1 // Copyright (C) 2007-2012 CEA/DEN, EDF R&D
3 // This library is free software; you can redistribute it and/or
4 // modify it under the terms of the GNU Lesser General Public
5 // License as published by the Free Software Foundation; either
6 // version 2.1 of the License.
8 // This library is distributed in the hope that it will be useful,
9 // but WITHOUT ANY WARRANTY; without even the implied warranty of
10 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
11 // Lesser General Public License for more details.
13 // You should have received a copy of the GNU Lesser General Public
14 // License along with this library; if not, write to the Free Software
15 // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
17 // See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
19 // Author : Anthony Geay (CEA/DEN)
21 #ifndef __VOLSURFFORMULAE_HXX__
22 #define __VOLSURFFORMULAE_HXX__
24 #include "InterpolationUtils.hxx"
25 #include "InterpKernelException.hxx"
26 #include "InterpKernelGeo2DQuadraticPolygon.hxx"
31 namespace INTERP_KERNEL
33 inline void calculateBarycenterDyn(const double **pts, int nbPts,
34 int dim, double *bary);
36 inline double calculateAreaForPolyg(const double **coords, int nbOfPtsInPolygs,
40 inline double calculateAreaForQPolyg(const double **coords, int nbOfPtsInPolygs,
43 inline double calculateLgthForSeg2(const double *p1, const double *p2, int spaceDim)
50 for(int i=0;i<spaceDim;i++)
51 ret+=(p2[i]-p1[i])*(p2[i]-p1[i]);
56 // ===========================
57 // Calculate Area for triangle
58 // ===========================
59 inline double calculateAreaForTria(const double *p1, const double *p2,
60 const double *p3, int spaceDim)
66 area = -((p2[0]-p1[0])*(p3[1]-p1[1]) - (p3[0]-p1[0])*(p2[1]-p1[1]))/2.0;
70 area = sqrt(((p2[1]-p1[1])*(p3[2]-p1[2]) - (p3[1]-p1[1])*(p2[2]-p1[2]))*
71 ((p2[1]-p1[1])*(p3[2]-p1[2]) - (p3[1]-p1[1])*(p2[2]-p1[2]))
73 ((p3[0]-p1[0])*(p2[2]-p1[2]) - (p2[0]-p1[0])*(p3[2]-p1[2]))*
74 ((p3[0]-p1[0])*(p2[2]-p1[2]) - (p2[0]-p1[0])*(p3[2]-p1[2]))
76 ((p2[0]-p1[0])*(p3[1]-p1[1]) - (p3[0]-p1[0])*(p2[1]-p1[1]))*
77 ((p2[0]-p1[0])*(p3[1]-p1[1]) - (p3[0]-p1[0])*(p2[1]-p1[1])))/2.0;
83 // =============================
84 // Calculate Area for quadrangle
85 // =============================
86 inline double calculateAreaForQuad(const double *p1, const double *p2,
87 const double *p3, const double *p4,
94 double a1 = (p2[0]-p1[0])/4.0, a2 = (p2[1]-p1[1])/4.0;
95 double b1 = (p3[0]-p4[0])/4.0, b2 = (p3[1]-p4[1])/4.0;
96 double c1 = (p3[0]-p2[0])/4.0, c2 = (p3[1]-p2[1])/4.0;
97 double d1 = (p4[0]-p1[0])/4.0, d2 = (p4[1]-p1[1])/4.0;
99 area = - 4.0*( b1*c2 - c1*b2 + a1*c2 - c1*a2
100 + b1*d2 - d1*b2 + a1*d2 - d1*a2);
104 area = (sqrt(((p2[1]-p1[1])*(p4[2]-p1[2]) - (p4[1]-p1[1])*(p2[2]-p1[2]))*
105 ((p2[1]-p1[1])*(p4[2]-p1[2]) - (p4[1]-p1[1])*(p2[2]-p1[2]))
106 + ((p4[0]-p1[0])*(p2[2]-p1[2]) - (p2[0]-p1[0])*(p4[2]-p1[2]))*
107 ((p4[0]-p1[0])*(p2[2]-p1[2]) - (p2[0]-p1[0])*(p4[2]-p1[2]))
108 + ((p2[0]-p1[0])*(p4[1]-p1[1]) - (p4[0]-p1[0])*(p2[1]-p1[1]))*
109 ((p2[0]-p1[0])*(p4[1]-p1[1]) - (p4[0]-p1[0])*(p2[1]-p1[1])))
