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BackgroundMesh.cpp
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Christophe Geuzaine authoredChristophe Geuzaine authored
BackgroundMesh.cpp 23.26 KiB
// Gmsh - Copyright (C) 1997-2019 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// issues on https://gitlab.onelab.info/gmsh/gmsh/issues.
#include "GmshMessage.h"
#include "BackgroundMesh.h"
#include "Numeric.h"
#include "Context.h"
#include "GVertex.h"
#include "GEdge.h"
#include "GFace.h"
#include "GModel.h"
#include "OS.h"
#include "Field.h"
#include "MElement.h"
#include "MElementOctree.h"
#include "MLine.h"
#include "MTriangle.h"
#include "MQuadrangle.h"
#include "MVertex.h"
#if defined(HAVE_SOLVER)
#include "dofManager.h"
#include "laplaceTerm.h"
#include "linearSystemCSR.h"
#include "linearSystemFull.h"
#include "linearSystemPETSc.h"
#endif
#if defined(HAVE_ANN)
static const int NBANN = 2;
#endif
static const int MAX_THREADS = 256;
std::vector<backgroundMesh *> backgroundMesh::_current =
std::vector<backgroundMesh *>(MAX_THREADS, (backgroundMesh *)0);
void backgroundMesh::set(GFace *gf)
{
int t = Msg::GetThreadNum();
if(t >= MAX_THREADS){
Msg::Error("Maximum number of threads (%d) exceeded in background mesh",
MAX_THREADS);
return;
}
if(_current[t]) delete _current[t];
_current[t] = new backgroundMesh(gf);
}
void backgroundMesh::setCrossFieldsByDistance(GFace *gf)
{
int t = Msg::GetThreadNum();
if(t >= MAX_THREADS) return;
if(_current[t]) delete _current[t];
_current[t] = new backgroundMesh(gf, true);
}
void backgroundMesh::unset()
{
int t = Msg::GetThreadNum();
if(t >= MAX_THREADS) return;
if(_current[t]) delete _current[t];
_current[t] = 0;
}
backgroundMesh *backgroundMesh::current()
{
int t = Msg::GetThreadNum();
if(t >= MAX_THREADS) return 0;
return _current[t];
}
backgroundMesh::backgroundMesh(GFace *_gf, bool cfd)
#if defined(HAVE_ANN)
: _octree(0), uv_kdtree(0), nodes(0), angle_nodes(0), angle_kdtree(0)
#endif
{
if(cfd) {
Msg::Debug("Building cross field using closest distance");
propagateCrossFieldByDistance(_gf);
return;
}
// create a bunch of triangles on the parametric space
// those triangles are local to the backgroundMesh so that
// they do not depend on the actual mesh that can be deleted
std::set<SPoint2> myBCNodes;
for(std::size_t i = 0; i < _gf->triangles.size(); i++) {
MTriangle *e = _gf->triangles[i];
MVertex *news[3];
for(int j = 0; j < 3; j++) {
MVertex *v = e->getVertex(j);
std::map<MVertex *, MVertex *>::iterator it = _3Dto2D.find(v);
MVertex *newv = 0;
if(it == _3Dto2D.end()) {
SPoint2 p;
reparamMeshVertexOnFace(v, _gf, p);
newv = new MVertex(p.x(), p.y(), 0.0);
_vertices.push_back(newv);
_3Dto2D[v] = newv;
_2Dto3D[newv] = v;
if(v->onWhat()->dim() < 2) myBCNodes.insert(p);
}
else
newv = it->second;
news[j] = newv;
}
MTriangle *T2D = new MTriangle(news[0], news[1], news[2]);
_triangles.push_back(T2D);
}
#if defined(HAVE_ANN)
index = new ANNidx[2];
dist = new ANNdist[2];
nodes = annAllocPts(myBCNodes.size(), 3);
