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Commit bffdbd1d authored by Emilie Marchandise's avatar Emilie Marchandise
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Geo/GRbf.cpp
+ 148
− 79
View file @ bffdbd1d
...@@ -47,23 +47,42 @@ static void printNodes(std::set<MVertex *> myNodes){ ...@@ -47,23 +47,42 @@ static void printNodes(std::set<MVertex *> myNodes){
fprintf(xyz,"View \"\"{\n"); fprintf(xyz,"View \"\"{\n");
for(std::set<MVertex *>::iterator itv = myNodes.begin(); itv !=myNodes.end() ; ++itv){ for(std::set<MVertex *>::iterator itv = myNodes.begin(); itv !=myNodes.end() ; ++itv){
MVertex *v = *itv; MVertex *v = *itv;
fprintf(xyz,"SP(%g,%g,%g){%g};\n", v->x(), v->y(), v->z(), 1.0); fprintf(xyz,"SP(%g,%g,%g){%d};\n", v->x(), v->y(), v->z(), v->getNum());
} }
fprintf(xyz,"};\n"); fprintf(xyz,"};\n");
fclose(xyz); fclose(xyz);
} }
static void exportParametrizedMesh(fullMatrix<double> &UV, int nbNodes){
FILE *f = fopen ("UV.pos", "w");
fprintf(f,"View \" uv \" {\n");
Msg::Info("*** RBF exporting 'UV.pos' ");
for(int id = 0; id < nbNodes; id++){
fprintf(f,"SP(%g,%g,%g){%d};\n", UV(id,0), UV(id,1), 0.0, id);
}
fprintf(f,"};\n");
fclose(f);
}
GRbf::GRbf (double sizeBox, int variableEps, int rbfFun, std::map<MVertex*, SVector3> _normals, GRbf::GRbf (double sizeBox, int variableEps, int rbfFun, std::map<MVertex*, SVector3> _normals,
std::set<MVertex *> allNodes, std::vector<MVertex*> bcNodes) std::set<MVertex *> allNodes, std::vector<MVertex*> bcNodes)
: sBox(sizeBox), variableShapeParam(variableEps), radialFunctionIndex (rbfFun), XYZkdtree(0), _inUV(0) : sBox(sizeBox), variableShapeParam(variableEps), radialFunctionIndex (rbfFun), XYZkdtree(0), _inUV(0)
{ {
allCenters.resize(allNodes.size(),3); allCenters.resize(allNodes.size(),3);
double tol= 5.e-2*sBox; double tol = 4.e-2*sBox;
//remove duplicate vertices //remove duplicate vertices
//add bc nodes //add bc nodes
for(unsigned int i = 0; i < bcNodes.size(); i++) myNodes.insert(bcNodes[i]); for(unsigned int i = 0; i < bcNodes.size(); i++){
myNodes.insert(bcNodes[i]);
//if (bcNodes.size() > 20) i+=3;
}
//then create Mvertex position //then create Mvertex position
std::vector<MVertex*> vertices( allNodes.begin(), allNodes.end() ); std::vector<MVertex*> vertices( allNodes.begin(), allNodes.end() );
MVertexPositionSet pos(vertices); MVertexPositionSet pos(vertices);
...@@ -99,7 +118,7 @@ GRbf::GRbf (double sizeBox, int variableEps, int rbfFun, std::map<MVertex*, SVec ...@@ -99,7 +118,7 @@ GRbf::GRbf (double sizeBox, int variableEps, int rbfFun, std::map<MVertex*, SVec
MVertex *v2 = *itv2; MVertex *v2 = *itv2;
double dist = sqrt((v1->x()-v2->x())*(v1->x()-v2->x())+(v1->y()-v2->y())*(v1->y()-v2->y()) double dist = sqrt((v1->x()-v2->x())*(v1->x()-v2->x())+(v1->y()-v2->y())*(v1->y()-v2->y())
+(v1->z()-v2->z())*(v1->z()-v2->z()))/sBox; +(v1->z()-v2->z())*(v1->z()-v2->z()))/sBox;
if (dist<dist_min && *itv != *itv2) dist_min = dist; if (dist<dist_min && *itv != *itv2 && dist > 1.e-6) dist_min = dist;
} }
index++; index++;
} }
