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Christophe Geuzaine authoredreorganized solver directory + added c++ solver example
Christophe Geuzaine authoredreorganized solver directory + added c++ solver example
surfaceFiller.cpp 14.27 KiB
#include "GmshConfig.h"
#include "surfaceFiller.h"
#include "Field.h"
#include "GModel.h"
#include <queue>
#include <stack>
/// Here, we aim at producing a set of points that
/// enables to generate a nice quad mesh
#if defined(HAVE_RTREE)
#include "rtree.h"
#endif
#include "MVertex.h"
#include "MElement.h"
//#include "directions3D.h"
#include "BackgroundMesh.h"
#include "intersectCurveSurface.h"
static const double FACTOR = .81;
static const int NUMDIR = 3;
//static const double DIRS [NUMDIR] = {0.0};
static const double DIRS [NUMDIR] = {0.0, M_PI/20.,-M_PI/20.};
/// a rectangle in the tangent plane is transformed
/// into a parallelogram. We define an exclusion zone
/// that is centered around a vertex and that is used
/// in a r-tree structure for generating points with the
/// right spacing in the tangent plane
#if defined(HAVE_RTREE)
struct surfacePointWithExclusionRegion {
MVertex *_v;
SPoint2 _center;
SPoint2 _p[4][NUMDIR];
SPoint2 _q[4];
SMetric3 _meshMetric;
double _distanceSummed;
/*
+ p3
p4 |
+----c-----+ p2
|
+ p1
*/
surfacePointWithExclusionRegion (MVertex *v, SPoint2 p[4][NUMDIR], SMetric3 & meshMetric, surfacePointWithExclusionRegion *father = 0){
_v = v;
_meshMetric = meshMetric;
_center = (p[0][0]+p[1][0]+p[2][0]+p[3][0])*.25;
for (int i=0;i<4;i++)_q[i] = _center + (p[i][0]+p[(i+1)%4][0]-_center*2)*FACTOR;
for (int i=0;i<4;i++)for (int j=0;j<NUMDIR;j++)_p[i][j] = p[i][j];
if (!father){
fullMatrix<double> V(3,3);
fullVector<double> S(3);
meshMetric.eig(V,S);
double l = std::max(std::max(S(0),S(1)),S(2));
_distanceSummed = sqrt(1/(l*l));
}
else {
_distanceSummed = father->_distanceSummed + distance (father->_v,_v);
}
}
bool inExclusionZone (const SPoint2 &p){
double mat[2][2];
double b[2] , uv[2];
mat[0][0]= _q[1].x()-_q[0].x(); mat[0][1]= _q[2].x()-_q[0].x();
mat[1][0]= _q[1].y()-_q[0].y();
mat[1][1]= _q[2].y()-_q[0].y();
b[0] = p.x() - _q[0].x();
b[1] = p.y() - _q[0].y();
sys2x2(mat, b, uv);
// printf("inversion 1 : %g %g \n",uv[0],uv[1]);
if (uv[0] >= 0 && uv[1] >= 0 && 1.-uv[0] - uv[1] >= 0)return true;
mat[0][0]= _q[3].x()-_q[2].x();
mat[0][1]= _q[0].x()-_q[2].x();
mat[1][0]= _q[3].y()-_q[2].y();
mat[1][1]= _q[0].y()-_q[2].y();
b[0] = p.x() - _q[2].x();
b[1] = p.y() - _q[2].y();
sys2x2(mat, b, uv);
// printf("inversion 2 : %g %g \n",uv[0],uv[1]);
if (uv[0] >= 0 && uv[1] >= 0 && 1.-uv[0] - uv[1] >= 0)return true;
return false;
}
void minmax (double _min[2], double _max[2]) const{
_min[0] = std::min(std::min(std::min(_q[0].x(),_q[1].x()),_q[2].x()),_q[3].x());
_min[1] = std::min(std::min(std::min(_q[0].y(),_q[1].y()),_q[2].y()),_q[3].y());
_max[0] = std::max(std::max(std::max(_q[0].x(),_q[1].x()),_q[2].x()),_q[3].x());
_max[1] = std::max(std::max(std::max(_q[0].y(),_q[1].y()),_q[2].y()),_q[3].y());
}
};
struct my_wrapper {
bool _tooclose;
SPoint2 _p;
my_wrapper (SPoint2 sp) : _tooclose (false), _p(sp) {}
};
class compareSurfacePointWithExclusionRegionPtr
{
public:
inline bool operator () (const surfacePointWithExclusionRegion *a, const surfacePointWithExclusionRegion *b) const
