void Polyhedra::Initialize(){ if (init) return; bool isRandom = false; //get vertices int N = (int) v.size(); if (N==0) { //generate randomly while ((int) v.size()<4) GenerateRandomGeometry(); N = (int) v.size(); isRandom = true; } //compute convex hull of vertices std::vector<CGALpoint> points; points.resize(v.size()); for(int i=0;i<N;i++) { points[i] = CGALpoint(v[i][0],v[i][1],v[i][2]); } CGAL::convex_hull_3(points.begin(), points.end(), P); //connect triagular facets if possible std::transform(P.facets_begin(), P.facets_end(), P.planes_begin(),Plane_equation()); P = Simplify(P, 1E-9); //modify order of v according to CGAl polyhedron int i = 0; v.clear(); for (Polyhedron::Vertex_iterator vIter = P.vertices_begin(); vIter != P.vertices_end(); ++vIter, i++){ v.push_back(Vector3r(vIter->point().x(),vIter->point().y(),vIter->point().z())); } //list surface triangles for plotting faceTri.clear(); std::transform(P.facets_begin(), P.facets_end(), P.planes_begin(),Plane_equation()); for (Polyhedron::Facet_iterator fIter = P.facets_begin(); fIter != P.facets_end(); fIter++){ Polyhedron::Halfedge_around_facet_circulator hfc0; int n = fIter->facet_degree(); hfc0 = fIter->facet_begin(); int a = std::distance(P.vertices_begin(), hfc0->vertex()); for (int i=2; i<n; i++){ ++hfc0; faceTri.push_back(a); faceTri.push_back(std::distance(P.vertices_begin(), hfc0->vertex())); faceTri.push_back(std::distance(P.vertices_begin(), hfc0->next()->vertex())); } } //compute centroid and volume P_volume_centroid(P, &volume, ¢roid); //check vierd behavior of CGAL in tessalation if(isRandom && volume*1.75<4./3.*3.14*size[0]/2.*size[1]/2.*size[2]/2.) { v.clear(); seed = rand(); Initialize(); } Vector3r translation((-1)*centroid); //set centroid to be [0,0,0] for(int i=0;i<N;i++) { v[i] = v[i]-centroid; } if(isRandom) centroid = Vector3r::Zero(); Vector3r origin(0,0,0); //move and rotate also the CGAL structure Polyhedron Transformation t_trans(1.,0.,0.,translation[0],0.,1.,0.,translation[1],0.,0.,1.,translation[2],1.); std::transform( P.points_begin(), P.points_end(), P.points_begin(), t_trans); //compute inertia Real vtet; Vector3r ctet; Matrix3r Itet1, Itet2; Matrix3r inertia_tensor(Matrix3r::Zero()); for(int i=0; i<(int) faceTri.size(); i+=3){ vtet = std::abs((origin-v[faceTri[i+2]]).dot((v[faceTri[i]]-v[faceTri[i+2]]).cross(v[faceTri[i+1]]-v[faceTri[i+2]]))/6.); ctet = (origin+v[faceTri[i]]+v[faceTri[i+1]]+v[faceTri[i+2]]) / 4.; Itet1 = TetraInertiaTensor(origin-ctet, v[faceTri[i]]-ctet, v[faceTri[i+1]]-ctet, v[faceTri[i+2]]-ctet); ctet = ctet-origin; Itet2<< ctet[1]*ctet[1]+ctet[2]*ctet[2], -ctet[0]*ctet[1], -ctet[0]*ctet[2], -ctet[0]*ctet[1], ctet[0]*ctet[0]+ctet[2]*ctet[2], -ctet[2]*ctet[1], -ctet[0]*ctet[2], -ctet[2]*ctet[1], ctet[1]*ctet[1]+ctet[0]*ctet[0]; inertia_tensor = inertia_tensor + Itet1 + Itet2*vtet; } if(std::abs(inertia_tensor(0,1))+std::abs(inertia_tensor(0,2))+std::abs(inertia_tensor(1,2)) < 1E-13){ // no need to rotate, inertia already diagonal orientation = Quaternionr::Identity(); inertia = Vector3r(inertia_tensor(0,0),inertia_tensor(1,1),inertia_tensor(2,2)); }else{ // calculate eigenvectors of I Vector3r rot; Matrix3r I_rot(Matrix3r::Zero()), I_new(Matrix3r::Zero()); matrixEigenDecomposition(inertia_tensor,I_rot,I_new); // I_rot = eigenvectors of inertia_tensors