...@@ -184,62 +203,47 @@ void GRbf::buildOctree(double radius){ ...@@ -184,62 +203,47 @@ void GRbf::buildOctree(double radius){
buildXYZkdtree(); buildXYZkdtree();
} }
//compute curvature from level set
void GRbf::computeCurvature(std::map<MVertex*, SPoint3> &rbf_curv){
void GRbf::curvature(double radius, fullMatrix<double> extX, surf, sx,sy,sz, sxx,syy,szz, sxy,sxz,syz,sLap;
const fullMatrix<double> &cntrs,
const fullMatrix<double> &node,
fullMatrix<double> &curvature){
// fullMatrix<double> nodes_in_sph,local_normals,level_set_nodes,level_set_funvals,
// sx,sy,sz, sxx,syy,szz, sxy,sxz,syz,sLap;
// isLocal = true; isLocal = true;
// curvature.resize(node.size1(), node.size1()); fullMatrix<double> curvature(centers.size1(), 1);
// if(nodesInSphere.size() == 0) buildOctree(radius); setup_level_set(centers,normals,extX, surf);
evalRbfDer(1,extX,centers,surf,sx);
evalRbfDer(2,extX,centers,surf,sy);
evalRbfDer(3,extX,centers,surf,sz);
evalRbfDer(11,extX,centers,surf,sxx);
evalRbfDer(12,extX,centers,surf,sxy);
evalRbfDer(13,extX,centers,surf,sxz);
evalRbfDer(22,extX,centers,surf,syy);
evalRbfDer(23,extX,centers,surf,syz);
evalRbfDer(33,extX,centers,surf,szz);
evalRbfDer(222,extX,centers,surf,sLap);
for (int i = 0; i < centers.size1(); i++) {
double norm_grad_s = sqrt(sx(i,0)*sx(i,0)+sy(i,0)*sy(i,0)+sz(i,0)*sz(i,0));
double curv = -sLap(i,0)/norm_grad_s; //+(sx(i,0)*sx(i,0)*sxx(i,0)+sy(i,0)*sy(i,0)*syy(i,0)+sz(i,0)*sz(i,0)*szz(i,0)+2*sx(i,0)*sy(i,0)*sxy(i,0)+2*sy(i,0)*sz(i,0)*syz(i,0)+2*sx(i,0)*sz(i,0)*sxz(i,0))/ (norm_grad_s*norm_grad_s*norm_grad_s);
curvature(i,0) = fabs(curv)/sBox;
}
// for (int i = 0;i<node.size1() ; ++i){ //interpolate
// #if defined (HAVE_ANN) fullMatrix<double> curvatureAll(allCenters.size1(), 1);
// double xyz[3] = {node(i,0), node(i,1), node(i,2) }; evalRbfDer(0,centers,allCenters,curvature,curvatureAll);
// XYZkdtree->annkSearch(xyz, num_neighbours, index, dist);
// std::vector<int> &pts = nodesInSphere[index[0]];
// #endif
// fullMatrix<double> nodes_in_sph(pts.size(),3), local_normals(pts.size(),3); //fill rbf_curv
// fullMatrix<double> LocalOper; std::map<MVertex*, int>::iterator itm = _mapAllV.begin();
for (; itm != _mapAllV.end(); itm++){
int index = itm->second;
SPoint3 coords(curvatureAll(index,0), 0.0, 0.0);
rbf_curv.insert(std::make_pair(itm->first,coords));
}
// for (int k=0; k< pts.size(); k++){
// nodes_in_sph(k,0) = cntrs(pts[k],0);
// nodes_in_sph(k,1) = cntrs(pts[k],1);
// nodes_in_sph(k,2) = cntrs(pts[k],2);
// local_normals(k,0)=normals(pts[k],0);
// local_normals(k,1)=normals(pts[k],1);
// local_normals(k,2)=normals(pts[k],2);
// }
// setup_level_set(nodes_in_sph,local_normals,level_set_nodes,level_set_funvals);
// evalRbfDer(1,level_set_nodes,node,level_set_funvals,sx);
// evalRbfDer(2,level_set_nodes,node,level_set_funvals,sy);
// evalRbfDer(3,level_set_nodes,node,level_set_funvals,sz);
// evalRbfDer(11,level_set_nodes,node,level_set_funvals,sxx);
// evalRbfDer(12,level_set_nodes,node,level_set_funvals,sxy);
// evalRbfDer(13,level_set_nodes,node,level_set_funvals,sxz);
// evalRbfDer(22,level_set_nodes,node,level_set_funvals,syy);