std::set<SPoint2>::iterator itp = myBCNodes.begin();
int ind = 0;
while(itp != myBCNodes.end()) {
SPoint2 pt = *itp;
nodes[ind][0] = pt.x();
nodes[ind][1] = pt.y();
nodes[ind][2] = 0.0;
itp++;
ind++;
}
uv_kdtree = new ANNkd_tree(nodes, myBCNodes.size(), 3);
#endif
// build a search structure
_octree = new MElementOctree(_triangles);
// compute the mesh sizes at nodes
if(CTX::instance()->mesh.lcFromPoints) {
propagate1dMesh(_gf);
}
else {
std::map<MVertex *, MVertex *>::iterator itv2 = _2Dto3D.begin();
for(; itv2 != _2Dto3D.end(); ++itv2) {
_sizes[itv2->first] = CTX::instance()->mesh.lcMax;
}
}
// ensure that other criteria are fullfilled
updateSizes(_gf);
// compute optimal mesh orientations
propagateCrossField(_gf);
_3Dto2D.clear();
_2Dto3D.clear();
}
backgroundMesh::~backgroundMesh()
{
for(std::size_t i = 0; i < _vertices.size(); i++) delete _vertices[i];
for(std::size_t i = 0; i < _triangles.size(); i++) delete _triangles[i];
if(_octree) delete _octree;
#if defined(HAVE_ANN)
if(uv_kdtree) delete uv_kdtree;
if(angle_kdtree) delete angle_kdtree;
if(nodes) annDeallocPts(nodes);
if(angle_nodes) annDeallocPts(angle_nodes);
delete[] index;
delete[] dist;
#endif
}
static void propagateValuesOnFace(GFace *_gf,
std::map<MVertex *, double> &dirichlet,
simpleFunction<double> *ONE,
bool in_parametric_plane = false)
{
#if defined(HAVE_SOLVER)
#if defined(HAVE_PETSC)
linearSystemPETSc<double> *_lsys = new linearSystemPETSc<double>;
#elif defined(HAVE_GMM)
linearSystemCSRGmm<double> *_lsys = new linearSystemCSRGmm<double>;
#else
linearSystemFull<double> *_lsys = new linearSystemFull<double>;
#endif
dofManager<double> myAssembler(_lsys);
// fix boundary conditions
std::map<MVertex *, double>::iterator itv = dirichlet.begin();
for(; itv != dirichlet.end(); ++itv) {
myAssembler.fixVertex(itv->first, 0, 1, itv->second);
}
// Number vertices
std::set<MVertex *> vs;
for(std::size_t k = 0; k < _gf->triangles.size(); k++)
for(int j = 0; j < 3; j++) vs.insert(_gf->triangles[k]->getVertex(j));
for(std::size_t k = 0; k < _gf->quadrangles.size(); k++)
for(int j = 0; j < 4; j++) vs.insert(_gf->quadrangles[k]->getVertex(j));
std::map<MVertex *, SPoint3> theMap;
if(in_parametric_plane) {
for(std::set<MVertex *>::iterator it = vs.begin(); it != vs.end(); ++it) {
SPoint2 p;
reparamMeshVertexOnFace(*it, _gf, p);
theMap[*it] = SPoint3((*it)->x(), (*it)->y(), (*it)->z());
(*it)->setXYZ(p.x(), p.y(), 0.0);
}
}
for(std::set<MVertex *>::iterator it = vs.begin(); it != vs.end(); ++it)
myAssembler.numberVertex(*it, 0, 1);
// Assemble
laplaceTerm l(0, 1, ONE);
for(std::size_t k = 0; k < _gf->triangles.size(); k++) {
MTriangle *t = _gf->triangles[k];
SElement se(t);
l.addToMatrix(myAssembler, &se);
}
// Solve
if(myAssembler.sizeOfR()) {
_lsys->systemSolve();
}
// save solution
for(std::set<MVertex *>::iterator it = vs.begin(); it != vs.end(); ++it) {
myAssembler.getDofValue(*it, 0, 1, dirichlet[*it]);
}
if(in_parametric_plane) {
for(std::set<MVertex *>::iterator it = vs.begin(); it != vs.end(); ++it) {
SPoint3 p = theMap[(*it)];
