]]+5*si)+i]>=0)

1086

inter[interct++]=i; /* numbering is local w.r.t. face */

1087

if (sctx->edgealpha[3*(bag->evti[edgeid[faceid][1]]+5*si)+i]>=0)

1088

inter[interct++]=3+i;

1089

if (sctx->edgealpha[3*(bag->evti[edgeid[faceid][2]]+5*si)+i]>=0)

1090

inter[interct++]=6+i;

1091

if (sctx->edgealpha[3*(bag->evti[edgeid[faceid][3]]+5*si)+i]>=0)

1092

inter[interct++]=9+i;

1093

}

1094

if (interct%2==1) { /* we need to look for a degeneracy */

1095

int k;

1096

for (k=cand_idx[pass]; k<cand_idx[pass+1]; k++) {

1097

ELL_2V_SET(sctx->facecoord+2*(faceid+4*si),((sctx->facecoord+2*(faceid+4*si))[0]=(candidates[2*k]), (
sctx->facecoord+2*(faceid+4*si))[1]=(candidates[2*k+1]))

1098

candidates[2*k], candidates[2*k+1])((sctx->facecoord+2*(faceid+4*si))[0]=(candidates[2*k]), (
sctx->facecoord+2*(faceid+4*si))[1]=(candidates[2*k+1]));

1099

if (!seekDescendToDeg(sctx->facecoord+2*(faceid+4*si),

1100

sctx->hess + 9*verti[faceid][0],

1101

sctx->hess + 9*verti[faceid][1],

1102

sctx->hess + 9*verti[faceid][2],

1103

sctx->hess + 9*verti[faceid][3],

1104

50, 1e-9, (bag->esIdx==2)?'l':'p')) {

1105

inter[interct++]=12; /* 12 means "deg. point on this face */

1106

break;

1107

}

1108

}

1109

if ((pass==2) && (inter[interct-1]!=12)) {

1110

/* nothing helped, so insert a dummy vertex */

1111

ELL_2V_SET(sctx->facecoord+2*(faceid+4*si), 0.5, 0.5)((sctx->facecoord+2*(faceid+4*si))[0]=(0.5), (sctx->facecoord
+2*(faceid+4*si))[1]=(0.5));

1112

inter[interct++]=12;

1113

}

1114

if (inter[interct-1]==12) {

1115

computeFaceGradient(sctx, sctx->facenorm+3*(faceid+4*si),

1116

xi, yi, faceid, sctx->facecoord+2*(faceid+4*si));

1117

switch (faceid) {

1118

case 0: ELL_3V_SET(sctx->faceicoord+3*(faceid+4*si),((sctx->faceicoord+3*(faceid+4*si))[0] = (xi+sctx->facecoord
[2*(faceid+4*si)]), (sctx->faceicoord+3*(faceid+4*si))[1] =
(yi+sctx->facecoord[2*(faceid+4*si)+1]), (sctx->faceicoord
+3*(faceid+4*si))[2] = (bag->zi))

1119

xi+sctx->facecoord[2*(faceid+4*si)],((sctx->faceicoord+3*(faceid+4*si))[0] = (xi+sctx->facecoord
[2*(faceid+4*si)]), (sctx->faceicoord+3*(faceid+4*si))[1] =
(yi+sctx->facecoord[2*(faceid+4*si)+1]), (sctx->faceicoord
+3*(faceid+4*si))[2] = (bag->zi))

1120

yi+sctx->facecoord[2*(faceid+4*si)+1], bag->zi)((sctx->faceicoord+3*(faceid+4*si))[0] = (xi+sctx->facecoord
[2*(faceid+4*si)]), (sctx->faceicoord+3*(faceid+4*si))[1] =
(yi+sctx->facecoord[2*(faceid+4*si)+1]), (sctx->faceicoord
+3*(faceid+4*si))[2] = (bag->zi));

1121

break;

1122

case 1: ELL_3V_SET(sctx->faceicoord+3*(faceid+4*si),((sctx->faceicoord+3*(faceid+4*si))[0] = (xi+sctx->facecoord
[2*(faceid+4*si)]), (sctx->faceicoord+3*(faceid+4*si))[1] =
(yi), (sctx->faceicoord+3*(faceid+4*si))[2] = (bag->zi
+sctx->facecoord[2*(faceid+4*si)+1]))

1123

xi+sctx->facecoord[2*(faceid+4*si)], yi,((sctx->faceicoord+3*(faceid+4*si))[0] = (xi+sctx->facecoord
[2*(faceid+4*si)]), (sctx->faceicoord+3*(faceid+4*si))[1] =
(yi), (sctx->faceicoord+3*(faceid+4*si))[2] = (bag->zi
+sctx->facecoord[2*(faceid+4*si)+1]))

1124

bag->zi+sctx->facecoord[2*(faceid+4*si)+1])((sctx->faceicoord+3*(faceid+4*si))[0] = (xi+sctx->facecoord
[2*(faceid+4*si)]), (sctx->faceicoord+3*(faceid+4*si))[1] =
(yi), (sctx->faceicoord+3*(faceid+4*si))[2] = (bag->zi
+sctx->facecoord[2*(faceid+4*si)+1]));

1125

break;

1126

case 2: ELL_3V_SET(sctx->faceicoord+3*(faceid+4*si), xi,((sctx->faceicoord+3*(faceid+4*si))[0] = (xi), (sctx->faceicoord
+3*(faceid+4*si))[1] = (yi+sctx->facecoord[2*(faceid+4*si)
]), (sctx->faceicoord+3*(faceid+4*si))[2] = (bag->zi+sctx
->facecoord[2*(faceid+4*si)+1]))

1127

yi+sctx->facecoord[2*(faceid+4*si)],((sctx->faceicoord+3*(faceid+4*si))[0] = (xi), (sctx->faceicoord
+3*(faceid+4*si))[1] = (yi+sctx->facecoord[2*(faceid+4*si)
]), (sctx->faceicoord+3*(faceid+4*si))[2] = (bag->zi+sctx
->facecoord[2*(faceid+4*si)+1]))

1128

bag->zi+sctx->facecoord[2*(faceid+4*si)+1])((sctx->faceicoord+3*(faceid+4*si))[0] = (xi), (sctx->faceicoord
+3*(faceid+4*si))[1] = (yi+sctx->facecoord[2*(faceid+4*si)
]), (sctx->faceicoord+3*(faceid+4*si))[2] = (bag->zi+sctx
->facecoord[2*(faceid+4*si)+1]));

1129

break;

1130

case 3: ELL_3V_SET(sctx->faceicoord+3*(faceid+4*si),((sctx->faceicoord+3*(faceid+4*si))[0] = (xi+sctx->facecoord
[2*(faceid+4*si)]), (sctx->faceicoord+3*(faceid+4*si))[1] =
(yi+sctx->facecoord[2*(faceid+4*si)+1]), (sctx->faceicoord
+3*(faceid+4*si))[2] = (bag->zi+1))

1131

1132

yi+sctx->facecoord[2*(faceid+4*si)+1], bag->zi+1)((sctx->faceicoord+3*(faceid+4*si))[0] = (xi+sctx->facecoord
[2*(faceid+4*si)]), (sctx->faceicoord+3*(faceid+4*si))[1] =
(yi+sctx->facecoord[2*(faceid+4*si)+1]), (sctx->faceicoord
+3*(faceid+4*si))[2] = (bag->zi+1));

1133

break;

1134

}

1135

}

1136

}

1137

if (interct%2==0) { /* we can break out */

1138

break;

1139

}

1140

}

1141

1142

if (interct<=1) { /* there is no connectivity on this face */

1143

ELL_4V_SET(sctx->pairs+12*(faceid+4*si),-1,-1,-1,-1)((sctx->pairs+12*(faceid+4*si))[0] = (-1), (sctx->pairs
+12*(faceid+4*si))[1] = (-1), (sctx->pairs+12*(faceid+4*si
))[2] = (-1), (sctx->pairs+12*(faceid+4*si))[3] = (-1));

1144

} else if (interct==2) { /* connectivity is straightforward */

1145

ELL_4V_SET(sctx->pairs+12*(faceid+4*si),inter[0],inter[1],-1,-1)((sctx->pairs+12*(faceid+4*si))[0] = (inter[0]), (sctx->
pairs+12*(faceid+4*si))[1] = (inter[1]), (sctx->pairs+12*(
faceid+4*si))[2] = (-1), (sctx->pairs+12*(faceid+4*si))[3]
= (-1));

1146

} else { /* we need gradients and coordinates to make a decision */

1147

double interc[24]; /* 2D coordinates of intersection points */

1148

double intern[24]; /* 2D normals at intersection points */

1149

/* used to find the best pairing without self-intersection */

1150

double bestscore=1e20;

1151

char idcs[12]; /* consider if we need to restrict this */

1152

for (i=0; i<interct; i++) {

1153

if (inter[i]<12) { /* edge feature */

1154

int resolved=edgeid[faceid][inter[i]/3];

1155

int offset=inter[i]%3;

1156

switch (faceid) {

1157

case 0: case 3:

1158

ELL_2V_SET(interc+2*i,((interc+2*i)[0]=(sctx->edgeicoord[9*(bag->evti[resolved
]+5*si)+3*offset]), (interc+2*i)[1]=(sctx->edgeicoord[9*(bag
->evti[resolved]+5*si)+3*offset+1]))

1159

sctx->edgeicoord[9*(bag->evti[resolved]+5*si)+3*offset],((interc+2*i)[0]=(sctx->edgeicoord[9*(bag->evti[resolved
]+5*si)+3*offset]), (interc+2*i)[1]=(sctx->edgeicoord[9*(bag
->evti[resolved]+5*si)+3*offset+1]))

1160

sctx->edgeicoord[9*(bag->evti[resolved]+5*si)+3*offset+1])((interc+2*i)[0]=(sctx->edgeicoord[9*(bag->evti[resolved
]+5*si)+3*offset]), (interc+2*i)[1]=(sctx->edgeicoord[9*(bag
->evti[resolved]+5*si)+3*offset+1]));

1161

ELL_2V_SET(intern+2*i,((intern+2*i)[0]=(sctx->edgenorm[9*(bag->evti[resolved]
+5*si)+3*offset]), (intern+2*i)[1]=(sctx->edgenorm[9*(bag->
evti[resolved]+5*si)+3*offset+1]))

1162

sctx->edgenorm[9*(bag->evti[resolved]+5*si)+3*offset],((intern+2*i)[0]=(sctx->edgenorm[9*(bag->evti[resolved]
+5*si)+3*offset]), (intern+2*i)[1]=(sctx->edgenorm[9*(bag->
evti[resolved]+5*si)+3*offset+1]))

1163

sctx->edgenorm[9*(bag->evti[resolved]+5*si)+3*offset+1])((intern+2*i)[0]=(sctx->edgenorm[9*(bag->evti[resolved]
+5*si)+3*offset]), (intern+2*i)[1]=(sctx->edgenorm[9*(bag->
evti[resolved]+5*si)+3*offset+1]));

1164

break;

1165

case 1:

1166

ELL_2V_SET(interc+2*i,((interc+2*i)[0]=(sctx->edgeicoord[9*(bag->evti[resolved
]+5*si)+3*offset]), (interc+2*i)[1]=(sctx->edgeicoord[9*(bag
->evti[resolved]+5*si)+3*offset+2]))