// evalRbfDer(23,level_set_nodes,node,level_set_funvals,syz);
// evalRbfDer(33,level_set_nodes,node,level_set_funvals,szz);
// evalRbfDer(222,level_set_nodes,node,level_set_funvals,sLap);
// double norm_grad_s = sqrt(sx(i,0)*sx(i,0)+sy(i,0)*sy(i,0)+sz(i,0)*sz(i,0));
// double curv = -sLap(i,0)/norm_grad_s +
// (sx(i,0)*sx(i,0)*sxx(i,0)+sy(i,0)*sy(i,0)*syy(i,0)+sz(i,0)*sz(i,0)*szz(i,0)+2*sx(i,0)*sy(i,0)*sxy(i,0)+2*sy(i,0)*sz(i,0)*syz(i,0)+2*sx(i,0)*sz(i,0)*sxz(i,0))/
// (norm_grad_s*norm_grad_s*norm_grad_s);
// curvature(i,0) = fabs(curv);
// }
} }
double GRbf::evalRadialFnDer (int p, double dx, double dy, double dz, double ep){ double GRbf::evalRadialFnDer (int p, double dx, double dy, double dz, double ep){
double r2 = dx*dx+dy*dy+dz*dz; //r^2 double r2 = dx*dx+dy*dy+dz*dz; //r^2
...@@ -283,7 +287,7 @@ fullMatrix<double> GRbf::generateRbfMat(int p, ...@@ -283,7 +287,7 @@ fullMatrix<double> GRbf::generateRbfMat(int p,
int n = nodes1.size1(); int n = nodes1.size1();
fullMatrix<double> rbfMat(m,n); fullMatrix<double> rbfMat(m,n);
double eps =0.5/delta; //0.0677*(nbNodes^0.28)/min_dist; double eps =0.5/delta; //0.0677*(nbNodes^0.28)/min_dist; //0.5
if (_inUV) eps = 0.4/deltaUV; if (_inUV) eps = 0.4/deltaUV;
for (int i = 0; i < m; i++) { for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) { for (int j = 0; j < n; j++) {
...@@ -298,6 +302,7 @@ fullMatrix<double> GRbf::generateRbfMat(int p, ...@@ -298,6 +302,7 @@ fullMatrix<double> GRbf::generateRbfMat(int p,
} }
//DL matrix (B*inv A)
void GRbf::RbfOp(int p, void GRbf::RbfOp(int p,
const fullMatrix<double> &cntrs, const fullMatrix<double> &cntrs,
const fullMatrix<double> &nodes, const fullMatrix<double> &nodes,
...@@ -326,7 +331,7 @@ void GRbf::RbfOp(int p, ...@@ -326,7 +331,7 @@ void GRbf::RbfOp(int p,
D.gemm(rbfMatB, rbfInvA, 1.0, 0.0); D.gemm(rbfMatB, rbfInvA, 1.0, 0.0);
} }
//Evaluates the RBF (p)th derivative w.r.t. the (q)th variable at the new nodes //U = DL * U
void GRbf::evalRbfDer(int p, void GRbf::evalRbfDer(int p,
const fullMatrix<double> &cntrs, const fullMatrix<double> &cntrs,
const fullMatrix<double> &nodes, const fullMatrix<double> &nodes,
...@@ -526,9 +531,10 @@ void GRbf::RbfLapSurface_local_CPM(bool isLow, ...@@ -526,9 +531,10 @@ void GRbf::RbfLapSurface_local_CPM(bool isLow,
} }
//NEW METHOD #1 CPM GLOBAL HIGH //NEW METHOD #1 CPM GLOBAL HIGH
void GRbf::RbfLapSurface_global_CPM_high(const fullMatrix<double> &cntrs, void GRbf::RbfLapSurface_global_CPM_high_2(const fullMatrix<double> &cntrs,
const fullMatrix<double> &normals, const fullMatrix<double> &normals,
fullMatrix<double> &Oper){ fullMatrix<double> &Oper){
Msg::Info("*** RBF ... building Laplacian operator");
int numNodes = cntrs.size1(); int numNodes = cntrs.size1();
int nnTot = 3*numNodes; int nnTot = 3*numNodes;
Oper.resize(nnTot,nnTot); Oper.resize(nnTot,nnTot);
...@@ -575,16 +581,19 @@ void GRbf::RbfLapSurface_global_CPM_high(const fullMatrix<double> &cntrs, ...@@ -575,16 +581,19 @@ void GRbf::RbfLapSurface_global_CPM_high(const fullMatrix<double> &cntrs,
} }
A.invertInPlace(); A.invertInPlace();