(*it)->setXYZ(p.x(), p.y(), p.z());
}
}
delete _lsys;
#endif
}
void backgroundMesh::propagate1dMesh(GFace *_gf)
{
std::vector<GEdge *> const &e = _gf->edges();
std::vector<GEdge *>::const_iterator it = e.begin();
std::map<MVertex *, double> sizes;
for(; it != e.end(); ++it) {
if(!(*it)->isSeam(_gf)) {
for(std::size_t i = 0; i < (*it)->lines.size(); i++) {
MVertex *v1 = (*it)->lines[i]->getVertex(0);
MVertex *v2 = (*it)->lines[i]->getVertex(1);
if(v1 != v2) {
double d = 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()));
for(int k = 0; k < 2; k++) {
MVertex *v = (*it)->lines[i]->getVertex(k);
std::map<MVertex *, double>::iterator itv = sizes.find(v);
if(itv == sizes.end())
sizes[v] = log(d);
else
itv->second = 0.5 * (itv->second + log(d));
}
}
}
}
}
simpleFunction<double> ONE(1.0);
propagateValuesOnFace(_gf, sizes, &ONE);
std::map<MVertex *, MVertex *>::iterator itv2 = _2Dto3D.begin();
for(; itv2 != _2Dto3D.end(); ++itv2) {
MVertex *v_2D = itv2->first;
MVertex *v_3D = itv2->second;
_sizes[v_2D] = exp(sizes[v_3D]);
}
}
crossField2d::crossField2d(MVertex *v, GEdge *ge)
{
double p;
bool success = reparamMeshVertexOnEdge(v, ge, p);
if(!success) {
Msg::Warning("cannot reparametrize a point in crossField");
_angle = 0;
return;
}
SVector3 t = ge->firstDer(p);
t.normalize();
_angle = atan2(t.y(), t.x());
crossField2d::normalizeAngle(_angle);
}
void backgroundMesh::propagateCrossFieldByDistance(GFace *_gf)
{
std::vector<GEdge *> const &e = _gf->edges();
std::vector<GEdge *>::const_iterator it = e.begin();
std::map<MVertex *, double> _cosines4, _sines4;
std::map<MVertex *, SPoint2> _param;
for(; it != e.end(); ++it) {
if(!(*it)->isSeam(_gf)) {
for(std::size_t i = 0; i < (*it)->lines.size(); i++) {
MVertex *v[2];
v[0] = (*it)->lines[i]->getVertex(0);
v[1] = (*it)->lines[i]->getVertex(1);
SPoint2 p1, p2;
reparamMeshEdgeOnFace(v[0], v[1], _gf, p1, p2);
/* a correct way of computing angles */
Pair<SVector3, SVector3> der = _gf->firstDer((p1 + p2) * .5);
SVector3 t1 = der.first();
SVector3 t2(v[1]->x() - v[0]->x(), v[1]->y() - v[0]->y(),
v[1]->z() - v[0]->z());
t1.normalize();
t2.normalize();
double _angle = angle(t1, t2);
// double angle = atan2 ( p1.y()-p2.y() , p1.x()-p2.x() );
crossField2d::normalizeAngle(_angle);
for(int i = 0; i < 2; i++) {
std::map<MVertex *, double>::iterator itc = _cosines4.find(v[i]);
std::map<MVertex *, double>::iterator its = _sines4.find(v[i]);
if(itc != _cosines4.end()) {
itc->second = 0.5 * (itc->second + cos(4 * _angle));
its->second = 0.5 * (its->second + sin(4 * _angle));
}
else {
_param[v[i]] = (i == 0) ? p1 : p2;
_cosines4[v[i]] = cos(4 * _angle);
_sines4[v[i]] = sin(4 * _angle);
}
}
}
}
}
#if defined(HAVE_ANN)
index = new ANNidx[NBANN];
dist = new ANNdist[NBANN];
angle_nodes = annAllocPts(_cosines4.size(), 3);
std::map<MVertex *, double>::iterator itp = _cosines4.begin();
int ind = 0;
_sin.clear();
_cos.clear();
while(itp != _cosines4.end()) {
MVertex *v = itp->first;
double c = itp->second;
SPoint2 pt = _param[v];
double s = _sines4[v];