111 sqrt(((p4[1]-p3[1])*(p2[2]-p3[2]) - (p2[1]-p3[1])*(p4[2]-p3[2]))*
112 ((p4[1]-p3[1])*(p2[2]-p3[2]) - (p2[1]-p3[1])*(p4[2]-p3[2]))
113 + ((p2[0]-p3[0])*(p4[2]-p3[2]) - (p4[0]-p3[0])*(p2[2]-p3[2]))*
114 ((p2[0]-p3[0])*(p4[2]-p3[2]) - (p4[0]-p3[0])*(p2[2]-p3[2]))
115 + ((p4[0]-p3[0])*(p2[1]-p3[1]) - (p2[0]-p3[0])*(p4[1]-p3[1]))*
116 ((p4[0]-p3[0])*(p2[1]-p3[1]) - (p2[0]-p3[0])*(p4[1]-p3[1])))
123 // ====================================
124 // Calculate Normal Vector for Triangle
125 // ====================================
126 inline void calculateNormalForTria(const double *p1, const double *p2,
127 const double *p3, double *normal)
129 normal[0] = ((p2[1]-p1[1])*(p3[2]-p1[2]) - (p3[1]-p1[1])*(p2[2]-p1[2]))/2.0;
130 normal[1] = ((p3[0]-p1[0])*(p2[2]-p1[2]) - (p2[0]-p1[0])*(p3[2]-p1[2]))/2.0;
131 normal[2] = ((p2[0]-p1[0])*(p3[1]-p1[1]) - (p3[0]-p1[0])*(p2[1]-p1[1]))/2.0;
134 // ======================================
135 // Calculate Normal Vector for Quadrangle
136 // ======================================
137 inline void calculateNormalForQuad(const double *p1, const double *p2,
138 const double *p3, const double *p4,
141 double xnormal1 = (p2[1]-p1[1])*(p4[2]-p1[2]) - (p4[1]-p1[1])*(p2[2]-p1[2]);
142 double xnormal2 = (p4[0]-p1[0])*(p2[2]-p1[2]) - (p2[0]-p1[0])*(p4[2]-p1[2]);
143 double xnormal3 = (p2[0]-p1[0])*(p4[1]-p1[1]) - (p4[0]-p1[0])*(p2[1]-p1[1]);
144 double xarea = sqrt(xnormal1*xnormal1 + xnormal2*xnormal2 + xnormal3*xnormal3);
145 xnormal1 = xnormal1/xarea;
146 xnormal2 = xnormal2/xarea;
147 xnormal3 = xnormal3/xarea;
148 xarea = calculateAreaForQuad(p1,p2,p3,p4,3);
149 normal[0] = xnormal1*xarea ;
150 normal[1] = xnormal2*xarea ;
151 normal[2] = xnormal3*xarea ;
154 // ===================================
155 // Calculate Normal Vector for Polygon
156 // ===================================
157 inline void calculateNormalForPolyg(const double **coords, int nbOfPtsInPolygs,
160 double coordOfBary[3];
162 calculateBarycenterDyn(coords,nbOfPtsInPolygs,3,coordOfBary);
163 double xnormal1 = (coords[0][1]-coords[1][1]) * (coordOfBary[2]-coords[1][2])
164 - (coords[0][2]-coords[1][2]) * (coordOfBary[1]-coords[1][1]);
166 double xnormal2 = (coords[0][2]-coords[1][2]) * (coordOfBary[0]-coords[1][0])
167 - (coords[0][0]-coords[1][0]) * (coordOfBary[2]-coords[1][2]);
169 double xnormal3 = (coords[0][0]-coords[1][0]) * (coordOfBary[1]-coords[1][1])
170 - (coords[0][1]-coords[1][1]) * (coordOfBary[0]-coords[1][0]);
172 double xarea=sqrt(xnormal1*xnormal1 + xnormal2*xnormal2 + xnormal3*xnormal3);
176 //std::string diagnosis"Can not calculate normal - polygon is singular";
177 throw std::exception();
180 xnormal1 = -xnormal1/xarea;
181 xnormal2 = -xnormal2/xarea;
182 xnormal3 = -xnormal3/xarea;
183 xarea = calculateAreaForPolyg(coords,nbOfPtsInPolygs,3);
184 normal[0] = xnormal1*xarea ;
185 normal[1] = xnormal2*xarea ;
186 normal[2] = xnormal3*xarea ;
189 // ==========================
190 // Calculate Area for Polygon
191 // ==========================
192 inline double calculateAreaForPolyg(const double **coords, int nbOfPtsInPolygs,
196 double coordOfBary[3];
198 calculateBarycenterDyn(coords,nbOfPtsInPolygs,spaceDim,coordOfBary);