Oper.gemm(AOper, A, 1.0, 0.0); Oper.gemm(AOper, A, 1.0, 0.0);
Msg::Info("*** RBF builded Laplacian operator");
} }
//NEW METHOD #2 CPM GLOBAL HIGH //NEW METHOD #2 CPM GLOBAL HIGH
//Produces a nxn differentiation matrix (like the projection method) //Produces a nxn differentiation matrix (like the projection method)
//So the local method for this is the local projection method //So the local method for this is the local projection method
void GRbf::RbfLapSurface_global_CPM_high_2(const fullMatrix<double> &cntrs, void GRbf::RbfLapSurface_global_CPM_high(const fullMatrix<double> &cntrs,
const fullMatrix<double> &normals, const fullMatrix<double> &normals,
fullMatrix<double> &Oper){ fullMatrix<double> &Oper){
Msg::Info("*** RBF ... building Laplacian operator");
int numNodes = cntrs.size1(); int numNodes = cntrs.size1();
int nnTot = 3*numNodes; int nnTot = 3*numNodes;
Oper.resize(numNodes,numNodes); Oper.resize(numNodes,numNodes);
...@@ -635,6 +644,8 @@ void GRbf::RbfLapSurface_global_CPM_high_2(const fullMatrix<double> &cntrs, ...@@ -635,6 +644,8 @@ void GRbf::RbfLapSurface_global_CPM_high_2(const fullMatrix<double> &cntrs,
Oper(i,j) = Temp(i,j); Oper(i,j) = Temp(i,j);
} }
} }
Msg::Info("*** RBF builded Laplacian operator");
} }
void GRbf::RbfLapSurface_global_CPM_low(const fullMatrix<double> &cntrs, void GRbf::RbfLapSurface_global_CPM_low(const fullMatrix<double> &cntrs,
...@@ -685,8 +696,8 @@ void GRbf::RbfLapSurface_global_CPM_low(const fullMatrix<double> &cntrs, ...@@ -685,8 +696,8 @@ void GRbf::RbfLapSurface_global_CPM_low(const fullMatrix<double> &cntrs,
double del = (i == j) ? -1.0: 0.0; double del = (i == j) ? -1.0: 0.0;
double pos1 = (i+numNodes == j) ? 1.0: 0.0; double pos1 = (i+numNodes == j) ? 1.0: 0.0;
double pos2 = (i+2*numNodes == j) ? 1.0: 0.0; double pos2 = (i+2*numNodes == j) ? 1.0: 0.0;
Oper(i+numNodes,j) = del + Ix2extX(i,j);//+ pos1; // Oper(i+numNodes,j) = del +Ix2extX(i,j);//+ pos1; //
Oper(i+2*numNodes,j) = del + Ix2extX(i+numNodes,j); //pos2; // Oper(i+2*numNodes,j) = del + Ix2extX(i+numNodes,j); //+ pos2; //
} }
} }
...@@ -696,23 +707,64 @@ void GRbf::solveHarmonicMap(fullMatrix<double> Oper, ...@@ -696,23 +707,64 @@ void GRbf::solveHarmonicMap(fullMatrix<double> Oper,
std::vector<MVertex*> bcNodes, std::vector<MVertex*> bcNodes,
std::vector<double> coords, std::vector<double> coords,
std::map<MVertex*, SPoint3> &rbf_param){ std::map<MVertex*, SPoint3> &rbf_param){
Msg::Info("*** RBF ... solving map");
int nb = Oper.size2(); int nb = Oper.size2();
UV.resize(nb,2); UV.resize(nb,2);
fullMatrix<double> F(nb,2); fullMatrix<double> F(nb,2);
F.scale(0.0); F.scale(0.0);
//UNIT CIRCLE
for (int i=0; i < bcNodes.size(); i++){ for (int i=0; i < bcNodes.size(); i++){
// std::set<MVertex *>::iterator itN = myNodes.find(bcNodes[i]); std::set<MVertex *>::iterator itN = myNodes.find(bcNodes[i]);
// if (itN != myNodes.end()){ if (itN != myNodes.end()){
std::map<MVertex*, int>::iterator itm = _mapV.find(bcNodes[i]); std::map<MVertex*, int>::iterator itm = _mapV.find(bcNodes[i]);
double theta = 2 * M_PI * coords[i]; double theta = 2 * M_PI * coords[i];