1167

1168

sctx->edgeicoord[9*(bag->evti[resolved]+5*si)+3*offset+2])((interc+2*i)[0]=(sctx->edgeicoord[9*(bag->evti[resolved
]+5*si)+3*offset]), (interc+2*i)[1]=(sctx->edgeicoord[9*(bag
->evti[resolved]+5*si)+3*offset+2]));

1169

ELL_2V_SET(intern+2*i,((intern+2*i)[0]=(sctx->edgenorm[9*(bag->evti[resolved]
+5*si)+3*offset]), (intern+2*i)[1]=(sctx->edgenorm[9*(bag->
evti[resolved]+5*si)+3*offset+2]))

1170

1171

sctx->edgenorm[9*(bag->evti[resolved]+5*si)+3*offset+2])((intern+2*i)[0]=(sctx->edgenorm[9*(bag->evti[resolved]
+5*si)+3*offset]), (intern+2*i)[1]=(sctx->edgenorm[9*(bag->
evti[resolved]+5*si)+3*offset+2]));

1172

break;

1173

case 2:

1174

ELL_2V_SET(interc+2*i,((interc+2*i)[0]=(sctx->edgeicoord[9*(bag->evti[resolved
]+5*si)+3*offset+1]), (interc+2*i)[1]=(sctx->edgeicoord[9*
(bag->evti[resolved]+5*si)+3*offset+2]))

1175

sctx->edgeicoord[9*(bag->evti[resolved]+5*si)+3*offset+1],((interc+2*i)[0]=(sctx->edgeicoord[9*(bag->evti[resolved
]+5*si)+3*offset+1]), (interc+2*i)[1]=(sctx->edgeicoord[9*
(bag->evti[resolved]+5*si)+3*offset+2]))

1176

sctx->edgeicoord[9*(bag->evti[resolved]+5*si)+3*offset+2])((interc+2*i)[0]=(sctx->edgeicoord[9*(bag->evti[resolved
]+5*si)+3*offset+1]), (interc+2*i)[1]=(sctx->edgeicoord[9*
(bag->evti[resolved]+5*si)+3*offset+2]));

1177

ELL_2V_SET(intern+2*i,((intern+2*i)[0]=(sctx->edgenorm[9*(bag->evti[resolved]
+5*si)+3*offset+1]), (intern+2*i)[1]=(sctx->edgenorm[9*(bag
->evti[resolved]+5*si)+3*offset+2]))

1178

sctx->edgenorm[9*(bag->evti[resolved]+5*si)+3*offset+1],((intern+2*i)[0]=(sctx->edgenorm[9*(bag->evti[resolved]
+5*si)+3*offset+1]), (intern+2*i)[1]=(sctx->edgenorm[9*(bag
->evti[resolved]+5*si)+3*offset+2]))

1179

sctx->edgenorm[9*(bag->evti[resolved]+5*si)+3*offset+2])((intern+2*i)[0]=(sctx->edgenorm[9*(bag->evti[resolved]
+5*si)+3*offset+1]), (intern+2*i)[1]=(sctx->edgenorm[9*(bag
->evti[resolved]+5*si)+3*offset+2]));

1180

break;

1181

}

1182

} else { /* face feature */

1183

switch (faceid) {

1184

case 0: case 3:

1185

ELL_2V_SET(interc+2*i, sctx->faceicoord[3*(faceid+4*si)],((interc+2*i)[0]=(sctx->faceicoord[3*(faceid+4*si)]), (interc
+2*i)[1]=(sctx->faceicoord[3*(faceid+4*si)+1]))

1186

sctx->faceicoord[3*(faceid+4*si)+1])((interc+2*i)[0]=(sctx->faceicoord[3*(faceid+4*si)]), (interc
+2*i)[1]=(sctx->faceicoord[3*(faceid+4*si)+1]));

1187

ELL_2V_SET(intern+2*i, sctx->facenorm[3*(faceid+4*si)],((intern+2*i)[0]=(sctx->facenorm[3*(faceid+4*si)]), (intern
+2*i)[1]=(sctx->facenorm[3*(faceid+4*si)+1]))

1188

sctx->facenorm[3*(faceid+4*si)+1])((intern+2*i)[0]=(sctx->facenorm[3*(faceid+4*si)]), (intern
+2*i)[1]=(sctx->facenorm[3*(faceid+4*si)+1]));

1189

break;

1190

case 1:

1191

ELL_2V_SET(interc+2*i, sctx->faceicoord[3*(faceid+4*si)],((interc+2*i)[0]=(sctx->faceicoord[3*(faceid+4*si)]), (interc
+2*i)[1]=(sctx->faceicoord[3*(faceid+4*si)+2]))

1192

sctx->faceicoord[3*(faceid+4*si)+2])((interc+2*i)[0]=(sctx->faceicoord[3*(faceid+4*si)]), (interc
+2*i)[1]=(sctx->faceicoord[3*(faceid+4*si)+2]));

1193

ELL_2V_SET(intern+2*i, sctx->facenorm[3*(faceid+4*si)],((intern+2*i)[0]=(sctx->facenorm[3*(faceid+4*si)]), (intern
+2*i)[1]=(sctx->facenorm[3*(faceid+4*si)+2]))

1194

sctx->facenorm[3*(faceid+4*si)+2])((intern+2*i)[0]=(sctx->facenorm[3*(faceid+4*si)]), (intern
+2*i)[1]=(sctx->facenorm[3*(faceid+4*si)+2]));

1195

break;

1196

case 2:

1197

ELL_2V_SET(interc+2*i, sctx->faceicoord[3*(faceid+4*si)+1],((interc+2*i)[0]=(sctx->faceicoord[3*(faceid+4*si)+1]), (interc
+2*i)[1]=(sctx->faceicoord[3*(faceid+4*si)+2]))

1198

sctx->faceicoord[3*(faceid+4*si)+2])((interc+2*i)[0]=(sctx->faceicoord[3*(faceid+4*si)+1]), (interc
+2*i)[1]=(sctx->faceicoord[3*(faceid+4*si)+2]));

1199

ELL_2V_SET(intern+2*i, sctx->facenorm[3*(faceid+4*si)+1],((intern+2*i)[0]=(sctx->facenorm[3*(faceid+4*si)+1]), (intern
+2*i)[1]=(sctx->facenorm[3*(faceid+4*si)+2]))

1200

sctx->facenorm[3*(faceid+4*si)+2])((intern+2*i)[0]=(sctx->facenorm[3*(faceid+4*si)+1]), (intern
+2*i)[1]=(sctx->facenorm[3*(faceid+4*si)+2]));

1201

break;

1202

}

1203

}

1204

}

1205

for (i=0; i<interct; i++) {

1206

sctx->pairs[12*(faceid+4*si)+i]=i;

1207

idcs[i]=i;

1208

}

1209

findConnectivity(sctx->pairs+12*(faceid+4*si), &bestscore, interct,

1210

idcs, 0, interc, intern);

1211

for (i=0; i<interct; i++)

1212

sctx->pairs[12*(faceid+4*si)+i]=inter[sctx->pairs[12*(faceid+4*si)+i]];

1213

for (i=interct; i<12; i++)

1214

sctx->pairs[12*(faceid+4*si)+i]=-1;

1215

}

1216

}

1217

1218

static void

1219

intersectionShuffleProbe(seekContext *sctx, baggage *bag) {

1220

unsigned int xi, yi, sx, sy, si;

1221

int i;

1222

1223

sx = AIR_CAST(unsigned int, sctx->sx)((unsigned int)(sctx->sx));

1224

sy = AIR_CAST(unsigned int, sctx->sy)((unsigned int)(sctx->sy));

1225

1226

for (yi=0; yi<sy; yi++) {

1227

for (xi=0; xi<sx; xi++) {

1228

si = xi + sx*yi;

1229

/* take care of facevidx array */

1230

if (!bag->zi) { /* initialize, else copy over */

1231

sctx->facevidx[0 + 4*si] = -1;

1232

} else {

1233

sctx->facevidx[0 + 4*si] = sctx->facevidx[3 + 4*si];

1234

}

1235

sctx->facevidx[1 + 4*si] = sctx->facevidx[2 + 4*si] =

1236

sctx->facevidx[3 + 4*si] = -1;

1237

1238

/* copy or reset data on the 5 unique edges */

1239

1240

if (sctx->treated[si]&_SEEK_TREATED_EDGE30x10) {

1241

/* has been treated, just copy results */

1242

ELL_3V_COPY(sctx->edgealpha+3*(0+5*si), sctx->edgealpha+3*(3+5*si))((sctx->edgealpha+3*(0+5*si))[0] = (sctx->edgealpha+3*(
3+5*si))[0], (sctx->edgealpha+3*(0+5*si))[1] = (sctx->edgealpha
+3*(3+5*si))[1], (sctx->edgealpha+3*(0+5*si))[2] = (sctx->
edgealpha+3*(3+5*si))[2]);

1243

ELL_3M_COPY(sctx->edgenorm+9*(0+5*si), sctx->edgenorm+9*(3+5*si))((((sctx->edgenorm+9*(0+5*si))+0)[0] = ((sctx->edgenorm
+9*(3+5*si))+0)[0], ((sctx->edgenorm+9*(0+5*si))+0)[1] = (
(sctx->edgenorm+9*(3+5*si))+0)[1], ((sctx->edgenorm+9*(
0+5*si))+0)[2] = ((sctx->edgenorm+9*(3+5*si))+0)[2]), (((sctx
->edgenorm+9*(0+5*si))+3)[0] = ((sctx->edgenorm+9*(3+5*
si))+3)[0], ((sctx->edgenorm+9*(0+5*si))+3)[1] = ((sctx->
edgenorm+9*(3+5*si))+3)[1], ((sctx->edgenorm+9*(0+5*si))+3
)[2] = ((sctx->edgenorm+9*(3+5*si))+3)[2]), (((sctx->edgenorm
+9*(0+5*si))+6)[0] = ((sctx->edgenorm+9*(3+5*si))+6)[0], (
(sctx->edgenorm+9*(0+5*si))+6)[1] = ((sctx->edgenorm+9*
(3+5*si))+6)[1], ((sctx->edgenorm+9*(0+5*si))+6)[2] = ((sctx
->edgenorm+9*(3+5*si))+6)[2]));

1244

ELL_3M_COPY(sctx->edgeicoord+9*(0+5*si), sctx->edgeicoord+9*(3+5*si))((((sctx->edgeicoord+9*(0+5*si))+0)[0] = ((sctx->edgeicoord
+9*(3+5*si))+0)[0], ((sctx->edgeicoord+9*(0+5*si))+0)[1] =
((sctx->edgeicoord+9*(3+5*si))+0)[1], ((sctx->edgeicoord
+9*(0+5*si))+0)[2] = ((sctx->edgeicoord+9*(3+5*si))+0)[2])
, (((sctx->edgeicoord+9*(0+5*si))+3)[0] = ((sctx->edgeicoord
+9*(3+5*si))+3)[0], ((sctx->edgeicoord+9*(0+5*si))+3)[1] =
((sctx->edgeicoord+9*(3+5*si))+3)[1], ((sctx->edgeicoord
+9*(0+5*si))+3)[2] = ((sctx->edgeicoord+9*(3+5*si))+3)[2])
, (((sctx->edgeicoord+9*(0+5*si))+6)[0] = ((sctx->edgeicoord
+9*(3+5*si))+6)[0], ((sctx->edgeicoord+9*(0+5*si))+6)[1] =
((sctx->edgeicoord+9*(3+5*si))+6)[1], ((sctx->edgeicoord
+9*(0+5*si))+6)[2] = ((sctx->edgeicoord+9*(3+5*si))+6)[2])
);