in columns // I_new = eigenvalues on diagonal // set positove direction of vectors - otherwise reloading does not work Matrix3r sign(Matrix3r::Zero()); Real max_v_signed = I_rot(0,0); Real max_v = std::abs(I_rot(0,0)); if (max_v < std::abs(I_rot(1,0))) {max_v_signed = I_rot(1,0); max_v = std::abs(I_rot(1,0));} if (max_v < std::abs(I_rot(2,0))) {max_v_signed = I_rot(2,0); max_v = std::abs(I_rot(2,0));} sign(0,0) = max_v_signed/max_v; max_v_signed = I_rot(0,1); max_v = std::abs(I_rot(0,1)); if (max_v < std::abs(I_rot(1,1))) {max_v_signed = I_rot(1,1); max_v = std::abs(I_rot(1,1));} if (max_v < std::abs(I_rot(2,1))) {max_v_signed = I_rot(2,1); max_v = std::abs(I_rot(2,1));} sign(1,1) = max_v_signed/max_v; sign(2,2) = 1.; I_rot = I_rot*sign; // force the eigenvectors to be right-hand oriented Vector3r third = (I_rot.col(0)).cross(I_rot.col(1)); I_rot(0,2) = third[0]; I_rot(1,2) = third[1]; I_rot(2,2) = third[2]; inertia = Vector3r(I_new(0,0),I_new(1,1),I_new(2,2)); orientation = Quaternionr(I_rot); //rotate the voronoi cell so that x - is maximal inertia axis and z - is minimal inertia axis //orientation.normalize(); //not needed for(int i=0; i< (int) v.size();i++) { v[i] = orientation.conjugate()*v[i]; } //rotate also the CGAL structure Polyhedron Matrix3r rot_mat = (orientation.conjugate()).toRotationMatrix(); Transformation t_rot(rot_mat(0,0),rot_mat(0,1),rot_mat(0,2),rot_mat(1,0),rot_mat(1,1),rot_mat(1,2),rot_mat(2,0),rot_mat(2,1),rot_mat(2,2),1.); std::transform( P.points_begin(), P.points_end(), P.points_begin(), t_rot); } //initialization done init = 1; }
void principal_comp(int n, atom_id index[], t_atom atom[], rvec x[], matrix trans, rvec d) { int i, j, ai, m, nrot; real mm, rx, ry, rz; double **inten, dd[NDIM], tvec[NDIM], **ev; #ifdef DEBUG real e[NDIM]; #endif real temp; snew(inten, NDIM); snew(ev, NDIM); for (i = 0; (i < NDIM); i++) { snew(inten[i], NDIM); snew(ev[i], NDIM); dd[i] = 0.0; #ifdef DEBUG e[i] = 0.0; #endif } for (i = 0; (i < NDIM); i++) { for (m = 0; (m < NDIM); m++) { inten[i][m] = 0; } } for (i = 0; (i < n); i++) { ai = index[i]; mm = atom[ai].m; rx = x[ai][XX]; ry = x[ai][YY]; rz = x[ai][ZZ]; inten[0][0] += mm*(sqr(ry)+sqr(rz)); inten[1][1] += mm*(sqr(rx)+sqr(rz)); inten[2][2] += mm*(sqr(rx)+sqr(ry)); inten[1][0] -= mm*(ry*rx); inten[2][0] -= mm*(rx*rz); inten[2][1] -= mm*(rz*ry); } inten[0][1] = inten[1][0]; inten[0][2] = inten[2][0]; inten[1][2] = inten[2][1]; #ifdef DEBUG ptrans("initial", inten, dd, e); #endif for (i = 0; (i < DIM); i++) { for (m = 0; (m < DIM); m++) { trans[i][m] = inten[i][m]; } } /* Call numerical recipe routines */ jacobi(inten, 3, dd, ev, &nrot); #ifdef DEBUG ptrans("jacobi", ev, dd, e); #endif /* Sort eigenvalues in ascending order */ #define SWAPPER(i) \ if (fabs(dd[i+1]) < fabs(dd[i])) { \ temp = dd[i]; \ for (j = 0; (j < NDIM); j++) { tvec[j] = ev[j][i]; } \ dd[i] = dd[i+1]; \ for (j = 0; (j < NDIM); j++) { ev[j][i] = ev[j][i+1]; } \ dd[i+1] = temp; \ for (j = 0; (j < NDIM); j++) { ev[j][i+1] = tvec[j]; } \ } SWAPPER(0) SWAPPER(1) SWAPPER(0) #ifdef DEBUG ptrans("swap", ev, dd, e); t_trans(trans, dd, ev); #endif for (i = 0; (i < DIM); i++) { d[i] = dd[i]; for (m = 0; (m < DIM); m++) { trans[i][m] = ev[m][i]; } } for (i = 0; (i < NDIM); i++) { sfree(inten[i]); sfree(ev[i]); } sfree(inten); sfree(ev); }