199 for ( int i=0; i<nbOfPtsInPolygs; i++ )
201 double tmp = calculateAreaForTria(coords[i],coords[(i+1)%nbOfPtsInPolygs],
202 coordOfBary,spaceDim);
208 double calculateAreaForQPolyg(const double **coords, int nbOfPtsInPolygs, int spaceDim)
211 if(nbOfPtsInPolygs%2==0)
215 std::vector<Node *> nodes(nbOfPtsInPolygs);
216 for(int i=0;i<nbOfPtsInPolygs;i++)
217 nodes[i]=new Node(coords[i][0],coords[i][1]);
218 QuadraticPolygon *pol=QuadraticPolygon::BuildArcCirclePolygon(nodes);
219 double ret=pol->getArea();
224 return calculateAreaForPolyg(coords,nbOfPtsInPolygs/2,spaceDim);
228 std::ostringstream oss; oss << "INTERP_KERNEL::calculateAreaForQPolyg : nb of points in quadratic polygon is " << nbOfPtsInPolygs << " should be even !";
229 throw INTERP_KERNEL::Exception(oss.str().c_str());
233 // ==========================
234 // Calculate Volume for Tetra
235 // ==========================
236 inline double calculateVolumeForTetra(const double *p1, const double *p2,
237 const double *p3, const double *p4)
239 return ( (p3[0]-p1[0])*( (p2[1]-p1[1])*(p4[2]-p1[2])
240 - (p2[2]-p1[2])*(p4[1]-p1[1]) )
241 - (p2[0]-p1[0])*( (p3[1]-p1[1])*(p4[2]-p1[2])
242 - (p3[2]-p1[2])*(p4[1]-p1[1]) )
243 + (p4[0]-p1[0])*( (p3[1]-p1[1])*(p2[2]-p1[2])
244 - (p3[2]-p1[2])*(p2[1]-p1[1]) )
248 // =========================
249 // Calculate Volume for Pyra
250 // =========================
251 inline double calculateVolumeForPyra(const double *p1, const double *p2,
252 const double *p3, const double *p4,
255 return ( ((p3[0]-p1[0])*( (p2[1]-p1[1])*(p5[2]-p1[2])
256 - (p2[2]-p1[2])*(p5[1]-p1[1]) )
257 -(p2[0]-p1[0])*( (p3[1]-p1[1])*(p5[2]-p1[2])
258 - (p3[2]-p1[2])*(p5[1]-p1[1]) )
259 +(p5[0]-p1[0])*( (p3[1]-p1[1])*(p2[2]-p1[2])
260 - (p3[2]-p1[2])*(p2[1]-p1[1]) ))
262 ((p4[0]-p1[0])*( (p3[1]-p1[1])*(p5[2]-p1[2])
263 - (p3[2]-p1[2])*(p5[1]-p1[1]) )
264 -(p3[0]-p1[0])*( (p4[1]-p1[1])*(p5[2]-p1[2])
265 - (p4[2]-p1[2])*(p5[1]-p1[1]))
266 +(p5[0]-p1[0])*( (p4[1]-p1[1])*(p3[2]-p1[2])
267 - (p4[2]-p1[2])*(p3[1]-p1[1]) ))
271 // ==========================
272 // Calculate Volume for Penta
273 // ==========================
274 inline double calculateVolumeForPenta(const double *p1, const double *p2,
275 const double *p3, const double *p4,
276 const double *p5, const double *p6)
278 double a1 = (p2[0]-p3[0])/2.0, a2 = (p2[1]-p3[1])/2.0, a3 = (p2[2]-p3[2])/2.0;
279 double b1 = (p5[0]-p6[0])/2.0, b2 = (p5[1]-p6[1])/2.0, b3 = (p5[2]-p6[2])/2.0;
280 double c1 = (p4[0]-p1[0])/2.0, c2 = (p4[1]-p1[1])/2.0, c3 = (p4[2]-p1[2])/2.0;
281 double d1 = (p5[0]-p2[0])/2.0, d2 = (p5[1]-p2[1])/2.0, d3 = (p5[2]-p2[2])/2.0;
282 double e1 = (p6[0]-p3[0])/2.0, e2 = (p6[1]-p3[1])/2.0, e3 = (p6[2]-p3[2])/2.0;
283 double f1 = (p1[0]-p3[0])/2.0, f2 = (p1[1]-p3[1])/2.0, f3 = (p1[2]-p3[2])/2.0;
284 double h1 = (p4[0]-p6[0])/2.0, h2 = (p4[1]-p6[1])/2.0, h3 = (p4[2]-p6[2])/2.0;
286 double A = a1*c2*f3 - a1*c3*f2 - a2*c1*f3 + a2*c3*f1 + a3*c1*f2 - a3*c2*f1;
287 double B = b1*c2*h3 - b1*c3*h2 - b2*c1*h3 + b2*c3*h1 + b3*c1*h2 - b3*c2*h1;
288 double C = (a1*c2*h3 + b1*c2*f3) - (a1*c3*h2 + b1*c3*f2)