int iFix = itm->second; int iFix = itm->second;
for (int j=0;j<nb ; ++j) Oper(iFix,j) = 0.0; for (int j=0;j<nb ; ++j) Oper(iFix,j) = 0.0;
Oper(iFix,iFix) = 1.0; Oper(iFix,iFix) = 1.0;
F(iFix,0) = cos(theta); F(iFix,0) = cos(theta);
F(iFix,1) = sin(theta); F(iFix,1) = sin(theta);
//} }
} }
//SQUARE
// for(std::set<MVertex *>::iterator itv = myNodes.begin(); itv !=myNodes.end() ; ++itv){
// MVertex *v = *itv;
// if (v->getNum() == 1){ //2900){
// std::map<MVertex*, int>::iterator itm = _mapV.find(v);
// int iFix = itm->second;
// for (int j=0;j<nb ; ++j) Oper(iFix,j) = 0.0;
// Oper(iFix,iFix) = 1.0;
// F(iFix,0) = 0.0;
// F(iFix,1) = 0.0;
// }
// if (v->getNum() == 2){//1911){
// std::map<MVertex*, int>::iterator itm = _mapV.find(v);
// int iFix = itm->second;
// for (int j=0;j<nb ; ++j) Oper(iFix,j) = 0.0;
// Oper(iFix,iFix) = 1.0;
// F(iFix,0) = 1.0;
// F(iFix,1) = 0.0;
// }
// if (v->getNum() == 3){//4844){
// std::map<MVertex*, int>::iterator itm = _mapV.find(v);
// int iFix = itm->second;
// for (int j=0;j<nb ; ++j) Oper(iFix,j) = 0.0;
// Oper(iFix,iFix) = 1.0;
// F(iFix,0) = 1.0;
// F(iFix,1) = 1.0;
// }
// if (v->getNum() == 4){//3187){
// std::map<MVertex*, int>::iterator itm = _mapV.find(v);
// int iFix = itm->second;
// for (int j=0;j<nb ; ++j) Oper(iFix,j) = 0.0;
// Oper(iFix,iFix) = 1.0;
// F(iFix,0) = 0.0;
// F(iFix,1) = 1.0;
// }
// }
Oper.invertInPlace(); Oper.invertInPlace();
Oper.mult(F,UV); Oper.mult(F,UV);
...@@ -747,6 +799,7 @@ void GRbf::solveHarmonicMap(fullMatrix<double> Oper, ...@@ -747,6 +799,7 @@ void GRbf::solveHarmonicMap(fullMatrix<double> Oper,
} }
Msg::Info("*** RBF solved map"); Msg::Info("*** RBF solved map");
exportParametrizedMesh(UV, nbNodes);
} }
...@@ -754,14 +807,22 @@ bool GRbf::UVStoXYZ(const double u_eval, const double v_eval, ...@@ -754,14 +807,22 @@ bool GRbf::UVStoXYZ(const double u_eval, const double v_eval,
double &XX, double &YY, double &ZZ, double &XX, double &YY, double &ZZ,
SVector3 &dXdu, SVector3& dXdv, int num_neighbours){ SVector3 &dXdu, SVector3& dXdv, int num_neighbours){
num_neighbours = 30; if (u_eval == lastU && v_eval == lastV){
fullMatrix<double> u_vec(num_neighbours,3), xyz_local(num_neighbours,3); XX = lastX;
fullMatrix<double> u_vec_eval(1, 3), nodes_eval(1,3), xu(1,3), xv(1,3); YY = lastY;
u_vec_eval(0,0) = u_eval; ZZ = lastZ;
u_vec_eval(0,1) = v_eval; dXdu = lastDXDU;
u_vec_eval(0,2) = 0.0; dXdv = lastDXDV;
return true;
}
num_neighbours = std::min(100, nbNodes);
fullMatrix<double> u_vec(num_neighbours,3), xyz_local(num_neighbours,3);
fullMatrix<double> u_vec_eval(1, 3), nodes_eval(1,3), xu(1,3), xv(1,3);
u_vec_eval(0,0) = u_eval;
u_vec_eval(0,1) = v_eval;
u_vec_eval(0,2) = 0.0;
//printf("uvw=%g %g %g \n", u_eval, v_eval, 0.0);
#if defined (HAVE_ANN) #if defined (HAVE_ANN)
double uvw[3] = { u_eval, v_eval, 0.0 }; double uvw[3] = { u_eval, v_eval, 0.0 };
ANNidxArray index = new ANNidx[num_neighbours]; ANNidxArray index = new ANNidx[num_neighbours];
...@@ -790,7 +851,7 @@ bool GRbf::UVStoXYZ(const double u_eval, const double v_eval, ...@@ -790,7 +851,7 @@ bool GRbf::UVStoXYZ(const double u_eval, const double v_eval,