{
if(a->_distanceSummed > b->_distanceSummed) return false;
if(a->_distanceSummed < b->_distanceSummed) return true;
return a<b;
}
};
bool rtree_callback(surfacePointWithExclusionRegion *neighbour,void* point){
my_wrapper *w = static_cast<my_wrapper*>(point);
if (neighbour->inExclusionZone(w->_p)){
w->_tooclose = true;
return false;
}
return true;
}
bool inExclusionZone (SPoint2 &p,
RTree<surfacePointWithExclusionRegion*,double,2,double> &rtree,
std::vector<surfacePointWithExclusionRegion*> & all ){
// should assert that the point is inside the domain
if (!backgroundMesh::current()->inDomain(p.x(),p.y(),0)) return true;
my_wrapper w (p);
double _min[2] = {p.x()-1.e-8, p.y()-1.e-8},_max[2] = {p.x()+1.e-8,p.y()+1.e-8};
rtree.Search(_min,_max,rtree_callback,&w);
return w._tooclose;
for (unsigned int i=0;i<all.size();++i){
if (all[i]->inExclusionZone(p)){
// printf("%g %g is in exclusion zone of %g %g\n",p.x(),p.y(),all[i]._center.x(),all[i]._center.y());
return true;
}
}
return false;
}
// assume a point on the surface, compute the 4 possible neighbors.
//
// ^ t2
// |
// |
// v2
// |
// |
// v1-----+------v3 -------> t1
// |
// |
// v4
//
// we aim at generating a rectangle with sizes size_1 and size_2 along t1 and t2
bool compute4neighbors (GFace *gf, // the surface
MVertex *v_center, // the wertex for which we wnt to generate 4 neighbors
bool goNonLinear, // do we compute the position in the real surface which is nonlinear
SPoint2 newP[4][NUMDIR], // look into other directions
SMetric3 &metricField) // the mesh metric
{
// we assume that v is on surface gf
// get the parameter of the point on the surface
SPoint2 midpoint;
reparamMeshVertexOnFace(v_center, gf, midpoint);
double L = backgroundMesh::current()->operator()(midpoint[0],midpoint[1],0.0);
metricField = SMetric3(1./(L*L));
FieldManager *fields = gf->model()->getFields();
if(fields->getBackgroundField() > 0){
Field *f = fields->get(fields->getBackgroundField());
if (!f->isotropic()){
(*f)(v_center->x(),v_center->y(),v_center->z(), metricField,gf);
}
else {
L = (*f)(v_center->x(),v_center->y(),v_center->z(), gf);
metricField = SMetric3(1./(L*L));
}
}
// printf("M = (%g %g %g)\n",metricField(0,0),metricField(1,1),metricField(0,1));
// get the unit normal at that point
Pair<SVector3, SVector3> der = gf->firstDer(SPoint2(midpoint[0],midpoint[1]));
SVector3 s1 = der.first();
SVector3 s2 = der.second();
SVector3 n = crossprod(s1,s2);
n.normalize();
for (int DIR = 0 ; DIR < NUMDIR ; DIR ++){
double quadAngle = backgroundMesh::current()->getAngle (midpoint[0],midpoint[1],0) + DIRS[DIR];
// normalize vector t1 that is tangent to gf at midpoint
SVector3 t1 = s1 * cos (quadAngle) + s2 * sin (quadAngle);
t1.normalize();
// compute the second direction t2 and normalize (t1,t2,n) is the tangent frame SVector3 t2 = crossprod(t1,n);
t2.normalize();
double size_1 = sqrt(1. / dot(t1,metricField,t1));
double size_2 = sqrt(1. / dot(t2,metricField,t2));
// compute the first fundamental form i.e. the metric tensor at the point
// M_{ij} = s_i \cdot s_j
double M = dot(s1,s1);
double N = dot(s2,s2);
double E = dot(s1,s2);
double metric[2][2] = {{M,E},{E,N}};
// compute covariant coordinates of t1 and t2
// t1 = a s1 + b s2 -->
// t1 . s1 = a M + b E