289 - (a2*c1*h3 + b2*c1*f3) + (a2*c3*h1 + b2*c3*f1)
290 + (a3*c1*h2 + b3*c1*f2) - (a3*c2*h1 + b3*c2*f1);
291 double D = a1*d2*f3 - a1*d3*f2 - a2*d1*f3 + a2*d3*f1 + a3*d1*f2 - a3*d2*f1;
292 double E = b1*d2*h3 - b1*d3*h2 - b2*d1*h3 + b2*d3*h1 + b3*d1*h2 - b3*d2*h1;
293 double F = (a1*d2*h3 + b1*d2*f3) - (a1*d3*h2 + b1*d3*f2)
294 - (a2*d1*h3 + b2*d1*f3) + (a2*d3*h1 + b2*d3*f1)
295 + (a3*d1*h2 + b3*d1*f2) - (a3*d2*h1 + b3*d2*f1);
296 double G = a1*e2*f3 - a1*e3*f2 - a2*e1*f3 + a2*e3*f1 + a3*e1*f2 - a3*e2*f1;
297 double H = b1*e2*h3 - b1*e3*h2 - b2*e1*h3 + b2*e3*h1 + b3*e1*h2 - b3*e2*h1;
298 double P = (a1*e2*h3 + b1*e2*f3) - (a1*e3*h2 + b1*e3*f2)
299 - (a2*e1*h3 + b2*e1*f3) + (a2*e3*h1 + b2*e3*f1)
300 + (a3*e1*h2 + b3*e1*f2) - (a3*e2*h1 + b3*e2*f1);
302 return (-2.0*(2.0*(A + B + D + E + G + H) + C + F + P)/9.0);
305 // =========================
306 // Calculate Volume for Hexa
307 // =========================
308 inline double calculateVolumeForHexa(const double *pt1, const double *pt2,
309 const double *pt3, const double *pt4,
310 const double *pt5, const double *pt6,
311 const double *pt7, const double *pt8)
313 double a1=(pt3[0]-pt4[0])/8.0, a2=(pt3[1]-pt4[1])/8.0, a3=(pt3[2]-pt4[2])/8.0;
314 double b1=(pt2[0]-pt1[0])/8.0, b2=(pt2[1]-pt1[1])/8.0, b3=(pt2[2]-pt1[2])/8.0;
315 double c1=(pt7[0]-pt8[0])/8.0, c2=(pt7[1]-pt8[1])/8.0, c3=(pt7[2]-pt8[2])/8.0;
316 double d1=(pt6[0]-pt5[0])/8.0, d2=(pt6[1]-pt5[1])/8.0, d3=(pt6[2]-pt5[2])/8.0;
317 double e1=(pt3[0]-pt2[0])/8.0, e2=(pt3[1]-pt2[1])/8.0, e3=(pt3[2]-pt2[2])/8.0;
318 double f1=(pt4[0]-pt1[0])/8.0, f2=(pt4[1]-pt1[1])/8.0, f3=(pt4[2]-pt1[2])/8.0;
319 double h1=(pt7[0]-pt6[0])/8.0, h2=(pt7[1]-pt6[1])/8.0, h3=(pt7[2]-pt6[2])/8.0;
320 double p1=(pt8[0]-pt5[0])/8.0, p2=(pt8[1]-pt5[1])/8.0, p3=(pt8[2]-pt5[2])/8.0;
321 double q1=(pt3[0]-pt7[0])/8.0, q2=(pt3[1]-pt7[1])/8.0, q3=(pt3[2]-pt7[2])/8.0;
322 double r1=(pt4[0]-pt8[0])/8.0, r2=(pt4[1]-pt8[1])/8.0, r3=(pt4[2]-pt8[2])/8.0;
323 double s1=(pt2[0]-pt6[0])/8.0, s2=(pt2[1]-pt6[1])/8.0, s3=(pt2[2]-pt6[2])/8.0;
324 double t1=(pt1[0]-pt5[0])/8.0, t2=(pt1[1]-pt5[1])/8.0, t3=(pt1[2]-pt5[2])/8.0;
326 double A = a1*e2*q3 - a1*e3*q2 - a2*e1*q3 + a2*e3*q1 + a3*e1*q2 - a3*e2*q1;
327 double B = c1*h2*q3 - c1*h3*q2 - c2*h1*q3 + c2*h3*q1 + c3*h1*q2 - c3*h2*q1;
328 double C = (a1*h2 + c1*e2)*q3 - (a1*h3 + c1*e3)*q2
329 - (a2*h1 + c2*e1)*q3 + (a2*h3 + c2*e3)*q1
330 + (a3*h1 + c3*e1)*q2 - (a3*h2 + c3*e2)*q1;
331 double D = b1*e2*s3 - b1*e3*s2 - b2*e1*s3 + b2*e3*s1 + b3*e1*s2 - b3*e2*s1;
332 double E = d1*h2*s3 - d1*h3*s2 - d2*h1*s3 + d2*h3*s1 + d3*h1*s2 - d3*h2*s1;
333 double F = (b1*h2 + d1*e2)*s3 - (b1*h3 + d1*e3)*s2
334 - (b2*h1 + d2*e1)*s3 + (b2*h3 + d2*e3)*s1
335 + (b3*h1 + d3*e1)*s2 - (b3*h2 + d3*e2)*s1;
336 double G = (a1*e2*s3 + b1*e2*q3) - (a1*e3*s2 + b1*e3*q2)
337 - (a2*e1*s3 + b2*e1*q3) + (a2*e3*s1 + b2*e3*q1)
338 + (a3*e1*s2 + b3*e1*q2) - (a3*e2*s1 + b3*e2*q1);
339 double H = (c1*h2*s3 + d1*h2*q3) - (c1*h3*s2 + d1*h3*q2)
340 - (c2*h1*s3 + d2*h1*q3) + (c2*h3*s1 + d2*h3*q1)
341 + (c3*h1*s2 + d3*h1*q2) - (c3*h2*s1 + d3*h2*q1);
342 double I = ((a1*h2 + c1*e2)*s3 + (b1*h2 + d1*e2)*q3)
