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/* |
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Teem: Tools to process and visualize scientific data and images . |
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Copyright (C) 2013, 2012, 2011, 2010, 2009 University of Chicago |
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Copyright (C) 2008, 2007, 2006, 2005 Gordon Kindlmann |
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Copyright (C) 2004, 2003, 2002, 2001, 2000, 1999, 1998 University of Utah |
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This library is free software; you can redistribute it and/or |
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modify it under the terms of the GNU Lesser General Public License |
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(LGPL) as published by the Free Software Foundation; either |
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version 2.1 of the License, or (at your option) any later version. |
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The terms of redistributing and/or modifying this software also |
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include exceptions to the LGPL that facilitate static linking. |
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This library is distributed in the hope that it will be useful, |
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but WITHOUT ANY WARRANTY; without even the implied warranty of |
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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Lesser General Public License for more details. |
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You should have received a copy of the GNU Lesser General Public License |
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along with this library; if not, write to Free Software Foundation, Inc., |
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51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA |
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*/ |
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#include "ell.h" |
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void |
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ell_4v_norm_f(float bv[4], const float av[4]) { |
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float len; |
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len = AIR_CAST(float, ELL_4V_LEN(av)); |
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ELL_4V_SCALE(bv, 1.0f/len, av); |
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return; |
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} |
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#define PERP \ |
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idx = 0; \ |
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if (b[0]*b[0] < b[1]*b[1]) \ |
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idx = 1; \ |
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if (b[idx]*b[idx] < b[2]*b[2]) \ |
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idx = 2; \ |
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switch (idx) { \ |
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case 0: \ |
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ELL_3V_SET(a, b[1] - b[2], -b[0], b[0]); \ |
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break; \ |
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case 1: \ |
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ELL_3V_SET(a, -b[1], b[0] - b[2], b[1]); \ |
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break; \ |
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case 2: \ |
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ELL_3V_SET(a, -b[2], b[2], b[0] - b[1]); \ |
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break; \ |
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} |
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/* |
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******** ell_3v_perp_f() |
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** |
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** Given a 3-vector, produce one which is perpendicular. |
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** Output length won't be same as input length, but it will always |
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** be non-zero, if input length is non-zero. This does NOT try to |
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** produce a unit-length vector, regardless of the length of the input. |
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*/ |
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void |
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ell_3v_perp_f(float a[3], const float b[3]) { |
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int idx; |
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PERP; |
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} |
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/* |
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******** ell_3v_perp_d() |
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** |
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** same as above, but for doubles |
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*/ |
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void |
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ell_3v_perp_d(double a[3], const double b[3]) { |
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int idx; |
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✓✓✓✓
✓✓✓✓
|
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PERP; |
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} |
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void |
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ell_3mv_mul_f(float v2[3], const float m[9], const float v1[3]) { |
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float tmp[3]; |
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ELL_3MV_MUL(tmp, m, v1); |
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ELL_3V_COPY(v2, tmp); |
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} |
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void |
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ell_3mv_mul_d(double v2[3], const double m[9], const double v1[3]) { |
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double tmp[3]; |
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ELL_3MV_MUL(tmp, m, v1); |
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ELL_3V_COPY(v2, tmp); |
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} |
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void |
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ell_4mv_mul_f(float v2[4], const float m[16], const float v1[4]) { |
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float tmp[4]; |
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ELL_4MV_MUL(tmp, m, v1); |
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ELL_4V_COPY(v2, tmp); |
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} |
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void |
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ell_4mv_mul_d(double v2[4], const double m[16], const double v1[4]) { |
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double tmp[4]; |
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ELL_4MV_MUL(tmp, m, v1); |
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ELL_4V_COPY(v2, tmp); |
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} |
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/* |
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** hat tip to http://www.plunk.org/~hatch/rightway.php |
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*/ |
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float |