// t1 . s2 = a E + b N --> solve the 2 x 2 system
// and get covariant coordinates a and b
double rhs1[2] = {dot(t1,s1),dot(t1,s2)}, covar1[2];
sys2x2(metric,rhs1,covar1);
double rhs2[2] = {dot(t2,s1),dot(t2,s2)}, covar2[2];
sys2x2(metric,rhs2,covar2);
// transform the sizes with respect to the metric
// consider a vector v of size 1 in the parameter plane
// its length is sqrt (v^T M v) --> if I want a real size
// of size1 in direction v, it should be sqrt(v^T M v) * size1
double l1 = sqrt(covar1[0]*covar1[0]+covar1[1]*covar1[1]);
double l2 = sqrt(covar2[0]*covar2[0]+covar2[1]*covar2[1]);
covar1[0] /= l1;covar1[1] /= l1;
covar2[0] /= l2;covar2[1] /= l2;
const double size_param_1 = size_1 / sqrt ( M*covar1[0]*covar1[0]+
2*E*covar1[1]*covar1[0]+
N*covar1[1]*covar1[1]);
const double size_param_2 = size_2 / sqrt ( M*covar2[0]*covar2[0]+
2*E*covar2[1]*covar2[0]+
N*covar2[1]*covar2[1]);
/* printf("%12.5E %12.5E %12.5E %12.5E %12.5E %12.5E %12.5E %12.5E %g %g %g %g %g %g %g %g %g %g %g\n",
M*covar1[0]*covar1[0]+
2*E*covar1[1]*covar1[0]+
N*covar1[1]*covar1[1],
M*covar2[0]*covar2[0]+
2*E*covar2[1]*covar2[0]+
N*covar2[1]*covar2[1]
,covar1[0],covar1[1],covar2[0],covar2[1],l1,l2,size_1,size_2,size_param_1,size_param_2,M,N,E,s1.x(),s1.y(),s2.x(),s2.y());*/
// this is the rectangle in the parameter plane.
double r1 = 0*1.e-8*(double)rand() / RAND_MAX;
double r2 = 0*1.e-8*(double)rand() / RAND_MAX;
double r3 = 0*1.e-8*(double)rand() / RAND_MAX;
double r4 = 0*1.e-8*(double)rand() / RAND_MAX;
double r5 = 0*1.e-8*(double)rand() / RAND_MAX;
double r6 = 0*1.e-8*(double)rand() / RAND_MAX;
double r7 = 0*1.e-8* (double)rand() / RAND_MAX;
double r8 = 0*1.e-8*(double)rand() / RAND_MAX;
double newPoint[4][2] = {{midpoint[0] - covar1[0] * size_param_1 +r1,
midpoint[1] - covar1[1] * size_param_1 +r2},
{midpoint[0] - covar2[0] * size_param_2 +r3,
midpoint[1] - covar2[1] * size_param_2 +r4},
{midpoint[0] + covar1[0] * size_param_1 +r5,
midpoint[1] + covar1[1] * size_param_1 +r6},
{midpoint[0] + covar2[0] * size_param_2 +r7,
midpoint[1] + covar2[1] * size_param_2 +r8 }};
// We could stop here. Yet, if the metric varies a lot, we can solve
// a nonlinear problem in order to find a better approximation in the real
// surface if (goNonLinear){//---------------------------------------------------//
surfaceFunctorGFace ss (gf); //
SVector3 dirs[4] = {t1*(-1.0),t2*(-1.0),t1,t2}; //
for (int i=0;i<4;i++){ //
double uvt[3] = {newPoint[i][0],newPoint[i][1],0.0}; //
curveFunctorCircle cf (n,dirs[i],
SVector3(v_center->x(),v_center->y(),v_center->z()),
(i%2==1 ?size_param_1:size_param_2)*.5); //
if (intersectCurveSurface (cf,ss,uvt,size_param_1*1.e-8)){ //
newPoint[i][0] = uvt[0]; //
newPoint[i][1] = uvt[1]; //
} //
} //
} /// end non linear -------------------------------------------------//
// return the four new vertices
for (int i=0;i<4;i++){
newP[i][DIR] = SPoint2(newPoint[i][0],newPoint[i][1]);
}
}
return true;
}
#endif
// fills a surface with points in order to build a nice
// quad mesh ------------
void packingOfParallelograms(GFace* gf, std::vector<MVertex*> &packed, std::vector<SMetric3> &metrics){
#if defined(HAVE_RTREE)
// FILE *f = fopen ("parallelograms.pos","w");
// get all the boundary vertices
std::set<MVertex*> bnd_vertices;