1245

sctx->treated[si]|=_SEEK_TREATED_EDGE00x02;

1246

} else if (xi!=sx-1) {

1247

ELL_3V_SET(sctx->edgealpha+3*(0+5*si),-1,-1,-1)((sctx->edgealpha+3*(0+5*si))[0] = (-1), (sctx->edgealpha
+3*(0+5*si))[1] = (-1), (sctx->edgealpha+3*(0+5*si))[2] = (
-1));

1248

sctx->treated[si]&=0xFF^_SEEK_TREATED_EDGE00x02;

1249

}

1250

1251

if (sctx->treated[si]&_SEEK_TREATED_EDGE40x20) {

1252

/* has been treated, just copy results */

1253

ELL_3V_COPY(sctx->edgealpha+3*(1+5*si), sctx->edgealpha+3*(4+5*si))((sctx->edgealpha+3*(1+5*si))[0] = (sctx->edgealpha+3*(
4+5*si))[0], (sctx->edgealpha+3*(1+5*si))[1] = (sctx->edgealpha
+3*(4+5*si))[1], (sctx->edgealpha+3*(1+5*si))[2] = (sctx->
edgealpha+3*(4+5*si))[2]);

1254

ELL_3M_COPY(sctx->edgenorm+9*(1+5*si), sctx->edgenorm+9*(4+5*si))((((sctx->edgenorm+9*(1+5*si))+0)[0] = ((sctx->edgenorm
+9*(4+5*si))+0)[0], ((sctx->edgenorm+9*(1+5*si))+0)[1] = (
(sctx->edgenorm+9*(4+5*si))+0)[1], ((sctx->edgenorm+9*(
1+5*si))+0)[2] = ((sctx->edgenorm+9*(4+5*si))+0)[2]), (((sctx
->edgenorm+9*(1+5*si))+3)[0] = ((sctx->edgenorm+9*(4+5*
si))+3)[0], ((sctx->edgenorm+9*(1+5*si))+3)[1] = ((sctx->
edgenorm+9*(4+5*si))+3)[1], ((sctx->edgenorm+9*(1+5*si))+3
)[2] = ((sctx->edgenorm+9*(4+5*si))+3)[2]), (((sctx->edgenorm
+9*(1+5*si))+6)[0] = ((sctx->edgenorm+9*(4+5*si))+6)[0], (
(sctx->edgenorm+9*(1+5*si))+6)[1] = ((sctx->edgenorm+9*
(4+5*si))+6)[1], ((sctx->edgenorm+9*(1+5*si))+6)[2] = ((sctx
->edgenorm+9*(4+5*si))+6)[2]));

1255

ELL_3M_COPY(sctx->edgeicoord+9*(1+5*si), sctx->edgeicoord+9*(4+5*si))((((sctx->edgeicoord+9*(1+5*si))+0)[0] = ((sctx->edgeicoord
+9*(4+5*si))+0)[0], ((sctx->edgeicoord+9*(1+5*si))+0)[1] =
((sctx->edgeicoord+9*(4+5*si))+0)[1], ((sctx->edgeicoord
+9*(1+5*si))+0)[2] = ((sctx->edgeicoord+9*(4+5*si))+0)[2])
, (((sctx->edgeicoord+9*(1+5*si))+3)[0] = ((sctx->edgeicoord
+9*(4+5*si))+3)[0], ((sctx->edgeicoord+9*(1+5*si))+3)[1] =
((sctx->edgeicoord+9*(4+5*si))+3)[1], ((sctx->edgeicoord
+9*(1+5*si))+3)[2] = ((sctx->edgeicoord+9*(4+5*si))+3)[2])
, (((sctx->edgeicoord+9*(1+5*si))+6)[0] = ((sctx->edgeicoord
+9*(4+5*si))+6)[0], ((sctx->edgeicoord+9*(1+5*si))+6)[1] =
((sctx->edgeicoord+9*(4+5*si))+6)[1], ((sctx->edgeicoord
+9*(1+5*si))+6)[2] = ((sctx->edgeicoord+9*(4+5*si))+6)[2])
);

1256

sctx->treated[si]|=_SEEK_TREATED_EDGE10x04;

1257

} else if (yi!=sy-1) {

1258

ELL_3V_SET(sctx->edgealpha+3*(1+5*si),-1,-1,-1)((sctx->edgealpha+3*(1+5*si))[0] = (-1), (sctx->edgealpha
+3*(1+5*si))[1] = (-1), (sctx->edgealpha+3*(1+5*si))[2] = (
-1));

1259

sctx->treated[si]&=0xFF^_SEEK_TREATED_EDGE10x04;

1260

}

1261

1262

/* edges within and at top of the slab are new */

1263

ELL_3V_SET(sctx->edgealpha+3*(2+5*si),-1,-1,-1)((sctx->edgealpha+3*(2+5*si))[0] = (-1), (sctx->edgealpha
+3*(2+5*si))[1] = (-1), (sctx->edgealpha+3*(2+5*si))[2] = (
-1));

1264

sctx->treated[si]&=0xFF^_SEEK_TREATED_EDGE20x08;

1265

1266

ELL_3V_SET(sctx->edgealpha+3*(3+5*si),-1,-1,-1)((sctx->edgealpha+3*(3+5*si))[0] = (-1), (sctx->edgealpha
+3*(3+5*si))[1] = (-1), (sctx->edgealpha+3*(3+5*si))[2] = (
-1));

1267

sctx->treated[si]&=0xFF^_SEEK_TREATED_EDGE30x10;

1268

1269

ELL_3V_SET(sctx->edgealpha+3*(4+5*si),-1,-1,-1)((sctx->edgealpha+3*(4+5*si))[0] = (-1), (sctx->edgealpha
+3*(4+5*si))[1] = (-1), (sctx->edgealpha+3*(4+5*si))[2] = (
-1));

1270

sctx->treated[si]&=0xFF^_SEEK_TREATED_EDGE40x20;

1271

}

1272

}

1273

1274

/* find missing deg. points, edge intersections, normals, and

1275

* connectivity on the four unique faces

1276

* this is done in a separate pass to make sure that all edge information

1277

* has been updated */

1278

for (yi=0; yi<sy; yi++) {

1279

for (xi=0; xi<sx; xi++) {

1280

si = xi + sx*yi;

1281

if (sctx->treated[si]&_SEEK_TREATED_FACE30x40) {

1282

/* we can copy previous results */

1283

ELL_2V_COPY(sctx->facecoord+2*(0+4*si), sctx->facecoord+2*(3+4*si))((sctx->facecoord+2*(0+4*si))[0] = (sctx->facecoord+2*(
3+4*si))[0], (sctx->facecoord+2*(0+4*si))[1] = (sctx->facecoord
+2*(3+4*si))[1]);

1284

ELL_3V_COPY(sctx->faceicoord+3*(0+4*si), sctx->faceicoord+3*(3+4*si))((sctx->faceicoord+3*(0+4*si))[0] = (sctx->faceicoord+3
*(3+4*si))[0], (sctx->faceicoord+3*(0+4*si))[1] = (sctx->
faceicoord+3*(3+4*si))[1], (sctx->faceicoord+3*(0+4*si))[2
] = (sctx->faceicoord+3*(3+4*si))[2]);

1285

ELL_3V_COPY(sctx->facenorm+3*(0+4*si), sctx->facenorm+3*(3+4*si))((sctx->facenorm+3*(0+4*si))[0] = (sctx->facenorm+3*(3+
4*si))[0], (sctx->facenorm+3*(0+4*si))[1] = (sctx->facenorm
+3*(3+4*si))[1], (sctx->facenorm+3*(0+4*si))[2] = (sctx->
facenorm+3*(3+4*si))[2]);

1286

for (i=0; i<3; i++)

1287

ELL_4V_COPY(sctx->pairs+12*(0+4*si)+4*i, sctx->pairs+12*(3+4*si)+4*i)((sctx->pairs+12*(0+4*si)+4*i)[0] = (sctx->pairs+12*(3+
4*si)+4*i)[0], (sctx->pairs+12*(0+4*si)+4*i)[1] = (sctx->
pairs+12*(3+4*si)+4*i)[1], (sctx->pairs+12*(0+4*si)+4*i)[2
] = (sctx->pairs+12*(3+4*si)+4*i)[2], (sctx->pairs+12*(
0+4*si)+4*i)[3] = (sctx->pairs+12*(3+4*si)+4*i)[3]);

1288

} else if (xi!=sx-1 && yi!=sy-1) {

1289

if (sctx->treated[si]&_SEEK_TREATED_REQUEST0x01)

1290

connectFace(sctx, bag, xi, yi, 0);

1291

else

1292

ELL_4V_SET(sctx->pairs+12*(0+4*si),-1,-1,-1,-1)((sctx->pairs+12*(0+4*si))[0] = (-1), (sctx->pairs+12*(
0+4*si))[1] = (-1), (sctx->pairs+12*(0+4*si))[2] = (-1), (
sctx->pairs+12*(0+4*si))[3] = (-1));

1293

}

1294

if (xi!=sx-1) {

1295

if (sctx->treated[si]&_SEEK_TREATED_REQUEST0x01 ||

1296

(yi!=0 && sctx->treated[xi+sx*(yi-1)]&_SEEK_TREATED_REQUEST0x01))

1297

connectFace(sctx, bag, xi, yi, 1);

1298

else ELL_4V_SET(sctx->pairs+12*(1+4*si),-1,-1,-1,-1)((sctx->pairs+12*(1+4*si))[0] = (-1), (sctx->pairs+12*(
1+4*si))[1] = (-1), (sctx->pairs+12*(1+4*si))[2] = (-1), (
sctx->pairs+12*(1+4*si))[3] = (-1));

1299

}

1300

if (yi!=sy-1) {

1301

if (sctx->treated[si]&_SEEK_TREATED_REQUEST0x01 ||

1302

(xi!=0 && sctx->treated[xi-1+sx*yi]&_SEEK_TREATED_REQUEST0x01))

1303

connectFace(sctx, bag, xi, yi, 2);

1304

else ELL_4V_SET(sctx->pairs+12*(2+4*si),-1,-1,-1,-1)((sctx->pairs+12*(2+4*si))[0] = (-1), (sctx->pairs+12*(
2+4*si))[1] = (-1), (sctx->pairs+12*(2+4*si))[2] = (-1), (
sctx->pairs+12*(2+4*si))[3] = (-1));

1305

if (xi!=sx-1) {

1306

if (sctx->treated[si]&_SEEK_TREATED_REQUEST0x01) {

1307

connectFace(sctx, bag, xi, yi, 3);

1308

sctx->treated[si]|=_SEEK_TREATED_FACE30x40;

1309

} else {

1310

ELL_4V_SET(sctx->pairs+12*(3+4*si),-1,-1,-1,-1)((sctx->pairs+12*(3+4*si))[0] = (-1), (sctx->pairs+12*(
3+4*si))[1] = (-1), (sctx->pairs+12*(3+4*si))[2] = (-1), (
sctx->pairs+12*(3+4*si))[3] = (-1));