angle_nodes[ind][0] = pt.x();
angle_nodes[ind][1] = pt.y();
angle_nodes[ind][2] = 0.0;
_cos.push_back(c);
_sin.push_back(s);
itp++;
ind++;
}
angle_kdtree = new ANNkd_tree(angle_nodes, _cosines4.size(), 3);
#endif
}
inline double myAngle(const SVector3 &a, const SVector3 &b, const SVector3 &d)
{
double cosTheta = dot(a, b);
double sinTheta = dot(crossprod(a, b), d);
return atan2(sinTheta, cosTheta);
}
// smoothness = h * (|grad (cos 4 a)| + |grad (sin 4 a)|)
// smoothness is of order 1 if not smooth
// smoothness is of order h/L if smooth
// h --> mesh size
// L --> domain size
double backgroundMesh::getSmoothness(MElement *e)
{
MVertex *v0 = _3Dto2D[e->getVertex(0)];
MVertex *v1 = _3Dto2D[e->getVertex(1)];
MVertex *v2 = _3Dto2D[e->getVertex(2)];
std::map<MVertex *, double>::const_iterator i0 = _angles.find(v0);
std::map<MVertex *, double>::const_iterator i1 = _angles.find(v1);
std::map<MVertex *, double>::const_iterator i2 = _angles.find(v2);
double a[3] = {cos(4 * i0->second), cos(4 * i1->second), cos(4 * i2->second)};
double b[3] = {sin(4 * i0->second), sin(4 * i1->second), sin(4 * i2->second)};
double f[3];
e->interpolateGrad(a, 0, 0, 0, f);
const double gradcos = sqrt(f[0] * f[0] + f[1] * f[1] + f[2] * f[2]);
e->interpolateGrad(b, 0, 0, 0, f);
// const double gradsin = sqrt (f[0]*f[0]+f[1]*f[1]+f[2]*f[2]);
const double h = e->maxEdge();
return (gradcos /*+ gradsin*/) * h;
}
double backgroundMesh::getSmoothness(double u, double v, double w)
{
if(!_octree) return 0.;
MElement *e = _octree->find(u, v, w, 2, true);
if(!e) return -1.0;
MVertex *v0 = e->getVertex(0);
MVertex *v1 = e->getVertex(1);
MVertex *v2 = e->getVertex(2);
std::map<MVertex *, double>::const_iterator i0 = _angles.find(v0);
std::map<MVertex *, double>::const_iterator i1 = _angles.find(v1);
std::map<MVertex *, double>::const_iterator i2 = _angles.find(v2);
double a[3] = {cos(4 * i0->second), cos(4 * i1->second), cos(4 * i2->second)};
double b[3] = {sin(4 * i0->second), sin(4 * i1->second), sin(4 * i2->second)};
double f[3];
e->interpolateGrad(a, 0, 0, 0, f);
const double gradcos = sqrt(f[0] * f[0] + f[1] * f[1] + f[2] * f[2]);
e->interpolateGrad(b, 0, 0, 0, f);
// const double gradsin = sqrt (f[0]*f[0]+f[1]*f[1]+f[2]*f[2]);
const double h = e->maxEdge();
return (gradcos /*+ gradsin*/) * h;
}
void backgroundMesh::propagateCrossField(GFace *_gf)
{
propagateCrossFieldHJ(_gf);
// solve the non liear problem
constantPerElement<double> C;
int ITER = 0;
// int NSMOOTH = _gf->triangles.size();
while(0) {
// int NSMOOTH_NOW = 0;
for(std::size_t i = 0; i < _gf->triangles.size(); i++) {
double smoothness = getSmoothness(_gf->triangles[i]);
double val = smoothness < .5 ? 1.0 : 1.e-3; // exp(-absf/10);
C.set(_gf->triangles[i], val);
}
// if(NSMOOTH_NOW == NSMOOTH) break;
// NSMOOTH = NSMOOTH_NOW;
// break;
_angles.clear();
propagateCrossField(_gf, &C);
if(++ITER > 0) break;
}
// printf("converged in %d iterations\n", ITER);
#if 0
char name[256];
sprintf(name, "cross-%d-%d.pos", _gf->tag(), ITER);
print(name, 0, 1);
