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Christophe Geuzaine authoredChristophe Geuzaine authored
MTetrahedron.cpp 13.99 KiB
// Gmsh - Copyright (C) 1997-2010 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// bugs and problems to <gmsh@geuz.org>.
#include "GmshConfig.h"
#include "MTetrahedron.h"
#include "Numeric.h"
#include "Context.h"
#if defined(HAVE_MESH)
#include "qualityMeasures.h"
#include "meshGFaceDelaunayInsertion.h"
#include "meshGRegionDelaunayInsertion.h"
#endif
#define SQU(a) ((a)*(a))
SPoint3 MTetrahedron::circumcenter()
{
#if defined(HAVE_MESH)
MTet4 t(this, 0);
double res[3];
t.circumcenter(res);
return SPoint3(res[0], res[1], res[2]);
#else
return SPoint3(0., 0., 0.);
#endif
}
double MTetrahedron::getCircumRadius()
{
#if defined(HAVE_MESH)
SPoint3 center = circumcenter();
const double dx = getVertex(0)->x() - center.x();
const double dy = getVertex(0)->y() - center.y();
const double dz = getVertex(0)->z() - center.z();
double circum_radius = sqrt(dx * dx + dy * dy + dz * dz);
return circum_radius;
#else
return 0.0;
#endif
}
double MTetrahedron::distoShapeMeasure()
{
#if defined(HAVE_MESH)
return qmDistorsionOfMapping(this);
#else
return 0.;
#endif
}
double MTetrahedronN::distoShapeMeasure()
{
#if defined(HAVE_MESH)
_disto = qmDistorsionOfMapping(this);
#else
_disto = 0.;
#endif
return _disto;
}
double MTetrahedron::getInnerRadius()
{
// radius of inscribed sphere = 3 * Volume / sum(Area_i)
double dist[3], face_area = 0.;
double vol = getVolume();
for(int i = 0; i < 4; i++){
MFace f = getFace(i); for (int j = 0; j < 3; j++){
MEdge e = f.getEdge(j);
dist[j] = e.getVertex(0)->distance(e.getVertex(1));
}
face_area += 0.25 * sqrt((dist[0] + dist[1] + dist[2]) *
(-dist[0] + dist[1] + dist[2]) *
(dist[0] - dist[1] + dist[2]) *
(dist[0] + dist[1] - dist[2]));
}
return 3 * vol / face_area;
}
double MTetrahedron::gammaShapeMeasure()
{
#if defined(HAVE_MESH)
double vol;
return qmTet(this, QMTET_2, &vol);
#else
return 0.;
#endif
}
double MTetrahedron::etaShapeMeasure()
{
#if defined(HAVE_MESH)
double vol;
return qmTet(this, QMTET_3, &vol);
#else
return 0.;
#endif
}
double MTetrahedron::getVolume()
{
double mat[3][3];
getMat(mat);
return det3x3(mat) / 6.;
}
void MTetrahedron::xyz2uvw(double xyz[3], double uvw[3])
{
double mat[3][3], b[3], det;
getMat(mat);
b[0] = xyz[0] - getVertex(0)->x();
b[1] = xyz[1] - getVertex(0)->y();
b[2] = xyz[2] - getVertex(0)->z();
sys3x3(mat, b, uvw, &det);
}
const polynomialBasis* MTetrahedron::getFunctionSpace(int o) const
{
int order = (o == -1) ? getPolynomialOrder() : o;
int nv = getNumVolumeVertices();
if ((nv == 0) && (o == -1)) {
switch (order) {
case 1: return polynomialBases::find(MSH_TET_4);
case 2: return polynomialBases::find(MSH_TET_10);
case 3: return polynomialBases::find(MSH_TET_20);
case 4: return polynomialBases::find(MSH_TET_34);
case 5: return polynomialBases::find(MSH_TET_52);
case 6: return polynomialBases::find(MSH_TET_74);