1311

sctx->treated[si]&=0xFF^_SEEK_TREATED_FACE30x40;

1312

}

1313

}

1314

}

1315

}

1316

}

1317

}

1318

1319

/* special triangulation routine for use with T-based extraction */

1320

int

1321

_seekTriangulateT(seekContext *sctx, baggage *bag, limnPolyData *lpld) {

1322

unsigned xi, yi, sx, sy, si, i;

1323

1324

/* map edge indices w.r.t. faces (as used in sctx->pairs) back to

1325

* edge indices w.r.t. voxel */

1326

char edges[6][5]={{0, 2, 3, 1,12},

1327

{0, 5, 8, 4,13},

1328

{2, 7,10, 5,14},

1329

{3, 7,11, 6,15},

1330

{1, 6, 9, 4,16},

1331

{8,10,11, 9,17}};

1332

1333

sx = AIR_CAST(unsigned int, sctx->sx)((unsigned int)(sctx->sx));

1334

sy = AIR_CAST(unsigned int, sctx->sy)((unsigned int)(sctx->sy));

1335

1336

for (yi=0; yi<sy-1; yi++) {

1337

for (xi=0; xi<sx-1; xi++) {

1338

int fvti[6]; /* indices into unique face array */

1339

char connections[84];/* (12 edges * 3 possible intersections+6 faces)*2 */

1340

char degeneracies[6];

1341

int degct=0;

1342

1343

unsigned int face;

1344

1345

if (sctx->strengthUse && sctx->stng[0+2*(xi+sx*yi)] < sctx->strength &&

1346

sctx->stng[1+2*(xi+sx*yi)] < sctx->strength &&

1347

sctx->stng[0+2*(xi+1+sx*yi)] < sctx->strength &&

1348

sctx->stng[1+2*(xi+1+sx*yi)] < sctx->strength &&

1349

sctx->stng[0+2*(xi+sx*(yi+1))] < sctx->strength &&

1350

sctx->stng[1+2*(xi+sx*(yi+1))] < sctx->strength &&

1351

sctx->stng[0+2*(xi+1+sx*(yi+1))] < sctx->strength &&

1352

sctx->stng[1+2*(xi+1+sx*(yi+1))] < sctx->strength)

1353

continue;/* all vertices below strength limit, do not create geometry */

1354

1355

si = xi + sx*yi;

1356

ELL_3V_SET(fvti, 0 + 4*si, 1 + 4*si, 2 + 4*(xi+1 + sx*yi))((fvti)[0] = (0 + 4*si), (fvti)[1] = (1 + 4*si), (fvti)[2] = (
2 + 4*(xi+1 + sx*yi)));

1357

ELL_3V_SET(fvti+3, 1 + 4*(xi + sx*(yi+1)), 2 + 4*si, 3 + 4*si)((fvti+3)[0] = (1 + 4*(xi + sx*(yi+1))), (fvti+3)[1] = (2 + 4
*si), (fvti+3)[2] = (3 + 4*si));

1358

1359

/* collect all intersection + connectivity info for this voxel */

1360

memset(connections,-1,sizeof(connections))__builtin___memset_chk (connections, -1, sizeof(connections),
__builtin_object_size (connections, 0));

1361

for (face=0; face<6; face++) {

1362

for (i=0; i<6; i++) {

1363

int idx1, offset1, idx2, offset2, idxmap1, idxmap2;

1364

if (sctx->pairs[12*fvti[face]+2*i]==-1) break;

1365

idx1=edges[face][sctx->pairs[12*fvti[face]+2*i]/3];

1366

offset1=sctx->pairs[12*fvti[face]+2*i]%3;

1367

idx2=edges[face][sctx->pairs[12*fvti[face]+2*i+1]/3];

1368

offset2=sctx->pairs[12*fvti[face]+2*i+1]%3;

1369

idxmap1=3*idx1+offset1;

1370

idxmap2=3*idx2+offset2;

1371

if (idx1>11) {

1372

idxmap1=idx1+24; /* +36-12 */

1373

degeneracies[degct++] = idxmap1;

1374

}

1375

if (idx2>11) {

1376

idxmap2=idx2+24;

1377

degeneracies[degct++] = idxmap2;

1378

}

1379

1380

if (connections[2*idxmap1]==-1)

1381

connections[2*idxmap1]=idxmap2;

1382

else

1383

connections[2*idxmap1+1]=idxmap2;

1384

if (connections[2*idxmap2]==-1)

1385

connections[2*idxmap2]=idxmap1;

1386

else

1387

connections[2*idxmap2+1]=idxmap1;

1388

}

1389

}

1390

1391

/* connect the degenerate points */

1392

if (degct==2) {

1393

connections[2*degeneracies[0]+1]=degeneracies[1];

1394

connections[2*degeneracies[1]+1]=degeneracies[0];

1395

} else if (degct==4) {

1396

int bestchoice=0;

1397

int eidcs[4], fidcs[4];

1398

int k;

1399

double bestscore, score;

1400

for (k=0; k<4; ++k) {

1401

eidcs[k]=3*(bag->evti[connections[2*degeneracies[k]]/3]+5*si)+

1402

connections[2*degeneracies[k]]%3;

1403

fidcs[k]=fvti[degeneracies[k]-36];

1404

}

1405

bestscore=evaluateDegConnection(sctx->edgeicoord+3*eidcs[0],

1406

sctx->faceicoord+3*fidcs[0],

1407

sctx->faceicoord+3*fidcs[1],

1408

sctx->edgeicoord+3*eidcs[1],

1409

sctx->edgeicoord+3*eidcs[2],

1410

sctx->faceicoord+3*fidcs[2],

1411

sctx->faceicoord+3*fidcs[3],

1412

sctx->edgeicoord+3*eidcs[3],

1413

NULL((void*)0), NULL((void*)0), NULL((void*)0), NULL((void*)0),

1414

sctx->facenorm+3*fidcs[0],

1415

sctx->facenorm+3*fidcs[1],

1416

sctx->facenorm+3*fidcs[2],

1417

sctx->facenorm+3*fidcs[3],

1418

NULL((void*)0), NULL((void*)0));

1419

score=evaluateDegConnection(sctx->edgeicoord+3*eidcs[0],

1420

sctx->faceicoord+3*fidcs[0],

1421

sctx->faceicoord+3*fidcs[2],

1422

sctx->edgeicoord+3*eidcs[2],

1423

sctx->edgeicoord+3*eidcs[1],

1424

sctx->faceicoord+3*fidcs[1],

1425

sctx->faceicoord+3*fidcs[3],

1426

sctx->edgeicoord+3*eidcs[3],

1427

NULL((void*)0), NULL((void*)0), NULL((void*)0), NULL((void*)0),

1428

sctx->facenorm+3*fidcs[0],

1429

sctx->facenorm+3*fidcs[2],

1430

sctx->facenorm+3*fidcs[1],

1431

sctx->facenorm+3*fidcs[3],

1432

NULL((void*)0), NULL((void*)0));

1433

if (score<bestscore) {

1434

bestscore=score;

1435

bestchoice=1;

1436

}

1437

score=evaluateDegConnection(sctx->edgeicoord+3*eidcs[0],

1438

sctx->faceicoord+3*fidcs[0],

1439

sctx->faceicoord+3*fidcs[3],

1440

sctx->edgeicoord+3*eidcs[3],

1441

sctx->edgeicoord+3*eidcs[1],

1442

sctx->faceicoord+3*fidcs[1],

1443

sctx->faceicoord+3*fidcs[2],

1444

sctx->edgeicoord+3*eidcs[2],

1445

NULL((void*)0), NULL((void*)0), NULL((void*)0), NULL((void*)0),

1446

sctx->facenorm+3*fidcs[0],

1447

sctx->facenorm+3*fidcs[3],

1448

sctx->facenorm+3*fidcs[1],

1449

sctx->facenorm+3*fidcs[2],

1450

NULL((void*)0), NULL((void*)0));

1451

if (score<bestscore) {

1452

bestscore=score;

1453

bestchoice=2;

1454

}

1455

switch (bestchoice) {

1456

case 0: connections[2*degeneracies[0]+1]=degeneracies[1];

1457

connections[2*degeneracies[1]+1]=degeneracies[0];

1458

connections[2*degeneracies[2]+1]=degeneracies[3];

1459

connections[2*degeneracies[3]+1]=degeneracies[2];

1460

break;

1461

case 1: connections[2*degeneracies[0]+1]=degeneracies[2];

1462

connections[2*degeneracies[2]+1]=degeneracies[0];

1463

connections[2*degeneracies[1]+1]=degeneracies[3];

1464

connections[2*degeneracies[3]+1]=degeneracies[1];

1465

break;

1466

case 2: connections[2*degeneracies[0]+1]=degeneracies[3];

1467

connections[2*degeneracies[3]+1]=degeneracies[0];

1468

connections[2*degeneracies[1]+1]=degeneracies[2];

1469

connections[2*degeneracies[2]+1]=degeneracies[1];

1470

break;

1471

}

1472

} else if (degct==6) {

1473

int bestchoice=0;

1474

int eidcs[6], fidcs[6];

1475

int k;

1476

double bestscore;

1477

int pairings[15][6]={{0,1,2,3,4,5},{0,1,2,4,3,5},{0,1,2,5,3,4},

1478

{0,2,1,3,4,5},{0,2,1,4,3,5},{0,2,1,5,3,4},

1479

{0,3,1,2,4,5},{0,3,1,4,2,5},{0,3,1,5,2,4},

1480

{0,4,1,2,3,5},{0,4,1,3,2,5},{0,4,1,5,2,3},

1481

{0,5,1,2,3,4},{0,5,1,3,2,4},{0,5,1,4,2,3}};

1482

for (k=0; k<6; ++k) {

1483

eidcs[k]=3*(bag->evti[connections[2*degeneracies[k]]/3]+5*si)+

1484

connections[2*degeneracies[k]]%3;

1485

fidcs[k]=fvti[degeneracies[k]-36];

1486

}

1487

bestscore=evaluateDegConnection(sctx->edgeicoord+3*eidcs[0],

1488

sctx->faceicoord+3*fidcs[0],

1489

sctx->faceicoord+3*fidcs[1],

1490

sctx->edgeicoord+3*eidcs[1],

1491

sctx->edgeicoord+3*eidcs[2],

1492

sctx->faceicoord+3*fidcs[2],

1493

sctx->faceicoord+3*fidcs[3],

1494

sctx->edgeicoord+3*eidcs[3],

1495

sctx->edgeicoord+3*eidcs[4],

1496

sctx->faceicoord+3*fidcs[4],

1497

sctx->faceicoord+3*fidcs[5],

1498

sctx->edgeicoord+3*eidcs[5],

1499

sctx->facenorm+3*fidcs[0],

1500

sctx->facenorm+3*fidcs[1],

1501

sctx->facenorm+3*fidcs[2],

1502

sctx->facenorm+3*fidcs[3],

1503

sctx->facenorm+3*fidcs[4],

1504

sctx->facenorm+3*fidcs[5]);