sprintf(name, "smooth-%d-%d.pos", _gf->tag(), ITER);
print(name, _gf, 2);
#endif
}
void backgroundMesh::propagateCrossFieldHJ(GFace *_gf)
{
simpleFunction<double> ONE(1.0);
propagateCrossField(_gf, &ONE);
}
void backgroundMesh::propagateCrossField(GFace *_gf,
simpleFunction<double> *ONE)
{
std::map<MVertex *, double> _cosines4, _sines4;
std::vector<GEdge *> const &e = _gf->edges();
std::vector<GEdge *>::const_iterator it = e.begin();
for(; it != e.end(); ++it) {
if(!(*it)->isSeam(_gf)) {
for(std::size_t i = 0; i < (*it)->lines.size(); i++) {
MVertex *v[2];
v[0] = (*it)->lines[i]->getVertex(0);
v[1] = (*it)->lines[i]->getVertex(1);
SPoint2 p1, p2;
reparamMeshEdgeOnFace(v[0], v[1], _gf, p1, p2);
Pair<SVector3, SVector3> der = _gf->firstDer((p1 + p2) * .5);
SVector3 t1 = der.first();
SVector3 t2 = der.second();
SVector3 n = crossprod(t1, t2);
n.normalize();
SVector3 d1(v[1]->x() - v[0]->x(), v[1]->y() - v[0]->y(),
v[1]->z() - v[0]->z());
t1.normalize();
d1.normalize();
double _angle = myAngle(t1, d1, n);
crossField2d::normalizeAngle(_angle);
for(int i = 0; i < 2; i++) {
std::map<MVertex *, double>::iterator itc = _cosines4.find(v[i]);
std::map<MVertex *, double>::iterator its = _sines4.find(v[i]);
if(itc != _cosines4.end()) {
itc->second = 0.5 * (itc->second + cos(4 * _angle));
its->second = 0.5 * (its->second + sin(4 * _angle));
}
else {
_cosines4[v[i]] = cos(4 * _angle);
_sines4[v[i]] = sin(4 * _angle);
}
}
}
}
}
propagateValuesOnFace(_gf, _cosines4, ONE, false);
propagateValuesOnFace(_gf, _sines4, ONE, false);
// print("cos4.pos",0,_cosines4,0);
// print("sin4.pos",0,_sines4,0);
std::map<MVertex *, MVertex *>::iterator itv2 = _2Dto3D.begin();
for(; itv2 != _2Dto3D.end(); ++itv2) {
MVertex *v_2D = itv2->first;
MVertex *v_3D = itv2->second;
double angle = atan2(_sines4[v_3D], _cosines4[v_3D]) / 4.0;
crossField2d::normalizeAngle(angle);
_angles[v_2D] = angle;
}
}
void backgroundMesh::updateSizes(GFace *_gf)
{
std::map<MVertex *, double>::iterator itv = _sizes.begin();
for(; itv != _sizes.end(); ++itv) {
SPoint2 p;
MVertex *v = _2Dto3D[itv->first];
double lc;
if(v->onWhat()->dim() == 0) {
lc = BGM_MeshSize(v->onWhat(), 0, 0, v->x(), v->y(), v->z());
}
else if(v->onWhat()->dim() == 1) {
double u;
v->getParameter(0, u);
lc = BGM_MeshSize(v->onWhat(), u, 0, v->x(), v->y(), v->z());
}
else {
reparamMeshVertexOnFace(v, _gf, p);
lc = BGM_MeshSize(_gf, p.x(), p.y(), v->x(), v->y(), v->z());
}
itv->second = std::min(lc, itv->second);
itv->second = std::max(itv->second, CTX::instance()->mesh.lcMin);
itv->second = std::min(itv->second, CTX::instance()->mesh.lcMax);
}
// do not allow large variations in the size field
// (Int. J. Numer. Meth. Engng. 43, 1143-1165 (1998) MESH GRADATION
// CONTROL, BOROUCHAKI, HECHT, FREY)
std::set<MEdge, Less_Edge> edges;
for(std::size_t i = 0; i < _triangles.size(); i++) {
for(int j = 0; j < _triangles[i]->getNumEdges(); j++) {
edges.insert(_triangles[i]->getEdge(j));
}
}
const double _beta = 1.3;
for(int i = 0; i < 3; i++) {