343 - ((a1*h3 + c1*e3)*s2 + (b1*h3 + d1*e3)*q2)
344 - ((a2*h1 + c2*e1)*s3 + (b2*h1 + d2*e1)*q3)
345 + ((a2*h3 + c2*e3)*s1 + (b2*h3 + d2*e3)*q1)
346 + ((a3*h1 + c3*e1)*s2 + (b3*h1 + d3*e1)*q2)
347 - ((a3*h2 + c3*e2)*s1 + (b3*h2 + d3*e2)*q1);
348 double J = a1*f2*r3 - a1*f3*r2 - a2*f1*r3 + a2*f3*r1 + a3*f1*r2 - a3*f2*r1;
349 double K = c1*p2*r3 - c1*p3*r2 - c2*p1*r3 + c2*p3*r1 + c3*p1*r2 - c3*p2*r1;
350 double L = (a1*p2 + c1*f2)*r3 - (a1*p3 + c1*f3)*r2
351 - (a2*p1 + c2*f1)*r3 + (a2*p3 + c2*f3)*r1
352 + (a3*p1 + c3*f1)*r2 - (a3*p2 + c3*f2)*r1;
353 double M = b1*f2*t3 - b1*f3*t2 - b2*f1*t3 + b2*f3*t1 + b3*f1*t2 - b3*f2*t1;
354 double N = d1*p2*t3 - d1*p3*t2 - d2*p1*t3 + d2*p3*t1 + d3*p1*t2 - d3*p2*t1;
355 double O = (b1*p2 + d1*f2)*t3 - (b1*p3 + d1*f3)*t2
356 - (b2*p1 + d2*f1)*t3 + (b2*p3 + d2*f3)*t1
357 + (b3*p1 + d3*f1)*t2 - (b3*p2 + d3*f2)*t1;
358 double P = (a1*f2*t3 + b1*f2*r3) - (a1*f3*t2 + b1*f3*r2)
359 - (a2*f1*t3 + b2*f1*r3) + (a2*f3*t1 + b2*f3*r1)
360 + (a3*f1*t2 + b3*f1*r2) - (a3*f2*t1 + b3*f2*r1);
361 double Q = (c1*p2*t3 + d1*p2*r3) - (c1*p3*t2 + d1*p3*r2)
362 - (c2*p1*t3 + d2*p1*r3) + (c2*p3*t1 + d2*p3*r1)
363 + (c3*p1*t2 + d3*p1*r2) - (c3*p2*t1 + d3*p2*r1);
364 double R = ((a1*p2 + c1*f2)*t3 + (b1*p2 + d1*f2)*r3)
365 - ((a1*p3 + c1*f3)*t2 + (b1*p3 + d1*f3)*r2)
366 - ((a2*p1 + c2*f1)*t3 + (b2*p1 + d2*f1)*r3)
367 + ((a2*p3 + c2*f3)*t1 + (b2*p3 + d2*f3)*r1)
368 + ((a3*p1 + c3*f1)*t2 + (b3*p1 + d3*f1)*r2)
369 - ((a3*p2 + c3*f2)*t1 + (b3*p2 + d3*f2)*r1);
370 double S = (a1*e2*r3 + a1*f2*q3) - (a1*e3*r2 + a1*f3*q2)
371 - (a2*e1*r3 + a2*f1*q3) + (a2*e3*r1 + a2*f3*q1)
372 + (a3*e1*r2 + a3*f1*q2) - (a3*e2*r1 + a3*f2*q1);
373 double T = (c1*h2*r3 + c1*p2*q3) - (c1*h3*r2 + c1*p3*q2)
374 - (c2*h1*r3 + c2*p1*q3) + (c2*h3*r1 + c2*p3*q1)
375 + (c3*h1*r2 + c3*p1*q2) - (c3*h2*r1 + c3*p2*q1);
376 double U = ((a1*h2 + c1*e2)*r3 + (a1*p2 + c1*f2)*q3)
377 - ((a1*h3 + c1*e3)*r2 + (a1*p3 + c1*f3)*q2)
378 - ((a2*h1 + c2*e1)*r3 + (a2*p1 + c2*f1)*q3)
379 + ((a2*h3 + c2*e3)*r1 + (a2*p3 + c2*f3)*q1)
380 + ((a3*h1 + c3*e1)*r2 + (a3*p1 + c3*f1)*q2)
381 - ((a3*h2 + c3*e2)*r1 + (a3*p2 + c3*f2)*q1);
382 double V = (b1*e2*t3 + b1*f2*s3) - (b1*e3*t2 + b1*f3*s2)
383 - (b2*e1*t3 + b2*f1*s3) + (b2*e3*t1 + b2*f3*s1)
384 + (b3*e1*t2 + b3*f1*s2) - (b3*e2*t1 + b3*f2*s1);
385 double W = (d1*h2*t3 + d1*p2*s3) - (d1*h3*t2 + d1*p3*s2)
386 - (d2*h1*t3 + d2*p1*s3) + (d2*h3*t1 + d2*p3*s1)
387 + (d3*h1*t2 + d3*p1*s2) - (d3*h2*t1 + d3*p2*s1);
388 double X = ((b1*h2 + d1*e2)*t3 + (b1*p2 + d1*f2)*s3)
389 - ((b1*h3 + d1*e3)*t2 + (b1*p3 + d1*f3)*s2)
390 - ((b2*h1 + d2*e1)*t3 + (b2*p1 + d2*f1)*s3)
391 + ((b2*h3 + d2*e3)*t1 + (b2*p3 + d2*f3)*s1)
392 + ((b3*h1 + d3*e1)*t2 + (b3*p1 + d3*f1)*s2)
393 - ((b3*h2 + d3*e2)*t1 + (b3*p2 + d3*f2)*s1);
394 double Y = (a1*e2*t3 + a1*f2*s3 + b1*e2*r3 + b1*f2*q3)
395 - (a1*e3*t2 + a1*f3*s2 + b1*e3*r2 + b1*f3*q2)
396 - (a2*e1*t3 + a2*f1*s3 + b2*e1*r3 + b2*f1*q3)
397 + (a2*e3*t1 + a2*f3*s1 + b2*e3*r1 + b2*f3*q1)
398 + (a3*e1*t2 + a3*f1*s2 + b3*e1*r2 + b3*f1*q2)
399 - (a3*e2*t1 + a3*f2*s1 + b3*e2*r1 + b3*f2*q1);
400 double Z = (c1*h2*t3 + c1*p2*s3 + d1*h2*r3 + d1*p2*q3)
401 - (c1*h3*t2 + c1*p3*s2 + d1*h3*r2 + d1*p3*q2)