1505

for (k=1; k<15; ++k) {

1506

double score=evaluateDegConnection

1507

(sctx->edgeicoord+3*eidcs[pairings[k][0]],

1508

sctx->faceicoord+3*fidcs[pairings[k][0]],

1509

sctx->faceicoord+3*fidcs[pairings[k][1]],

1510

sctx->edgeicoord+3*eidcs[pairings[k][1]],

1511

sctx->edgeicoord+3*eidcs[pairings[k][2]],

1512

sctx->faceicoord+3*fidcs[pairings[k][2]],

1513

sctx->faceicoord+3*fidcs[pairings[k][3]],

1514

sctx->edgeicoord+3*eidcs[pairings[k][3]],

1515

sctx->edgeicoord+3*eidcs[pairings[k][4]],

1516

sctx->faceicoord+3*fidcs[pairings[k][4]],

1517

sctx->faceicoord+3*fidcs[pairings[k][5]],

1518

sctx->edgeicoord+3*eidcs[pairings[k][5]],

1519

sctx->facenorm+3*fidcs[pairings[k][0]],

1520

sctx->facenorm+3*fidcs[pairings[k][1]],

1521

sctx->facenorm+3*fidcs[pairings[k][2]],

1522

sctx->facenorm+3*fidcs[pairings[k][3]],

1523

sctx->facenorm+3*fidcs[pairings[k][4]],

1524

sctx->facenorm+3*fidcs[pairings[k][5]]);

1525

if (score<bestscore) {

1526

bestscore=score; bestchoice=k;

1527

}

1528

}

1529

connections[2*degeneracies[pairings[bestchoice][0]]+1]=

1530

degeneracies[pairings[bestchoice][1]];

1531

connections[2*degeneracies[pairings[bestchoice][1]]+1]=

1532

degeneracies[pairings[bestchoice][0]];

1533

connections[2*degeneracies[pairings[bestchoice][2]]+1]=

1534

degeneracies[pairings[bestchoice][3]];

1535

connections[2*degeneracies[pairings[bestchoice][3]]+1]=

1536

degeneracies[pairings[bestchoice][2]];

1537

connections[2*degeneracies[pairings[bestchoice][4]]+1]=

1538

degeneracies[pairings[bestchoice][5]];

1539

connections[2*degeneracies[pairings[bestchoice][5]]+1]=

1540

degeneracies[pairings[bestchoice][4]];

1541

}

1542

1543

/* sufficient to run to 36: each polygon will contain at least

1544

* one edge vertex */

1545

for (i=0; i<36; i++) {

1546

if (connections[2*i]!=-1) {

1547

/* extract polygon from connections array */

1548

signed char polygon[42];

1549

unsigned char polyct=0;

1550

char thiz=i;

1551

char next=connections[2*i];

1552

polygon[polyct++]=i;

1553

connections[2*i]=-1;

1554

while (next!=-1) {

1555

char helpnext;

1556

polygon[polyct++]=next;

1557

if (connections[2*next]==thiz) {

1558

helpnext=connections[2*next+1];

1559

} else {

1560

helpnext=connections[2*next];

1561

}

1562

connections[2*next]=connections[2*next+1]=-1;

1563

thiz = next; next = helpnext;

1564

if (next==polygon[0])

1565

break; /* polygon is closed */

1566

}

1567

if (next!=-1) { /* else: discard unclosed polygon */

1568

/* make sure all required vertices are there */

1569

int j;

1570

for (j=0; j<polyct; ++j) {

1571

double tvertA[4], tvertB[4];

1572

if (polygon[j]<36) { /* we may need to insert an edge vertex */

1573

int eidx=3*(bag->evti[polygon[j]/3] + 5*si)+polygon[j]%3;

1574

if (-1 == sctx->vidx[eidx]) {

1575

int ovi;

1576

ELL_3V_COPY(tvertA, sctx->edgeicoord+3*eidx)((tvertA)[0] = (sctx->edgeicoord+3*eidx)[0], (tvertA)[1] =
(sctx->edgeicoord+3*eidx)[1], (tvertA)[2] = (sctx->edgeicoord
+3*eidx)[2]);

1577

tvertA[3]=1.0;

1578

1579

/* tvertB in input index space */

1580

ELL_4MV_MUL(tvertB, sctx->txfIdx, tvertA)((tvertB)[0]=(sctx->txfIdx)[ 0]*(tvertA)[0]+(sctx->txfIdx
)[ 1]*(tvertA)[1]+(sctx->txfIdx)[ 2]*(tvertA)[2]+(sctx->
txfIdx)[ 3]*(tvertA)[3], (tvertB)[1]=(sctx->txfIdx)[ 4]*(tvertA
)[0]+(sctx->txfIdx)[ 5]*(tvertA)[1]+(sctx->txfIdx)[ 6]*
(tvertA)[2]+(sctx->txfIdx)[ 7]*(tvertA)[3], (tvertB)[2]=(sctx
->txfIdx)[ 8]*(tvertA)[0]+(sctx->txfIdx)[ 9]*(tvertA)[1
]+(sctx->txfIdx)[10]*(tvertA)[2]+(sctx->txfIdx)[11]*(tvertA
)[3], (tvertB)[3]=(sctx->txfIdx)[12]*(tvertA)[0]+(sctx->
txfIdx)[13]*(tvertA)[1]+(sctx->txfIdx)[14]*(tvertA)[2]+(sctx
->txfIdx)[15]*(tvertA)[3]);

1581

/* tvertA in world space */

1582

ELL_4MV_MUL(tvertA, sctx->shape->ItoW, tvertB)((tvertA)[0]=(sctx->shape->ItoW)[ 0]*(tvertB)[0]+(sctx->
shape->ItoW)[ 1]*(tvertB)[1]+(sctx->shape->ItoW)[ 2]
*(tvertB)[2]+(sctx->shape->ItoW)[ 3]*(tvertB)[3], (tvertA
)[1]=(sctx->shape->ItoW)[ 4]*(tvertB)[0]+(sctx->shape
->ItoW)[ 5]*(tvertB)[1]+(sctx->shape->ItoW)[ 6]*(tvertB
)[2]+(sctx->shape->ItoW)[ 7]*(tvertB)[3], (tvertA)[2]=(
sctx->shape->ItoW)[ 8]*(tvertB)[0]+(sctx->shape->
ItoW)[ 9]*(tvertB)[1]+(sctx->shape->ItoW)[10]*(tvertB)[
2]+(sctx->shape->ItoW)[11]*(tvertB)[3], (tvertA)[3]=(sctx
->shape->ItoW)[12]*(tvertB)[0]+(sctx->shape->ItoW
)[13]*(tvertB)[1]+(sctx->shape->ItoW)[14]*(tvertB)[2]+(
sctx->shape->ItoW)[15]*(tvertB)[3]);

1583

ELL_4V_HOMOG(tvertA, tvertA)((tvertA)[0] = (tvertA)[0]/(tvertA)[3], (tvertA)[1] = (tvertA
)[1]/(tvertA)[3], (tvertA)[2] = (tvertA)[2]/(tvertA)[3], (tvertA
)[3] = 1.0);

1584

1585

ovi = sctx->vidx[eidx] =

1586

airArrayLenIncr(bag->xyzwArr, 1);

1587

ELL_4V_SET_TT(lpld->xyzw + 4*ovi, float,((lpld->xyzw + 4*ovi)[0] = ((float)((tvertA[0]))), (lpld->
xyzw + 4*ovi)[1] = ((float)((tvertA[1]))), (lpld->xyzw + 4
*ovi)[2] = ((float)((tvertA[2]))), (lpld->xyzw + 4*ovi)[3]
= ((float)((1.0))))

1588

tvertA[0], tvertA[1], tvertA[2], 1.0)((lpld->xyzw + 4*ovi)[0] = ((float)((tvertA[0]))), (lpld->
xyzw + 4*ovi)[1] = ((float)((tvertA[1]))), (lpld->xyzw + 4
*ovi)[2] = ((float)((tvertA[2]))), (lpld->xyzw + 4*ovi)[3]
= ((float)((1.0))));

1589

1590

if (sctx->normalsFind) {

1591

double len=ELL_3V_LEN(sctx->edgenorm+3*eidx)(sqrt((((sctx->edgenorm+3*eidx))[0]*((sctx->edgenorm+3*
eidx))[0] + ((sctx->edgenorm+3*eidx))[1]*((sctx->edgenorm
+3*eidx))[1] + ((sctx->edgenorm+3*eidx))[2]*((sctx->edgenorm
+3*eidx))[2])));

1592

airArrayLenIncr(bag->normArr, 1);

1593

ELL_3V_SCALE_TT(lpld->norm + 3*ovi, float, 1.0/len,((lpld->norm + 3*ovi)[0] = ((float)((1.0/len)*(sctx->edgenorm
+3*eidx)[0])), (lpld->norm + 3*ovi)[1] = ((float)((1.0/len
)*(sctx->edgenorm+3*eidx)[1])), (lpld->norm + 3*ovi)[2]
= ((float)((1.0/len)*(sctx->edgenorm+3*eidx)[2])))

1594

sctx->edgenorm+3*eidx)((lpld->norm + 3*ovi)[0] = ((float)((1.0/len)*(sctx->edgenorm
+3*eidx)[0])), (lpld->norm + 3*ovi)[1] = ((float)((1.0/len
)*(sctx->edgenorm+3*eidx)[1])), (lpld->norm + 3*ovi)[2]
= ((float)((1.0/len)*(sctx->edgenorm+3*eidx)[2])));

1595

}

1596

1597

sctx->vertNum++;

1598

}

1599

} else { /* we may need to insert a face vertex */

1600

int fidx=fvti[polygon[j]-36];

1601

if (-1 == sctx->facevidx[fidx]) {

1602

int ovi;

1603

ELL_3V_COPY(tvertA, sctx->faceicoord+3*fidx)((tvertA)[0] = (sctx->faceicoord+3*fidx)[0], (tvertA)[1] =
(sctx->faceicoord+3*fidx)[1], (tvertA)[2] = (sctx->faceicoord
+3*fidx)[2]);

1604

tvertA[3]=1.0;

1605

/* tvertB in input index space */

1606

1607

/* tvertA in world space */

1608

1609

ELL_4V_HOMOG(tvertA, tvertA)((tvertA)[0] = (tvertA)[0]/(tvertA)[3], (tvertA)[1] = (tvertA
)[1]/(tvertA)[3], (tvertA)[2] = (tvertA)[2]/(tvertA)[3], (tvertA
)[3] = 1.0);

1610

1611

ovi = sctx->facevidx[fidx] =

1612

airArrayLenIncr(bag->xyzwArr, 1);

1613

1614

1615

1616

if (sctx->normalsFind) {

1617

double len=ELL_3V_LEN(sctx->facenorm+3*fidx)(sqrt((((sctx->facenorm+3*fidx))[0]*((sctx->facenorm+3*
fidx))[0] + ((sctx->facenorm+3*fidx))[1]*((sctx->facenorm
+3*fidx))[1] + ((sctx->facenorm+3*fidx))[2]*((sctx->facenorm
+3*fidx))[2])));

1618

airArrayLenIncr(bag->normArr, 1);

1619

ELL_3V_SCALE_TT(lpld->norm + 3*ovi, float, 1.0/len,((lpld->norm + 3*ovi)[0] = ((float)((1.0/len)*(sctx->facenorm
+3*fidx)[0])), (lpld->norm + 3*ovi)[1] = ((float)((1.0/len
)*(sctx->facenorm+3*fidx)[1])), (lpld->norm + 3*ovi)[2]
= ((float)((1.0/len)*(sctx->facenorm+3*fidx)[2])))