std::set<MEdge, Less_Edge>::iterator it = edges.begin();
for(; it != edges.end(); ++it) {
MVertex *v0 = it->getVertex(0);
MVertex *v1 = it->getVertex(1);
MVertex *V0 = _2Dto3D[v0];
MVertex *V1 = _2Dto3D[v1];
std::map<MVertex *, double>::iterator s0 = _sizes.find(V0);
std::map<MVertex *, double>::iterator s1 = _sizes.find(V1);
if(s0->second < s1->second)
s1->second = std::min(s1->second, _beta * s0->second);
else
s0->second = std::min(s0->second, _beta * s1->second);
}
}
}
bool backgroundMesh::inDomain(double u, double v, double w) const
{
if(!_octree) return false;
return _octree->find(u, v, w, 2, true) != 0;
}
double backgroundMesh::operator()(double u, double v, double w) const
{
if(!_octree){
Msg::Error("No octree in background mesh");
return 0.;
}
double uv[3] = {u, v, w};
double uv2[3];
MElement *e = _octree->find(u, v, w, 2, true);
if(!e) {
#if defined(HAVE_ANN)
if(uv_kdtree->nPoints() < 2) return -1000.;
double pt[3] = {u, v, 0.0};
#if defined(_OPENMP)
#pragma omp critical // just to avoid crash (still incorrect) - should use nanoflann
#endif
uv_kdtree->annkSearch(pt, 2, index, dist);
SPoint3 p1(nodes[index[0]][0], nodes[index[0]][1], nodes[index[0]][2]);
SPoint3 p2(nodes[index[1]][0], nodes[index[1]][1], nodes[index[1]][2]);
SPoint3 pnew;
double d;
signedDistancePointLine(p1, p2, SPoint3(u, v, 0.), d, pnew);
e = _octree->find(pnew.x(), pnew.y(), 0.0, 2, true);
#endif
if(!e) {
Msg::Error("BGM octree: cannot find UVW=%g %g %g", u, v, w);
return -1000.0; // 0.4;
}
}
e->xyz2uvw(uv, uv2);
std::map<MVertex *, double>::const_iterator itv1 =
_sizes.find(e->getVertex(0));
std::map<MVertex *, double>::const_iterator itv2 =
_sizes.find(e->getVertex(1));
std::map<MVertex *, double>::const_iterator itv3 =
_sizes.find(e->getVertex(2));
return itv1->second * (1 - uv2[0] - uv2[1]) + itv2->second * uv2[0] +
itv3->second * uv2[1];
}
double backgroundMesh::getAngle(double u, double v, double w) const
{
// use closest point for computing cross field angles: this allows NOT to
// generate a spurious mesh and solve a PDE
if(!_octree) {
#if defined(HAVE_ANN)
double angle = 0.;
if(angle_kdtree->nPoints() >= NBANN) {
double pt[3] = {u, v, 0.0};
#if defined(_OPENMP)
#pragma omp critical // just to avoid crash (still incorrect) - should use nanoflann
#endif
angle_kdtree->annkSearch(pt, NBANN, index, dist);
double SINE = 0.0, COSINE = 0.0;
for(int i = 0; i < NBANN; i++) {
SINE += _sin[index[i]];
COSINE += _cos[index[i]];
}
angle = atan2(SINE, COSINE) / 4.0;
}
crossField2d::normalizeAngle(angle);
return angle;
#endif
}
// HACK FOR LEWIS
// h = 1+30(y-x^2)^2 + (1-x)^2
// double x = u;
// double y = v;
// double dhdx = 30 * 2 * (y-x*x) * (-2*x) - 2 * (1-x);
// double dhdy = 30 * 2 * (y-x*x);
// double angles = atan2(y,x*x);
// crossField2d::normalizeAngle (angles);
// return angles;
double uv[3] = {u, v, w};
double uv2[3];
MElement *e = _octree->find(u, v, w, 2, true);
if(!e) {
#if defined(HAVE_ANN)
if(uv_kdtree->nPoints() < 2) return -1000.0;
double pt[3] = {u, v, 0.0};
#if defined(_OPENMP)