402 - (c2*h1*t3 + c2*p1*s3 + d2*h1*r3 + d2*p1*q3)
403 + (c2*h3*t1 + c2*p3*s1 + d2*h3*r1 + d2*p3*q1)
404 + (c3*h1*t2 + c3*p1*s2 + d3*h1*r2 + d3*p1*q2)
405 - (c3*h2*t1 + c3*p2*s1 + d3*h2*r1 + d3*p2*q1);
406 double AA = ((a1*h2 + c1*e2)*t3 + (a1*p2 + c1*f2)*s3
407 +(b1*h2 + d1*e2)*r3 + (b1*p2 + d1*f2)*q3)
408 - ((a1*h3 + c1*e3)*t2 + (a1*p3 + c1*f3)*s2
409 +(b1*h3 + d1*e3)*r2 + (b1*p3 + d1*f3)*q2)
410 - ((a2*h1 + c2*e1)*t3 + (a2*p1 + c2*f1)*s3
411 +(b2*h1 + d2*e1)*r3 + (b2*p1 + d2*f1)*q3)
412 + ((a2*h3 + c2*e3)*t1 + (a2*p3 + c2*f3)*s1
413 +(b2*h3 + d2*e3)*r1 + (b2*p3 + d2*f3)*q1)
414 + ((a3*h1 + c3*e1)*t2 + (a3*p1 + c3*f1)*s2
415 +(b3*h1 + d3*e1)*r2 + (b3*p1 + d3*f1)*q2)
416 - ((a3*h2 + c3*e2)*t1 + (a3*p2 + c3*f2)*s1
417 + (b3*h2 + d3*e2)*r1 + (b3*p2 + d3*f2)*q1);
419 return 64.0*( 8.0*(A + B + D + E + J + K + M + N)
420 + 4.0*(C + F + G + H + L + O + P + Q + S + T + V + W)
421 + 2.0*(I + R + U + X + Y + Z) + AA ) / 27.0 ;
424 // =========================================================================================================================
425 // Calculate Volume for Generic Polyedron, even not convex one, WARNING !!! The polyedron's faces must be correctly ordered
426 // =========================================================================================================================
427 inline double calculateVolumeForPolyh(const double ***pts,
428 const int *nbOfNodesPerFaces,
434 for ( int i=0; i<nbOfFaces; i++ )
439 calculateNormalForPolyg(pts[i],nbOfNodesPerFaces[i],normal);
440 vecForAlt[0]=bary[0]-pts[i][0][0];
441 vecForAlt[1]=bary[1]-pts[i][0][1];
442 vecForAlt[2]=bary[2]-pts[i][0][2];
443 volume+=vecForAlt[0]*normal[0]+vecForAlt[1]*normal[1]+vecForAlt[2]*normal[2];
449 * Calculate Volume for Generic Polyedron, even not convex one, WARNING !!! The polyedron's faces must be correctly ordered.
450 * 2nd API avoiding to create double** arrays. The returned value could be negative if polyhedrons faces are not oriented with normal outside of the
453 template<class ConnType, NumberingPolicy numPol>
454 inline double calculateVolumeForPolyh2(const ConnType *connec, int lgth, const double *coords)
456 std::size_t nbOfFaces=std::count(connec,connec+lgth,-1)+1;
458 const int *work=connec;
459 for(std::size_t iFace=0;iFace<nbOfFaces;iFace++)
461 const int *work2=std::find(work+1,connec+lgth,-1);
462 std::size_t nbOfNodesOfCurFace=std::distance(work,work2);
463 double areaVector[3]={0.,0.,0.};
464 for(std::size_t ptId=0;ptId<nbOfNodesOfCurFace;ptId++)
466 const double *pti=coords+3*OTT<ConnType,numPol>::coo2C(work[ptId]);
467 const double *pti1=coords+3*OTT<ConnType,numPol>::coo2C(work[(ptId+1)%nbOfNodesOfCurFace]);
468 areaVector[0]+=pti[1]*pti1[2]-pti[2]*pti1[1];
469 areaVector[1]+=pti[2]*pti1[0]-pti[0]*pti1[2];
470 areaVector[2]+=pti[0]*pti1[1]-pti[1]*pti1[0];
472 const double *pt=coords+3*work[0];
473 volume+=pt[0]*areaVector[0]+pt[1]*areaVector[1]+pt[2]*areaVector[2];
480 * This method returns the area oriented vector of a polygon. This method is useful for normal computation without
481 * any troubles if several edges are colinears.