for(unsigned int i=0;i<gf->getNumMeshElements();i++){
MElement* element = gf->getMeshElement(i);
for(int j=0;j<element->getNumVertices();j++){
MVertex *vertex = element->getVertex(j);
if (vertex->onWhat()->dim() < 2)bnd_vertices.insert(vertex);
}
}
// put boundary vertices in a fifo queue
// std::queue<surfacePointWithExclusionRegion*> fifo;
std::set<surfacePointWithExclusionRegion*, compareSurfacePointWithExclusionRegionPtr> fifo;
std::vector<surfacePointWithExclusionRegion*> vertices;
// put the RTREE
RTree<surfacePointWithExclusionRegion*,double,2,double> rtree;
SMetric3 metricField(1.0);
SPoint2 newp[4][NUMDIR];
std::set<MVertex*>::iterator it = bnd_vertices.begin() ;
for (; it != bnd_vertices.end() ; ++it){
compute4neighbors (gf, *it, false, newp, metricField);
surfacePointWithExclusionRegion *sp =
new surfacePointWithExclusionRegion (*it, newp, metricField);
// fifo.push(sp);
fifo.insert(sp);
vertices.push_back(sp);
double _min[2],_max[2];
sp->minmax(_min,_max);
// printf("%g %g .. %g %g\n",_min[0],_min[1],_max[0],_max[1]);
rtree.Insert(_min,_max,sp);
// sp->print(f);
}
// printf("initially : %d vertices in the domain\n",vertices.size());
while(!fifo.empty()){
//surfacePointWithExclusionRegion & parent = fifo.top();
// surfacePointWithExclusionRegion * parent = fifo.front(); surfacePointWithExclusionRegion * parent = *fifo.begin();
// fifo.pop();
fifo.erase(fifo.begin());
for (int dir=0;dir<NUMDIR;dir++){
// printf("dir = %d\n",dir);
int countOK = 0;
for (int i=0;i<4;i++){
// printf("i = %d %12.5E %12.5E \n",i,parent._p[i][dir].x(),parent._p[i][dir].y());
// if (!w._tooclose){
if (!inExclusionZone (parent->_p[i][dir], rtree, vertices) ){
countOK++;
GPoint gp = gf->point(parent->_p[i][dir]);
MFaceVertex *v = new MFaceVertex(gp.x(),gp.y(),gp.z(),gf,gp.u(),gp.v());
// printf(" %g %g %g %g\n",parent._center.x(),parent._center.y(),gp.u(),gp.v());
compute4neighbors (gf, v, false, newp, metricField);
surfacePointWithExclusionRegion *sp =
new surfacePointWithExclusionRegion (v, newp, metricField, parent);
// fifo.push(sp);
fifo.insert(sp);
vertices.push_back(sp);
double _min[2],_max[2];
sp->minmax(_min,_max);
rtree.Insert(_min,_max,sp);
}
}
if (countOK)break;
}
// printf("%d\n",vertices.size());
}
// printf("done\n");
// add the vertices as additional vertices in the
// surface mesh
FILE *f = fopen("points.pos","w");
fprintf(f,"View \"\"{\n");
for (int i=0;i<vertices.size();i++){
if(vertices[i]->_v->onWhat() == gf) {
packed.push_back(vertices[i]->_v);
metrics.push_back(vertices[i]->_meshMetric);
SPoint2 midpoint;
reparamMeshVertexOnFace(vertices[i]->_v, gf, midpoint);
fprintf(f,"TP(%22.15E,%22.15E,%g){%22.15E,%22.15E,%22.15E,%22.15E,%22.15E,%22.15E,%22.15E,%22.15E,%22.15E};\n",vertices[i]->_v->x(),vertices[i]->_v->y(),vertices[i]->_v->z(),
vertices[i]->_meshMetric(0,0),vertices[i]->_meshMetric(0,1),vertices[i]->_meshMetric(0,2),
vertices[i]->_meshMetric(1,0),vertices[i]->_meshMetric(1,1),vertices[i]->_meshMetric(1,2),
vertices[i]->_meshMetric(2,0),vertices[i]->_meshMetric(2,1),vertices[i]->_meshMetric(2,2));
//fprintf(f,"SP(%22.15E,%22.15E,%g){1};\n",midpoint.x(),midpoint.y(),0.0);
}
delete vertices[i];
}
fprintf(f,"};");
fclose(f);
// printf("packed.size = %d\n",packed.size());
// delete rtree;
#endif
}