#pragma omp critical // just to avoid crash (still incorrect) - should use nanoflann
#endif
uv_kdtree->annkSearch(pt, 2, index, dist);
SPoint3 p1(nodes[index[0]][0], nodes[index[0]][1], nodes[index[0]][2]);
SPoint3 p2(nodes[index[1]][0], nodes[index[1]][1], nodes[index[1]][2]);
SPoint3 pnew;
double d;
signedDistancePointLine(p1, p2, SPoint3(u, v, 0.), d, pnew);
e = _octree->find(pnew.x(), pnew.y(), 0., 2, true);
#endif
if(!e) {
Msg::Error("BGM octree angle: cannot find UVW=%g %g %g", u, v, w);
return -1000.0;
}
}
e->xyz2uvw(uv, uv2);
std::map<MVertex *, double>::const_iterator itv1 =
_angles.find(e->getVertex(0));
std::map<MVertex *, double>::const_iterator itv2 =
_angles.find(e->getVertex(1));
std::map<MVertex *, double>::const_iterator itv3 =
_angles.find(e->getVertex(2));
double cos4 = cos(4 * itv1->second) * (1 - uv2[0] - uv2[1]) +
cos(4 * itv2->second) * uv2[0] + cos(4 * itv3->second) * uv2[1];
double sin4 = sin(4 * itv1->second) * (1 - uv2[0] - uv2[1]) +
sin(4 * itv2->second) * uv2[0] + sin(4 * itv3->second) * uv2[1];
double angle = atan2(sin4, cos4) / 4.0;
crossField2d::normalizeAngle(angle);
return angle;
}
void backgroundMesh::print(const std::string &filename, GFace *gf,
const std::map<MVertex *, double> &_whatToPrint,
int smooth)
{
FILE *f = Fopen(filename.c_str(), "w");
if(!f) {
Msg::Error("Could not open file '%s'", filename.c_str());
return;
}
fprintf(f, "View \"Background Mesh\"{\n");
if(smooth) {
for(std::size_t i = 0; i < gf->triangles.size(); i++) {
MVertex *v1 = gf->triangles[i]->getVertex(0);
MVertex *v2 = gf->triangles[i]->getVertex(1);
MVertex *v3 = gf->triangles[i]->getVertex(2);
double x = getSmoothness(gf->triangles[i]);
fprintf(f, "ST(%g,%g,%g,%g,%g,%g,%g,%g,%g) {%g,%g,%g};\n", v1->x(),
v1->y(), v1->z(), v2->x(), v2->y(), v2->z(), v3->x(), v3->y(),
v3->z(), x, x, x);
}
}
else {
for(std::size_t i = 0; i < _triangles.size(); i++) {
MVertex *v1 = _triangles[i]->getVertex(0);
MVertex *v2 = _triangles[i]->getVertex(1);
MVertex *v3 = _triangles[i]->getVertex(2);
std::map<MVertex *, double>::const_iterator itv1 = _whatToPrint.find(v1);
std::map<MVertex *, double>::const_iterator itv2 = _whatToPrint.find(v2);
std::map<MVertex *, double>::const_iterator itv3 = _whatToPrint.find(v3);
if(!gf) {
fprintf(f, "ST(%g,%g,%g,%g,%g,%g,%g,%g,%g) {%g,%g,%g};\n", v1->x(),
v1->y(), v1->z(), v2->x(), v2->y(), v2->z(), v3->x(), v3->y(),
v3->z(), itv1->second, itv2->second, itv3->second);
}
else {
GPoint p1 = gf->point(SPoint2(v1->x(), v1->y()));
GPoint p2 = gf->point(SPoint2(v2->x(), v2->y()));
GPoint p3 = gf->point(SPoint2(v3->x(), v3->y()));
fprintf(f, "ST(%g,%g,%g,%g,%g,%g,%g,%g,%g) {%g,%g,%g};\n", p1.x(),
p1.y(), p1.z(), p2.x(), p2.y(), p2.z(), p3.x(), p3.y(), p3.z(),
itv1->second, itv2->second, itv3->second);
}
}
}
fprintf(f, "};\n");
fclose(f);
}
MElement *backgroundMesh::getMeshElementByCoord(double u, double v, double w,
bool strict)
{
if(!_octree) {
Msg::Debug("Rebuilding BackgroundMesh element octree");
_octree = new MElementOctree(_triangles);
}
return _octree->find(u, v, w, 2, strict);
}