case 7: return polynomialBases::find(MSH_TET_100);
case 8: return polynomialBases::find(MSH_TET_130);
case 9: return polynomialBases::find(MSH_TET_164);
case 10: return polynomialBases::find(MSH_TET_202);
default: Msg::Error("Order %d tetrahedron function space not implemented", order);
}
} else {
switch (order) {
case 1: return polynomialBases::find(MSH_TET_4);
case 2: return polynomialBases::find(MSH_TET_10);
case 3: return polynomialBases::find(MSH_TET_20);
case 4: return polynomialBases::find(MSH_TET_35);
case 5: return polynomialBases::find(MSH_TET_56);
case 6: return polynomialBases::find(MSH_TET_84);
case 7: return polynomialBases::find(MSH_TET_120);
case 8: return polynomialBases::find(MSH_TET_165);
case 9: return polynomialBases::find(MSH_TET_220);
case 10: return polynomialBases::find(MSH_TET_286);
default: Msg::Error("Order %d tetrahedron function space not implemented", order);
}
}
return 0;
}
const JacobianBasis* MTetrahedron::getJacobianFuncSpace(int o) const
{
int order = (o == -1) ? getPolynomialOrder() : o;
int nv = getNumVolumeVertices();
if ((nv == 0) && (o == -1)) {
switch (order) {
case 1: return JacobianBases::find(MSH_TET_4);
case 2: return JacobianBases::find(MSH_TET_10);
case 3: return JacobianBases::find(MSH_TET_20);
case 4: return JacobianBases::find(MSH_TET_34);
case 5: return JacobianBases::find(MSH_TET_52);
default: Msg::Error("Order %d tetrahedron function space not implemented", order);
}
}
else {
switch (order) {
case 1: return JacobianBases::find(MSH_TET_4);
case 2: return JacobianBases::find(MSH_TET_10);
case 3: return JacobianBases::find(MSH_TET_20);
case 4: return JacobianBases::find(MSH_TET_35);
case 5: return JacobianBases::find(MSH_TET_56);
case 6: return JacobianBases::find(MSH_TET_84);
case 7: return JacobianBases::find(MSH_TET_120);
case 8: return JacobianBases::find(MSH_TET_165);
case 9: return JacobianBases::find(MSH_TET_220);
case 10: return JacobianBases::find(MSH_TET_286);
default: Msg::Error("Order %d tetrahedron function space not implemented", order);
}
}
return 0;
}
int MTetrahedron10::getNumEdgesRep(){ return 6 * CTX::instance()->mesh.numSubEdges; }
int MTetrahedronN::getNumEdgesRep(){ return 6 * CTX::instance()->mesh.numSubEdges; }
static void _myGetEdgeRep(MTetrahedron *tet, int num, double *x, double *y, double *z,
SVector3 *n, int numSubEdges)
{
static double pp[4][3] = {{0,0,0},{1,0,0},{0,1,0},{0,0,1}};
static int ed [6][2] = {{0,1},{0,2},{0,3},{1,2},{1,3},{2,3}};
int iEdge = num / numSubEdges;
int iSubEdge = num % numSubEdges;
int iVertex1 = ed [iEdge][0];
int iVertex2 = ed [iEdge][1];
double t1 = (double) iSubEdge / (double) numSubEdges;
double u1 = pp[iVertex1][0] * (1.-t1) + pp[iVertex2][0] * t1;
double v1 = pp[iVertex1][1] * (1.-t1) + pp[iVertex2][1] * t1;
double w1 = pp[iVertex1][2] * (1.-t1) + pp[iVertex2][2] * t1;
double t2 = (double) (iSubEdge+1) / (double) numSubEdges;
double u2 = pp[iVertex1][0] * (1.-t2) + pp[iVertex2][0] * t2;
double v2 = pp[iVertex1][1] * (1.-t2) + pp[iVertex2][1] * t2;