1620

sctx->facenorm+3*fidx)((lpld->norm + 3*ovi)[0] = ((float)((1.0/len)*(sctx->facenorm
+3*fidx)[0])), (lpld->norm + 3*ovi)[1] = ((float)((1.0/len
)*(sctx->facenorm+3*fidx)[1])), (lpld->norm + 3*ovi)[2]
= ((float)((1.0/len)*(sctx->facenorm+3*fidx)[2])));

1621

}

1622

1623

sctx->vertNum++;

1624

}

1625

}

1626

}

1627

if (polyct>4) { /* we need to insert a helper vertex */

1628

double tvertA[4], tvertB[4], tvertAsum[4]={0,0,0,0},

1629

normsum[3]={0,0,0};

1630

int ovi;

1631

unsigned int vii[3];

1632

1633

for (j=0; j<polyct; j++) {

1634

if (polygon[j]<36) {

1635

int eidx=3*(bag->evti[polygon[j]/3] + 5*si)+polygon[j]%3;

1636

ELL_3V_COPY(tvertA, sctx->edgeicoord+3*eidx)((tvertA)[0] = (sctx->edgeicoord+3*eidx)[0], (tvertA)[1] =
(sctx->edgeicoord+3*eidx)[1], (tvertA)[2] = (sctx->edgeicoord
+3*eidx)[2]);

1637

tvertA[3]=1.0;

1638

ELL_4V_INCR(tvertAsum,tvertA)((tvertAsum)[0] += (tvertA)[0], (tvertAsum)[1] += (tvertA)[1]
, (tvertAsum)[2] += (tvertA)[2], (tvertAsum)[3] += (tvertA)[3
]);

1639

if (ELL_3V_DOT(normsum,sctx->edgenorm+3*eidx)((normsum)[0]*(sctx->edgenorm+3*eidx)[0] + (normsum)[1]*(sctx
->edgenorm+3*eidx)[1] + (normsum)[2]*(sctx->edgenorm+3*
eidx)[2])<0)

1640

ELL_3V_SUB(normsum,normsum,sctx->edgenorm+3*eidx)((normsum)[0] = (normsum)[0] - (sctx->edgenorm+3*eidx)[0],
(normsum)[1] = (normsum)[1] - (sctx->edgenorm+3*eidx)[1],
(normsum)[2] = (normsum)[2] - (sctx->edgenorm+3*eidx)[2]);

1641

else

1642

ELL_3V_INCR(normsum,sctx->edgenorm+3*eidx)((normsum)[0] += (sctx->edgenorm+3*eidx)[0], (normsum)[1] +=
(sctx->edgenorm+3*eidx)[1], (normsum)[2] += (sctx->edgenorm
+3*eidx)[2]);

1643

} else {

1644

int fidx=fvti[polygon[j]-36];

1645

ELL_3V_COPY(tvertA, sctx->faceicoord+3*fidx)((tvertA)[0] = (sctx->faceicoord+3*fidx)[0], (tvertA)[1] =
(sctx->faceicoord+3*fidx)[1], (tvertA)[2] = (sctx->faceicoord
+3*fidx)[2]);

1646

tvertA[3]=1.0;

1647

ELL_4V_INCR(tvertAsum,tvertA)((tvertAsum)[0] += (tvertA)[0], (tvertAsum)[1] += (tvertA)[1]
, (tvertAsum)[2] += (tvertA)[2], (tvertAsum)[3] += (tvertA)[3
]);

1648

if (ELL_3V_DOT(normsum,sctx->facenorm+3*fidx)((normsum)[0]*(sctx->facenorm+3*fidx)[0] + (normsum)[1]*(sctx
->facenorm+3*fidx)[1] + (normsum)[2]*(sctx->facenorm+3*
fidx)[2])<0)

1649

ELL_3V_SUB(normsum,normsum,sctx->facenorm+3*fidx)((normsum)[0] = (normsum)[0] - (sctx->facenorm+3*fidx)[0],
(normsum)[1] = (normsum)[1] - (sctx->facenorm+3*fidx)[1],
(normsum)[2] = (normsum)[2] - (sctx->facenorm+3*fidx)[2]);

1650

else

1651

ELL_3V_INCR(normsum,sctx->facenorm+3*fidx)((normsum)[0] += (sctx->facenorm+3*fidx)[0], (normsum)[1] +=
(sctx->facenorm+3*fidx)[1], (normsum)[2] += (sctx->facenorm
+3*fidx)[2]);

1652

}

1653

}

1654

/* tvertB in input index space */

1655

ELL_4MV_MUL(tvertB, sctx->txfIdx, tvertAsum)((tvertB)[0]=(sctx->txfIdx)[ 0]*(tvertAsum)[0]+(sctx->txfIdx
)[ 1]*(tvertAsum)[1]+(sctx->txfIdx)[ 2]*(tvertAsum)[2]+(sctx
->txfIdx)[ 3]*(tvertAsum)[3], (tvertB)[1]=(sctx->txfIdx
)[ 4]*(tvertAsum)[0]+(sctx->txfIdx)[ 5]*(tvertAsum)[1]+(sctx
->txfIdx)[ 6]*(tvertAsum)[2]+(sctx->txfIdx)[ 7]*(tvertAsum
)[3], (tvertB)[2]=(sctx->txfIdx)[ 8]*(tvertAsum)[0]+(sctx->
txfIdx)[ 9]*(tvertAsum)[1]+(sctx->txfIdx)[10]*(tvertAsum)[
2]+(sctx->txfIdx)[11]*(tvertAsum)[3], (tvertB)[3]=(sctx->
txfIdx)[12]*(tvertAsum)[0]+(sctx->txfIdx)[13]*(tvertAsum)[
1]+(sctx->txfIdx)[14]*(tvertAsum)[2]+(sctx->txfIdx)[15]
*(tvertAsum)[3]);

1656

/* tvertA in world space */

1657

1658

ELL_4V_HOMOG(tvertA, tvertA)((tvertA)[0] = (tvertA)[0]/(tvertA)[3], (tvertA)[1] = (tvertA
)[1]/(tvertA)[3], (tvertA)[2] = (tvertA)[2]/(tvertA)[3], (tvertA
)[3] = 1.0);

1659

1660

ovi = airArrayLenIncr(bag->xyzwArr, 1);

1661

1662

1663

if (sctx->normalsFind) {

1664

double len=ELL_3V_LEN(normsum)(sqrt((((normsum))[0]*((normsum))[0] + ((normsum))[1]*((normsum
))[1] + ((normsum))[2]*((normsum))[2])));

1665

airArrayLenIncr(bag->normArr, 1);

1666

ELL_3V_SCALE_TT(lpld->norm + 3*ovi, float, 1.0/len, normsum)((lpld->norm + 3*ovi)[0] = ((float)((1.0/len)*(normsum)[0]
)), (lpld->norm + 3*ovi)[1] = ((float)((1.0/len)*(normsum)
[1])), (lpld->norm + 3*ovi)[2] = ((float)((1.0/len)*(normsum
)[2])));

1667

}

1668

sctx->vertNum++;

1669

1670

vii[0]=ovi;

1671

vii[1]=sctx->vidx[3*(bag->evti[polygon[0]/3]+5*si)+polygon[0]%3];

1672

for (j=0; j<polyct; ++j) {

1673

double edgeA[3], edgeB[3];

1674

double norm[3];

1675

vii[2]=vii[1];

1676

if (j==polyct-1) {

1677

if (polygon[0]<36)

1678

vii[1]=sctx->vidx[3*(bag->evti[polygon[0]/3] + 5*si)+

1679

polygon[0]%3];

1680

else vii[1]=sctx->facevidx[fvti[polygon[0]-36]];

1681

} else {

1682

if (polygon[j+1]<36)

1683

vii[1]=sctx->vidx[3*(bag->evti[polygon[j+1]/3] + 5*si)+

1684

polygon[j+1]%3];

1685

else vii[1]=sctx->facevidx[fvti[polygon[j+1]-36]];

1686

}

1687

1688

/* check for degenerate tris */

1689

ELL_3V_SUB(edgeA, lpld->xyzw+4*vii[1], lpld->xyzw+4*vii[0])((edgeA)[0] = (lpld->xyzw+4*vii[1])[0] - (lpld->xyzw+4*
vii[0])[0], (edgeA)[1] = (lpld->xyzw+4*vii[1])[1] - (lpld->
xyzw+4*vii[0])[1], (edgeA)[2] = (lpld->xyzw+4*vii[1])[2] -
(lpld->xyzw+4*vii[0])[2]);

1690

ELL_3V_SUB(edgeB, lpld->xyzw+4*vii[2], lpld->xyzw+4*vii[0])((edgeB)[0] = (lpld->xyzw+4*vii[2])[0] - (lpld->xyzw+4*
vii[0])[0], (edgeB)[1] = (lpld->xyzw+4*vii[2])[1] - (lpld->
xyzw+4*vii[0])[1], (edgeB)[2] = (lpld->xyzw+4*vii[2])[2] -
(lpld->xyzw+4*vii[0])[2]);

1691

ELL_3V_CROSS(norm, edgeA, edgeB)((norm)[0] = (edgeA)[1]*(edgeB)[2] - (edgeA)[2]*(edgeB)[1], (
norm)[1] = (edgeA)[2]*(edgeB)[0] - (edgeA)[0]*(edgeB)[2], (norm
)[2] = (edgeA)[0]*(edgeB)[1] - (edgeA)[1]*(edgeB)[0]);

1692

if (ELL_3V_DOT(norm,norm)((norm)[0]*(norm)[0] + (norm)[1]*(norm)[1] + (norm)[2]*(norm)
[2])!=0) {

1693

unsigned iii = airArrayLenIncr(bag->indxArr, 3);

1694

ELL_3V_COPY(lpld->indx + iii, vii)((lpld->indx + iii)[0] = (vii)[0], (lpld->indx + iii)[1
] = (vii)[1], (lpld->indx + iii)[2] = (vii)[2]);

1695

lpld->icnt[0] += 3;

1696

sctx->faceNum++;

1697

}

1698

/* else: degeneracies are caused by intersections that

1699

* more or less coincide with a grid vertex. They

1700

* should be harmless, so just don't create

1701

* deg. triangles in this case */

1702

}

1703

} else if (polyct>2) {

1704

/* insert the actual triangles */

1705

unsigned int vii[3], iii;

1706

if (polygon[0]<36)

1707

vii[0]=sctx->vidx[3*(bag->evti[polygon[0]/3] + 5*si)+

1708

polygon[0]%3];

1709

else vii[0]=sctx->facevidx[fvti[polygon[0]-36]];

1710

if (polygon[1]<36)

1711

vii[1]=sctx->vidx[3*(bag->evti[polygon[1]/3] + 5*si)+

1712

polygon[1]%3];

1713

else vii[1]=sctx->facevidx[fvti[polygon[1]-36]];

1714

if (polygon[2]<36)

1715

vii[2]=sctx->vidx[3*(bag->evti[polygon[2]/3] + 5*si)+

1716

polygon[2]%3];

1717

else vii[2]=sctx->facevidx[fvti[polygon[2]-36]];

1718

iii = airArrayLenIncr(bag->indxArr, 3);