482 * @param res must be of size at least 3 to store the result.
484 template<class ConnType, NumberingPolicy numPol>
485 inline void areaVectorOfPolygon(const ConnType *connec, int lgth, const double *coords, double *res)
487 res[0]=0.; res[1]=0.; res[2]=0.;
488 for(int ptId=0;ptId<lgth;ptId++)
490 const double *pti=coords+3*OTT<ConnType,numPol>::coo2C(connec[ptId]);
491 const double *pti1=coords+3*OTT<ConnType,numPol>::coo2C(connec[(ptId+1)%lgth]);
492 res[0]+=pti[1]*pti1[2]-pti[2]*pti1[1];
493 res[1]+=pti[2]*pti1[0]-pti[0]*pti1[2];
494 res[2]+=pti[0]*pti1[1]-pti[1]*pti1[0];
498 inline double integrationOverA3DLine(double u1, double v1, double u2, double v2, double A, double B, double C)
500 return (u1-u2)*(6.*C*C*(v1+v2)+B*B*(v1*v1*v1+v1*v1*v2+v1*v2*v2+v2*v2*v2)+A*A*(2.*u1*u2*(v1+v2)+u1*u1*(3.*v1+v2)+u2*u2*(v1+3.*v2))+
501 4.*C*(A*(2*u1*v1+u2*v1+u1*v2+2.*u2*v2)+B*(v1*v1+v1*v2+v2*v2))+A*B*(u1*(3.*v1*v1+2.*v1*v2+v2*v2)+u2*(v1*v1+2.*v1*v2+3.*v2*v2)))/24.;
504 template<class ConnType, NumberingPolicy numPol>
505 inline void barycenterOfPolyhedron(const ConnType *connec, int lgth, const double *coords, double *res)
507 std::size_t nbOfFaces=std::count(connec,connec+lgth,-1)+1;
508 res[0]=0.; res[1]=0.; res[2]=0.;
509 const int *work=connec;
510 for(std::size_t i=0;i<nbOfFaces;i++)
512 const int *work2=std::find(work+1,connec+lgth,-1);
513 int nbOfNodesOfCurFace=(int)std::distance(work,work2);
514 // projection to (u,v) of each faces of polyh to compute integral(x^2/2) on each faces.
516 areaVectorOfPolygon<ConnType,numPol>(work,nbOfNodesOfCurFace,coords,normal);
517 double normOfNormal=sqrt(normal[0]*normal[0]+normal[1]*normal[1]+normal[2]*normal[2]);
518 normal[0]/=normOfNormal; normal[1]/=normOfNormal; normal[2]/=normOfNormal;
519 double u[2]={normal[1],-normal[0]};
520 double s=sqrt(u[0]*u[0]+u[1]*u[1]);
524 u[0]/=std::abs(s); u[1]/=std::abs(s);
527 { u[0]=1.; u[1]=0.; }
528 //C : high in plane of polyhedron face : always constant
529 double w=normal[0]*coords[3*OTT<ConnType,numPol>::coo2C(work[0])]+
530 normal[1]*coords[3*OTT<ConnType,numPol>::coo2C(work[0])+1]+
531 normal[2]*coords[3*OTT<ConnType,numPol>::coo2C(work[0])+2];
532 // A,B,D,F,G,H,L,M,N coeffs of rotation matrix defined by (u,c,s)
533 double A=u[0]*u[0]*(1-c)+c;
534 double B=u[0]*u[1]*(1-c);
537 double G=u[1]*u[1]*(1-c)+c;
545 for(int j=0;j<nbOfNodesOfCurFace;j++)
547 const double *p1=coords+3*OTT<ConnType,numPol>::coo2C(work[j]);
548 const double *p2=coords+3*OTT<ConnType,numPol>::coo2C(work[(j+1)%nbOfNodesOfCurFace]);
549 double u1=A*p1[0]+B*p1[1]+D*p1[2];
550 double u2=A*p2[0]+B*p2[1]+D*p2[2];
551 double v1=F*p1[0]+G*p1[1]+H*p1[2];
552 double v2=F*p2[0]+G*p2[1]+H*p2[2];
554 double gx=integrationOverA3DLine(u1,v1,u2,v2,A,B,CX);
555 double gy=integrationOverA3DLine(u1,v1,u2,v2,F,G,CY);
556 double gz=integrationOverA3DLine(u1,v1,u2,v2,L,M,CZ);
557 res[0]+=gx*normal[0];
558 res[1]+=gy*normal[1];
559 res[2]+=gz*normal[2];
563 double vol=calculateVolumeForPolyh2<ConnType,numPol>(connec,lgth,coords);
564 res[0]/=vol; res[1]/=vol; res[2]/=vol;
567 // ============================================================================================================================================
568 // Calculate Volume for NON Generic Polyedron. Only polydrons with bary included in pts is supported by this method. Result is always positive.