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ell_3v_angle_f(const float _uu[3], const float _vv[3]) { |
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float tmp[3], len, uu[3], vv[3], ret; |
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ELL_3V_NORM_TT(uu, float, _uu, len); |
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ELL_3V_NORM_TT(vv, float, _vv, len); |
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if (ELL_3V_DOT(uu, vv) < 0.0) { |
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ELL_3V_ADD2(tmp, uu, vv); |
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ret = AIR_CAST(float, AIR_PI - 2*asin(ELL_3V_LEN(tmp)/2.0)); |
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} else { |
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ELL_3V_SUB(tmp, uu, vv); |
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ret = AIR_CAST(float, 2*asin(ELL_3V_LEN(tmp)/2.0)); |
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} |
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return ret; |
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} |
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/* HEY: copy and paste */ |
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double |
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ell_3v_angle_d(const double _uu[3], const double _vv[3]) { |
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double tmp[3], len, uu[3], vv[3], ret; |
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ELL_3V_NORM(uu, _uu, len); |
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ELL_3V_NORM(vv, _vv, len); |
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✓✓ |
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if (ELL_3V_DOT(uu, vv) < 0.0) { |
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ELL_3V_ADD2(tmp, uu, vv); |
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ret = AIR_PI - 2*asin(ELL_3V_LEN(tmp)/2.0); |
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} else { |
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ELL_3V_SUB(tmp, uu, vv); |
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ret = 2*asin(ELL_3V_LEN(tmp)/2.0); |
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} |
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return ret; |
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} |
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/* HEY: copy and paste */ |
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float |
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ell_2v_angle_f(const float _uu[2], const float _vv[2]) { |
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float tmp[2], len, uu[2], vv[2], ret; |
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ELL_2V_NORM_TT(uu, float, _uu, len); |
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ELL_2V_NORM_TT(vv, float, _vv, len); |
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if (ELL_2V_DOT(uu, vv) < 0.0) { |
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ELL_2V_ADD2(tmp, uu, vv); |
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ret = AIR_CAST(float, AIR_PI - 2*asin(ELL_2V_LEN(tmp)/2.0)); |
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} else { |
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ELL_2V_SUB(tmp, uu, vv); |
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ret = AIR_CAST(float, 2*asin(ELL_2V_LEN(tmp)/2.0)); |
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} |
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return ret; |
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} |
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/* HEY: copy and paste */ |
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double |
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ell_2v_angle_d(const double _uu[2], const double _vv[2]) { |
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double tmp[2], len, uu[2], vv[2], ret; |
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ELL_2V_NORM(uu, _uu, len); |
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ELL_2V_NORM(vv, _vv, len); |
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if (ELL_2V_DOT(uu, vv) < 0.0) { |
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ELL_2V_ADD2(tmp, uu, vv); |
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ret = AIR_PI - 2*asin(ELL_2V_LEN(tmp)/2.0); |
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} else { |
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ELL_2V_SUB(tmp, uu, vv); |
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ret = 2*asin(ELL_2V_LEN(tmp)/2.0); |
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} |
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return ret; |
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} |
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/* |
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** input vectors have to be normalized! |
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*/ |
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double |
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ell_3v_area_spherical_d(const double avec[3], |
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const double bvec[3], |
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const double cvec[3]) { |
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double axb[3], bxc[3], cxa[3], A, B, C, tmp; |
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ELL_3V_CROSS(axb, avec, bvec); |
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ELL_3V_CROSS(bxc, bvec, cvec); |
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ELL_3V_CROSS(cxa, cvec, avec); |
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ELL_3V_NORM(axb, axb, tmp); |
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ELL_3V_NORM(bxc, bxc, tmp); |
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ELL_3V_NORM(cxa, cxa, tmp); |
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A = AIR_PI - ell_3v_angle_d(axb, cxa); |
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B = AIR_PI - ell_3v_angle_d(bxc, axb); |
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C = AIR_PI - ell_3v_angle_d(cxa, bxc); |
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return A + B + C - AIR_PI; |
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} |
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/* |
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** all input vectors {a,b,c}vec, dir must be normalized |
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*/ |
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void |
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ell_3v_barycentric_spherical_d(double bary[3], |
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const double av[3], |
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const double bv[3], |
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const double cv[3], |
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const double vv[3]) { |
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double sum; |
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bary[0] = ell_3v_area_spherical_d(vv, bv, cv); |
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bary[1] = ell_3v_area_spherical_d(vv, cv, av); |
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bary[2] = ell_3v_area_spherical_d(vv, av, bv); |
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sum = bary[0] + bary[1] + bary[2]; |
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if (sum) { |
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ELL_3V_SCALE(bary, 1.0/sum, bary); |
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} |
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return; |
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} |