1719

ELL_3V_COPY(lpld->indx + iii, vii)((lpld->indx + iii)[0] = (vii)[0], (lpld->indx + iii)[1
] = (vii)[1], (lpld->indx + iii)[2] = (vii)[2]);

1720

lpld->icnt[0] += 3;

1721

sctx->faceNum++;

1722

1723

if (polyct==4) {

1724

vii[1]=vii[2];

1725

if (polygon[3]<36)

1726

vii[2]=sctx->vidx[3*(bag->evti[polygon[3]/3] + 5*si)+

1727

polygon[3]%3];

1728

else vii[2]=sctx->facevidx[fvti[polygon[3]-36]];

1729

iii = airArrayLenIncr(bag->indxArr, 3);

1730

ELL_3V_COPY(lpld->indx + iii, vii)((lpld->indx + iii)[0] = (vii)[0], (lpld->indx + iii)[1
] = (vii)[1], (lpld->indx + iii)[2] = (vii)[2]);

1731

lpld->icnt[0] += 3;

1732

sctx->faceNum++;

1733

}

1734

}

1735

}

1736

}

1737

}

1738

}

1739

}

1740

return 0;

1741

}

1742

1743

static void

1744

shuffleT(seekContext *sctx, baggage *bag) {

1745

unsigned int xi, yi, sx, sy, si;

1746

1747

sx = AIR_CAST(unsigned int, sctx->sx)((unsigned int)(sctx->sx));

1748

sy = AIR_CAST(unsigned int, sctx->sy)((unsigned int)(sctx->sy));

1749

1750

if (sctx->strengthUse) { /* requests need to be cleared initially */

1751

for (yi=0; yi<sy; yi++) {

1752

for (xi=0; xi<sx; xi++) {

1753

sctx->treated[xi+sx*yi] &= 0xFF^_SEEK_TREATED_REQUEST0x01;

1754

}

1755

}

1756

} /* else, the request bits are always on */

1757

1758

for (yi=0; yi<sy; yi++) {

1759

for (xi=0; xi<sx; xi++) {

1760

si = xi + sx*yi;

1761

1762

/* vidx neither needs past nor future context */

1763

if (!bag->zi) {

1764

ELL_3V_SET(sctx->vidx+3*(0+5*si), -1, -1, -1)((sctx->vidx+3*(0+5*si))[0] = (-1), (sctx->vidx+3*(0+5*
si))[1] = (-1), (sctx->vidx+3*(0+5*si))[2] = (-1));

1765

ELL_3V_SET(sctx->vidx+3*(1+5*si), -1, -1, -1)((sctx->vidx+3*(1+5*si))[0] = (-1), (sctx->vidx+3*(1+5*
si))[1] = (-1), (sctx->vidx+3*(1+5*si))[2] = (-1));

1766

} else {

1767

ELL_3V_COPY(sctx->vidx+3*(0+5*si), sctx->vidx+3*(3+5*si))((sctx->vidx+3*(0+5*si))[0] = (sctx->vidx+3*(3+5*si))[0
], (sctx->vidx+3*(0+5*si))[1] = (sctx->vidx+3*(3+5*si))
[1], (sctx->vidx+3*(0+5*si))[2] = (sctx->vidx+3*(3+5*si
))[2]);

1768

ELL_3V_COPY(sctx->vidx+3*(1+5*si), sctx->vidx+3*(4+5*si))((sctx->vidx+3*(1+5*si))[0] = (sctx->vidx+3*(4+5*si))[0
], (sctx->vidx+3*(1+5*si))[1] = (sctx->vidx+3*(4+5*si))
[1], (sctx->vidx+3*(1+5*si))[2] = (sctx->vidx+3*(4+5*si
))[2]);

1769

}

1770

ELL_3V_SET(sctx->vidx+3*(2+5*si),-1,-1,-1)((sctx->vidx+3*(2+5*si))[0] = (-1), (sctx->vidx+3*(2+5*
si))[1] = (-1), (sctx->vidx+3*(2+5*si))[2] = (-1));

1771

ELL_3V_SET(sctx->vidx+3*(3+5*si),-1,-1,-1)((sctx->vidx+3*(3+5*si))[0] = (-1), (sctx->vidx+3*(3+5*
si))[1] = (-1), (sctx->vidx+3*(3+5*si))[2] = (-1));

1772

ELL_3V_SET(sctx->vidx+3*(4+5*si),-1,-1,-1)((sctx->vidx+3*(4+5*si))[0] = (-1), (sctx->vidx+3*(4+5*
si))[1] = (-1), (sctx->vidx+3*(4+5*si))[2] = (-1));

1773

1774

/* strength only has future context */

1775

if (sctx->strengthUse) {

1776

sctx->stng[0 + 2*si] = sctx->stng[1 + 2*si];

1777

sctx->stng[1 + 2*si] = sctx->stngcontext[si];

1778

if (sctx->stng[0+2*si]>sctx->strength ||

1779

sctx->stng[1+2*si]>sctx->strength) {

1780

/* set up to four request bits */

1781

sctx->treated[si] |= _SEEK_TREATED_REQUEST0x01;

1782

if (xi!=0) sctx->treated[xi-1+sx*yi] |= _SEEK_TREATED_REQUEST0x01;

1783

if (yi!=0) sctx->treated[xi+sx*(yi-1)] |= _SEEK_TREATED_REQUEST0x01;

1784

if (xi!=0 && yi!=0)

1785

sctx->treated[xi-1+sx*(yi-1)] |= _SEEK_TREATED_REQUEST0x01;

1786

}

1787

}

1788

1789

/* shuffle grad, hess and t in three steps: move to past context,

1790

* shuffle in slab itself, move from future context */

1791

1792

ELL_3V_COPY(sctx->gradcontext + 3*(0+2*si), sctx->grad + 3*(0+2*si))((sctx->gradcontext + 3*(0+2*si))[0] = (sctx->grad + 3*
(0+2*si))[0], (sctx->gradcontext + 3*(0+2*si))[1] = (sctx->
grad + 3*(0+2*si))[1], (sctx->gradcontext + 3*(0+2*si))[2]
= (sctx->grad + 3*(0+2*si))[2]);

1793

ELL_3V_COPY(sctx->grad + 3*(0+2*si), sctx->grad + 3*(1+2*si))((sctx->grad + 3*(0+2*si))[0] = (sctx->grad + 3*(1+2*si
))[0], (sctx->grad + 3*(0+2*si))[1] = (sctx->grad + 3*(
1+2*si))[1], (sctx->grad + 3*(0+2*si))[2] = (sctx->grad
+ 3*(1+2*si))[2]);

1794

ELL_3V_COPY(sctx->grad + 3*(1+2*si), sctx->gradcontext + 3*(1+2*si))((sctx->grad + 3*(1+2*si))[0] = (sctx->gradcontext + 3*
(1+2*si))[0], (sctx->grad + 3*(1+2*si))[1] = (sctx->gradcontext
+ 3*(1+2*si))[1], (sctx->grad + 3*(1+2*si))[2] = (sctx->
gradcontext + 3*(1+2*si))[2]);

1795

1796

ELL_3M_COPY(sctx->hesscontext + 9*(0+2*si), sctx->hess + 9*(0+2*si))((((sctx->hesscontext + 9*(0+2*si))+0)[0] = ((sctx->hess
+ 9*(0+2*si))+0)[0], ((sctx->hesscontext + 9*(0+2*si))+0)
[1] = ((sctx->hess + 9*(0+2*si))+0)[1], ((sctx->hesscontext
+ 9*(0+2*si))+0)[2] = ((sctx->hess + 9*(0+2*si))+0)[2]), (
((sctx->hesscontext + 9*(0+2*si))+3)[0] = ((sctx->hess +
9*(0+2*si))+3)[0], ((sctx->hesscontext + 9*(0+2*si))+3)[1
] = ((sctx->hess + 9*(0+2*si))+3)[1], ((sctx->hesscontext
+ 9*(0+2*si))+3)[2] = ((sctx->hess + 9*(0+2*si))+3)[2]), (
((sctx->hesscontext + 9*(0+2*si))+6)[0] = ((sctx->hess +
9*(0+2*si))+6)[0], ((sctx->hesscontext + 9*(0+2*si))+6)[1
] = ((sctx->hess + 9*(0+2*si))+6)[1], ((sctx->hesscontext
+ 9*(0+2*si))+6)[2] = ((sctx->hess + 9*(0+2*si))+6)[2]));

1797

ELL_3M_COPY(sctx->hess + 9*(0+2*si), sctx->hess + 9*(1+2*si))((((sctx->hess + 9*(0+2*si))+0)[0] = ((sctx->hess + 9*(
1+2*si))+0)[0], ((sctx->hess + 9*(0+2*si))+0)[1] = ((sctx->
hess + 9*(1+2*si))+0)[1], ((sctx->hess + 9*(0+2*si))+0)[2]
= ((sctx->hess + 9*(1+2*si))+0)[2]), (((sctx->hess + 9
*(0+2*si))+3)[0] = ((sctx->hess + 9*(1+2*si))+3)[0], ((sctx
->hess + 9*(0+2*si))+3)[1] = ((sctx->hess + 9*(1+2*si))
+3)[1], ((sctx->hess + 9*(0+2*si))+3)[2] = ((sctx->hess
+ 9*(1+2*si))+3)[2]), (((sctx->hess + 9*(0+2*si))+6)[0] =
((sctx->hess + 9*(1+2*si))+6)[0], ((sctx->hess + 9*(0+
2*si))+6)[1] = ((sctx->hess + 9*(1+2*si))+6)[1], ((sctx->
hess + 9*(0+2*si))+6)[2] = ((sctx->hess + 9*(1+2*si))+6)[2
]));

1798

ELL_3M_COPY(sctx->hess + 9*(1+2*si), sctx->hesscontext + 9*(1+2*si))((((sctx->hess + 9*(1+2*si))+0)[0] = ((sctx->hesscontext
+ 9*(1+2*si))+0)[0], ((sctx->hess + 9*(1+2*si))+0)[1] = (
(sctx->hesscontext + 9*(1+2*si))+0)[1], ((sctx->hess + 9
*(1+2*si))+0)[2] = ((sctx->hesscontext + 9*(1+2*si))+0)[2]
), (((sctx->hess + 9*(1+2*si))+3)[0] = ((sctx->hesscontext
+ 9*(1+2*si))+3)[0], ((sctx->hess + 9*(1+2*si))+3)[1] = (
(sctx->hesscontext + 9*(1+2*si))+3)[1], ((sctx->hess + 9
*(1+2*si))+3)[2] = ((sctx->hesscontext + 9*(1+2*si))+3)[2]
), (((sctx->hess + 9*(1+2*si))+6)[0] = ((sctx->hesscontext
+ 9*(1+2*si))+6)[0], ((sctx->hess + 9*(1+2*si))+6)[1] = (
(sctx->hesscontext + 9*(1+2*si))+6)[1], ((sctx->hess + 9
*(1+2*si))+6)[2] = ((sctx->hesscontext + 9*(1+2*si))+6)[2]
));