569 // ============================================================================================================================================
570 inline double calculateVolumeForPolyhAbs(const double ***pts,
571 const int *nbOfNodesPerFaces,
577 for ( int i=0; i<nbOfFaces; i++ )
582 calculateNormalForPolyg(pts[i],nbOfNodesPerFaces[i],normal);
583 vecForAlt[0]=bary[0]-pts[i][0][0];
584 vecForAlt[1]=bary[1]-pts[i][0][1];
585 vecForAlt[2]=bary[2]-pts[i][0][2];
586 volume+=fabs(vecForAlt[0]*normal[0]+vecForAlt[1]*normal[1]+vecForAlt[2]*normal[2]);
592 inline double addComponentsOfVec(const double **pts, int rk)
594 return pts[N-1][rk]+addComponentsOfVec<N-1>(pts,rk);
598 inline double addComponentsOfVec<1>(const double **pts, int rk)
603 template<int N, int DIM>
604 inline void calculateBarycenter(const double **pts, double *bary)
606 bary[DIM-1]=addComponentsOfVec<N>(pts,DIM-1)/N;
607 calculateBarycenter<N,DIM-1>(pts,bary);
611 inline void calculateBarycenter<2,0>(const double **/*pts*/, double */*bary*/)
616 inline void calculateBarycenter<3,0>(const double **/*pts*/, double */*bary*/)
621 inline void calculateBarycenter<4,0>(const double **/*pts*/, double */*bary*/)
626 inline void calculateBarycenter<5,0>(const double **/*pts*/, double */*bary*/)
631 inline void calculateBarycenter<6,0>(const double **/*pts*/, double */*bary*/)
636 inline void calculateBarycenter<7,0>(const double **/*pts*/, double */*bary*/)
641 inline void calculateBarycenter<8,0>(const double **/*pts*/, double */*bary*/)
645 inline void calculateBarycenterDyn(const double **pts, int nbPts,
646 int dim, double *bary)
648 for(int i=0;i<dim;i++)
651 for(int j=0;j<nbPts;j++)
659 template<int SPACEDIM>
660 inline void calculateBarycenterDyn2(const double *pts, int nbPts, double *bary)
662 for(int i=0;i<SPACEDIM;i++)
665 for(int j=0;j<nbPts;j++)
667 temp+=pts[j*SPACEDIM+i];
673 template<class ConnType, NumberingPolicy numPol>
674 inline void computePolygonBarycenter2D(const ConnType *connec, int lgth, const double *coords, double *res)
677 res[0]=0.; res[1]=0.;
678 for(int i=0;i<lgth;i++)
680 double cp=coords[2*OTT<ConnType,numPol>::coo2C(connec[i])]*coords[2*OTT<ConnType,numPol>::coo2C(connec[(i+1)%lgth])+1]-
681 coords[2*OTT<ConnType,numPol>::coo2C(connec[i])+1]*coords[2*OTT<ConnType,numPol>::coo2C(connec[(i+1)%lgth])];
683 res[0]+=cp*(coords[2*OTT<ConnType,numPol>::coo2C(connec[i])]+coords[2*OTT<ConnType,numPol>::coo2C(connec[(i+1)%lgth])]);
684 res[1]+=cp*(coords[2*OTT<ConnType,numPol>::coo2C(connec[i])+1]+coords[2*OTT<ConnType,numPol>::coo2C(connec[(i+1)%lgth])+1]);
690 template<class ConnType, NumberingPolicy numPol>
691 inline void computePolygonBarycenter3D(const ConnType *connec, int lgth, const double *coords, double *res)
694 areaVectorOfPolygon<ConnType,numPol>(connec,lgth,coords,area);
695 double norm=sqrt(area[0]*area[0]+area[1]*area[1]+area[2]*area[2]);
696 area[0]/=norm; area[1]/=norm; area[2]/=norm;
697 res[0]=0.; res[1]=0.; res[2]=0.;
698 for(int i=1;i<lgth-1;i++)
702 v[0]=(coords[3*OTT<ConnType,numPol>::coo2C(connec[0])]+
703 coords[3*OTT<ConnType,numPol>::coo2C(connec[i])]+
704 coords[3*OTT<ConnType,numPol>::coo2C(connec[i+1])])/3.;
705 v[1]=(coords[3*OTT<ConnType,numPol>::coo2C(connec[0])+1]+
706 coords[3*OTT<ConnType,numPol>::coo2C(connec[i])+1]+
707 coords[3*OTT<ConnType,numPol>::coo2C(connec[i+1])+1])/3.;
708 v[2]=(coords[3*OTT<ConnType,numPol>::coo2C(connec[0])+2]+
709 coords[3*OTT<ConnType,numPol>::coo2C(connec[i])+2]+
710 coords[3*OTT<ConnType,numPol>::coo2C(connec[i+1])+2])/3.;
711 ConnType tmpConn[3]={connec[0],connec[i],connec[i+1]};
712 areaVectorOfPolygon<ConnType,numPol>(tmpConn,3,coords,tmpArea);
713 double norm2=sqrt(tmpArea[0]*tmpArea[0]+tmpArea[1]*tmpArea[1]+tmpArea[2]*tmpArea[2]);
716 tmpArea[0]/=norm2; tmpArea[1]/=norm2; tmpArea[2]/=norm2;
717 double signOfArea=area[0]*tmpArea[0]+area[1]*tmpArea[1]+area[2]*tmpArea[2];
718 res[0]+=signOfArea*norm2*v[0]/norm; res[1]+=signOfArea*norm2*v[1]/norm; res[2]+=signOfArea*norm2*v[2]/norm;