#endif #endif
_inUV = 1; _inUV = 1;
deltaUV = 0.6*dist_min; deltaUV = 0.3*dist_min;
evalRbfDer(0, u_vec, u_vec_eval,xyz_local, nodes_eval); evalRbfDer(0, u_vec, u_vec_eval,xyz_local, nodes_eval);
evalRbfDer(1, u_vec, u_vec_eval,xyz_local, xu); evalRbfDer(1, u_vec, u_vec_eval,xyz_local, xu);
evalRbfDer(2, u_vec, u_vec_eval,xyz_local, xv); evalRbfDer(2, u_vec, u_vec_eval,xyz_local, xv);
...@@ -802,6 +863,14 @@ bool GRbf::UVStoXYZ(const double u_eval, const double v_eval, ...@@ -802,6 +863,14 @@ bool GRbf::UVStoXYZ(const double u_eval, const double v_eval,
dXdu = SVector3(xu(0,0)*sBox, xu(0,1)*sBox, xu(0,2)*sBox); dXdu = SVector3(xu(0,0)*sBox, xu(0,1)*sBox, xu(0,2)*sBox);
dXdv = SVector3(xv(0,0)*sBox, xv(0,1)*sBox, xv(0,2)*sBox); dXdv = SVector3(xv(0,0)*sBox, xv(0,1)*sBox, xv(0,2)*sBox);
//store last computation
lastU = u_eval;
lastV = v_eval;
lastX = XX;
lastY = YY;
lastZ = ZZ;
lastDXDU = dXdu ;
lastDXDV = dXdv ;
return true; return true;
} }
......
Geo/GRbf.h
+ 7
− 7
View file @ bffdbd1d
...@@ -40,13 +40,16 @@ class GRbf { ...@@ -40,13 +40,16 @@ class GRbf {
double radius; double radius;
double sBox; double sBox;
SVector3 lastDXDU, lastDXDV;
double lastX, lastY, lastZ, lastU, lastV;
int variableShapeParam; int variableShapeParam;
int radialFunctionIndex; // Index for the radial function used (0 - GA,1 - MQ, ... ) int radialFunctionIndex; // Index for the radial function used (0 - GA,1 - MQ, ... )
std::set<MVertex *> myNodes; std::set<MVertex *> myNodes; //Used mesh vertices for light rbf
fullMatrix<double> centers; // Data centers (without duplicates) fullMatrix<double> centers; // Data centers (without duplicates)
fullMatrix<double> allCenters; // Data centers fullMatrix<double> allCenters; // Data centers
fullMatrix<double> normals; // Data normals fullMatrix<double> normals; // Data normals(without Duplicates)
fullMatrix<double> surfInterp;//level set fullMatrix<double> surfInterp;//level set
fullMatrix<double> extendedX;//X values extend in and out fullMatrix<double> extendedX;//X values extend in and out
fullMatrix<double> UV;//solution harmonic map laplu=0 and laplV=0 fullMatrix<double> UV;//solution harmonic map laplu=0 and laplV=0
...@@ -131,11 +134,8 @@ class GRbf { ...@@ -131,11 +134,8 @@ class GRbf {
const fullMatrix<double> &normals, const fullMatrix<double> &normals,
fullMatrix<double> &D); fullMatrix<double> &D);
// Calculates the curvature of a surface at a certain node // Calculates the curvature of a surface at centers
void curvature(double radius, void computeCurvature(std::map<MVertex*, SPoint3> &rbf_curv);
const fullMatrix<double> &cntrs,
const fullMatrix<double> &node,
fullMatrix<double> &curvature);
//Finds the U,V,S (in the 0-level set) that are the 'num_neighbours' closest to u_eval and v_eval. //Finds the U,V,S (in the 0-level set) that are the 'num_neighbours' closest to u_eval and v_eval.
//Thus in total, we're working with '3*num_neighbours' nodes //Thus in total, we're working with '3*num_neighbours' nodes
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