1799

1800

ELL_3M_COPY(sctx->tcontext + 9*(0+2*si), sctx->t + 9*(0+2*si))((((sctx->tcontext + 9*(0+2*si))+0)[0] = ((sctx->t + 9*
(0+2*si))+0)[0], ((sctx->tcontext + 9*(0+2*si))+0)[1] = ((
sctx->t + 9*(0+2*si))+0)[1], ((sctx->tcontext + 9*(0+2*
si))+0)[2] = ((sctx->t + 9*(0+2*si))+0)[2]), (((sctx->tcontext
+ 9*(0+2*si))+3)[0] = ((sctx->t + 9*(0+2*si))+3)[0], ((sctx
->tcontext + 9*(0+2*si))+3)[1] = ((sctx->t + 9*(0+2*si)
)+3)[1], ((sctx->tcontext + 9*(0+2*si))+3)[2] = ((sctx->
t + 9*(0+2*si))+3)[2]), (((sctx->tcontext + 9*(0+2*si))+6)
[0] = ((sctx->t + 9*(0+2*si))+6)[0], ((sctx->tcontext +
9*(0+2*si))+6)[1] = ((sctx->t + 9*(0+2*si))+6)[1], ((sctx
->tcontext + 9*(0+2*si))+6)[2] = ((sctx->t + 9*(0+2*si)
)+6)[2]));

1801

ELL_3M_COPY(sctx->t + 9*(0+2*si), sctx->t + 9*(1+2*si))((((sctx->t + 9*(0+2*si))+0)[0] = ((sctx->t + 9*(1+2*si
))+0)[0], ((sctx->t + 9*(0+2*si))+0)[1] = ((sctx->t + 9
*(1+2*si))+0)[1], ((sctx->t + 9*(0+2*si))+0)[2] = ((sctx->
t + 9*(1+2*si))+0)[2]), (((sctx->t + 9*(0+2*si))+3)[0] = (
(sctx->t + 9*(1+2*si))+3)[0], ((sctx->t + 9*(0+2*si))+3
)[1] = ((sctx->t + 9*(1+2*si))+3)[1], ((sctx->t + 9*(0+
2*si))+3)[2] = ((sctx->t + 9*(1+2*si))+3)[2]), (((sctx->
t + 9*(0+2*si))+6)[0] = ((sctx->t + 9*(1+2*si))+6)[0], ((sctx
->t + 9*(0+2*si))+6)[1] = ((sctx->t + 9*(1+2*si))+6)[1]
, ((sctx->t + 9*(0+2*si))+6)[2] = ((sctx->t + 9*(1+2*si
))+6)[2]));

1802

ELL_3M_COPY(sctx->t + 9*(1+2*si), sctx->tcontext + 9*(1+2*si))((((sctx->t + 9*(1+2*si))+0)[0] = ((sctx->tcontext + 9*
(1+2*si))+0)[0], ((sctx->t + 9*(1+2*si))+0)[1] = ((sctx->
tcontext + 9*(1+2*si))+0)[1], ((sctx->t + 9*(1+2*si))+0)[2
] = ((sctx->tcontext + 9*(1+2*si))+0)[2]), (((sctx->t +
9*(1+2*si))+3)[0] = ((sctx->tcontext + 9*(1+2*si))+3)[0],
((sctx->t + 9*(1+2*si))+3)[1] = ((sctx->tcontext + 9*(
1+2*si))+3)[1], ((sctx->t + 9*(1+2*si))+3)[2] = ((sctx->
tcontext + 9*(1+2*si))+3)[2]), (((sctx->t + 9*(1+2*si))+6)
[0] = ((sctx->tcontext + 9*(1+2*si))+6)[0], ((sctx->t +
9*(1+2*si))+6)[1] = ((sctx->tcontext + 9*(1+2*si))+6)[1],
((sctx->t + 9*(1+2*si))+6)[2] = ((sctx->tcontext + 9*(
1+2*si))+6)[2]));

1803

}

1804

}

1805

}

1806

1807

static void

1808

probeT(seekContext *sctx, baggage *bag, double zi) {

1809

unsigned int xi, yi, sx, sy, si;

1810

1811

sx = AIR_CAST(unsigned int, sctx->sx)((unsigned int)(sctx->sx));

1812

sy = AIR_CAST(unsigned int, sctx->sy)((unsigned int)(sctx->sy));

1813

1814

for (yi=0; yi<sy; yi++) {

1815

for (xi=0; xi<sx; xi++) {

1816

si = xi + sx*yi;

1817

1818

if (sctx->gctx) { /* HEY: need this check, what's the right way? */

1819

_seekIdxProbe(sctx, bag, xi, yi, zi);

1820

}

1821

if (sctx->strengthUse) {

1822

sctx->stngcontext[si] = sctx->strengthSign*sctx->stngAns[0];

1823

if (sctx->strengthSeenMax==AIR_NAN(airFloatQNaN.f)) {

1824

sctx->strengthSeenMax = sctx->stngcontext[si];

1825

}

1826

sctx->strengthSeenMax = AIR_MAX(sctx->strengthSeenMax,((sctx->strengthSeenMax) > (sctx->stngcontext[si]) ?
(sctx->strengthSeenMax) : (sctx->stngcontext[si]))

1827

sctx->stngcontext[si])((sctx->strengthSeenMax) > (sctx->stngcontext[si]) ?
(sctx->strengthSeenMax) : (sctx->stngcontext[si]));

1828

}

1829

ELL_3V_COPY(sctx->gradcontext + 3*(1 + 2*si), sctx->gradAns)((sctx->gradcontext + 3*(1 + 2*si))[0] = (sctx->gradAns
)[0], (sctx->gradcontext + 3*(1 + 2*si))[1] = (sctx->gradAns
)[1], (sctx->gradcontext + 3*(1 + 2*si))[2] = (sctx->gradAns
)[2]);

1830

ELL_3M_COPY(sctx->hesscontext + 9*(1 + 2*si), sctx->hessAns)((((sctx->hesscontext + 9*(1 + 2*si))+0)[0] = ((sctx->hessAns
)+0)[0], ((sctx->hesscontext + 9*(1 + 2*si))+0)[1] = ((sctx
->hessAns)+0)[1], ((sctx->hesscontext + 9*(1 + 2*si))+0
)[2] = ((sctx->hessAns)+0)[2]), (((sctx->hesscontext + 9
*(1 + 2*si))+3)[0] = ((sctx->hessAns)+3)[0], ((sctx->hesscontext
+ 9*(1 + 2*si))+3)[1] = ((sctx->hessAns)+3)[1], ((sctx->
hesscontext + 9*(1 + 2*si))+3)[2] = ((sctx->hessAns)+3)[2]
), (((sctx->hesscontext + 9*(1 + 2*si))+6)[0] = ((sctx->
hessAns)+6)[0], ((sctx->hesscontext + 9*(1 + 2*si))+6)[1] =
((sctx->hessAns)+6)[1], ((sctx->hesscontext + 9*(1 + 2
*si))+6)[2] = ((sctx->hessAns)+6)[2]));

1831

_seekHess2T(sctx->tcontext + 9*(1 + 2*si), sctx->evalAns, sctx->evecAns,

1832

sctx->evalDiffThresh, (sctx->type==seekTypeRidgeSurfaceT));

1833

}

1834

}

1835

}

1836

1837

/* it has now become much easier to make this its own routine

1838

* (vs. adding many more case distinctions to shuffleProbe)

1839

* this only duplicates little (and trivial) code */

1840

int

1841

_seekShuffleProbeT(seekContext *sctx, baggage *bag) {

1842

/* for high-quality normal estimation, we need two slices of data

1843

* context; to keep the code simple, separate shuffle and probe

1844

* operations - let's hope this doesn't destroy cache performance */

1845

1846

if (!bag->zi) {

1847

if (sctx->strengthUse)

1848

/* before the first round, initialize treated to zero */

1849

memset(sctx->treated, 0, sizeof(char)*sctx->sx*sctx->sy)__builtin___memset_chk (sctx->treated, 0, sizeof(char)*sctx
->sx*sctx->sy, __builtin_object_size (sctx->treated,
0));

1850

else /* request all edges */

1851

memset(sctx->treated, _SEEK_TREATED_REQUEST,__builtin___memset_chk (sctx->treated, 0x01, sizeof(char)*
sctx->sx*sctx->sy, __builtin_object_size (sctx->treated
, 0))

1852

sizeof(char)*sctx->sx*sctx->sy)__builtin___memset_chk (sctx->treated, 0x01, sizeof(char)*
sctx->sx*sctx->sy, __builtin_object_size (sctx->treated
, 0));

1853

probeT(sctx, bag, 0);

1854

shuffleT(sctx, bag);

1855

probeT(sctx, bag, 1);

1856

}

1857

shuffleT(sctx, bag);

1858

if (bag->zi!=sctx->sz-2)

1859

probeT(sctx, bag, bag->zi+2);

1860

1861

intersectionShuffleProbe(sctx, bag);

1862

1863

return 0;

1864

}

1865

1866

/* For all vertices in pld, use sctx to probe the strength measure,

1867

* and return the answer (times strengthSign) in nval. The intended

1868

* use is postfiltering (with limnPolyDataClip), which is obligatory

1869

* when using seekType*SurfaceT

1870

1871

* Returns 1 and adds a message to biff upon error

1872

* Returns 0 on success, -n when probing n vertices failed (strength

1873

* is set to AIR_NAN for those); note that positions outside the field

1874

* are clamped to lie on its boundary.

1875

1876

* This routine assumes that a strength has been set in sctx and

1877

* seekUpdate() has been run.

1878

* This routine does not modify sctx->strengthSeenMax.

1879

1880

int

1881

seekVertexStrength(Nrrd *nval, seekContext *sctx, limnPolyData *pld) {

1882

static const char me[]="seekVertexStrength";

1883

unsigned int i;

1884

double *data;

1885

int E=0;

1886

1887

if (!(nval && sctx && pld)) {

1888

biffAddf(SEEKseekBiffKey, "%s: got NULL pointer", me);

1889

return 1;

1890

}

1891

if (!(sctx->gctx && sctx->pvl)) {

1892

biffAddf(SEEKseekBiffKey, "%s: need sctx with attached gageContext", me);

1893

return 1;

1894

}

1895

if (!sctx->stngAns) {

1896

biffAddf(SEEKseekBiffKey, "%s: no strength item found. Did you enable strengthUse?",

1897

me);

1898

return 1;

1899

}

1900

if (nrrdAlloc_va(nval, nrrdTypeDouble, 1, (size_t) pld->xyzwNum)) {

1901

biffAddf(SEEKseekBiffKey, "%s: could not allocate output", me);

1902

return 1;

1903

}

1904

1905

data = (double*) nval->data;

1906

for (i=0; i<pld->xyzwNum; i++) {

1907

float homog[4];

1908

ELL_4V_HOMOG(homog, pld->xyzw+4*i)((homog)[0] = (pld->xyzw+4*i)[0]/(pld->xyzw+4*i)[3], (homog
)[1] = (pld->xyzw+4*i)[1]/(pld->xyzw+4*i)[3], (homog)[2
] = (pld->xyzw+4*i)[2]/(pld->xyzw+4*i)[3], (homog)[3] =
1.0);

1909

if (!gageProbeSpace(sctx->gctx,homog[0],homog[1],homog[2],0,1)) {

1910

*(data++)=*(sctx->stngAns)*sctx->strengthSign;

1911

} else {

1912

*(data++)=AIR_NAN(airFloatQNaN.f);

1913

E--;

1914

}

1915

}

1916

return E;

1917

}