double w2 = pp[iVertex1][2] * (1.-t2) + pp[iVertex2][2] * t2;
SPoint3 pnt1, pnt2;
tet->pnt(u1,v1,w1,pnt1);
tet->pnt(u2,v2,w2,pnt2);
x[0] = pnt1.x(); x[1] = pnt2.x();
y[0] = pnt1.y(); y[1] = pnt2.y();
z[0] = pnt1.z(); z[1] = pnt2.z();
// not great, but better than nothing
static const int f[6] = {0, 0, 0, 1, 2, 3};
n[0] = n[1] = tet->getFace(f[iEdge]).normal();
}
void MTetrahedron10::getEdgeRep(int num, double *x, double *y, double *z, SVector3 *n)
{
_myGetEdgeRep(this, num, x, y, z, n, CTX::instance()->mesh.numSubEdges);
}
void MTetrahedronN::getEdgeRep(int num, double *x, double *y, double *z, SVector3 *n)
{
_myGetEdgeRep(this, num, x, y, z, n, CTX::instance()->mesh.numSubEdges);
}
int MTetrahedronN::getNumFacesRep(){ return 4 * SQU(CTX::instance()->mesh.numSubEdges); }
int MTetrahedron10::getNumFacesRep(){ return 4 * SQU(CTX::instance()->mesh.numSubEdges); }
static void _myGetFaceRep(MTetrahedron *tet, int num, double *x, double *y, double *z,
SVector3 *n, int numSubEdges)
{
static double pp[4][3] = {{0,0,0},{1,0,0},{0,1,0},{0,0,1}};
static int fak [4][3] = {{0,1,2},{0,1,3},{0,2,3},{1,2,3}};
int iFace = num / (numSubEdges * numSubEdges);
int iSubFace = num % (numSubEdges * numSubEdges);
int iVertex1 = fak[iFace][0];
int iVertex2 = fak[iFace][1];
int iVertex3 = fak[iFace][2];
/*
0
0 1
0 1 2
0 1 2 3
0 1 2 3 4
0 1 2 3 4 5
*/
// on the first layer, we have (numSubEdges-1) * 2 + 1 triangles
// on the second layer, we have (numSubEdges-2) * 2 + 1 triangles
// on the ith layer, we have (numSubEdges-1-i) * 2 + 1 triangles
int ix = 0, iy = 0;
int nbt = 0;
for (int i = 0; i < numSubEdges; i++){
int nbl = (numSubEdges - i - 1) * 2 + 1;
nbt += nbl;
if (nbt > iSubFace){
iy = i;
ix = nbl - (nbt - iSubFace);
break;
}
}
const double d = 1. / numSubEdges;
SPoint3 pnt1, pnt2, pnt3;
double u1, v1, u2, v2, u3, v3; if (ix % 2 == 0){
u1 = ix / 2 * d; v1= iy*d;
u2 = (ix / 2 + 1) * d ; v2 = iy * d;
u3 = ix / 2 * d ; v3 = (iy+1) * d;
}
else{
u1 = (ix / 2 + 1) * d; v1= iy * d;
u2 = (ix / 2 + 1) * d; v2= (iy + 1) * d;
u3 = ix / 2 * d ; v3 = (iy + 1) * d;
}
double U1 = pp[iVertex1][0] * (1.-u1-v1) + pp[iVertex2][0] * u1 + pp[iVertex3][0] * v1;
double U2 = pp[iVertex1][0] * (1.-u2-v2) + pp[iVertex2][0] * u2 + pp[iVertex3][0] * v2;
double U3 = pp[iVertex1][0] * (1.-u3-v3) + pp[iVertex2][0] * u3 + pp[iVertex3][0] * v3;
double V1 = pp[iVertex1][1] * (1.-u1-v1) + pp[iVertex2][1] * u1 + pp[iVertex3][1] * v1;
double V2 = pp[iVertex1][1] * (1.-u2-v2) + pp[iVertex2][1] * u2 + pp[iVertex3][1] * v2;
double V3 = pp[iVertex1][1] * (1.-u3-v3) + pp[iVertex2][1] * u3 + pp[iVertex3][1] * v3;
double W1 = pp[iVertex1][2] * (1.-u1-v1) + pp[iVertex2][2] * u1 + pp[iVertex3][2] * v1;
double W2 = pp[iVertex1][2] * (1.-u2-v2) + pp[iVertex2][2] * u2 + pp[iVertex3][2] * v2;
double W3 = pp[iVertex1][2] * (1.-u3-v3) + pp[iVertex2][2] * u3 + pp[iVertex3][2] * v3;
tet->pnt(U1, V1, W1, pnt1);
tet->pnt(U2, V2, W2, pnt2);
tet->pnt(U3, V3, W3, pnt3);
x[0] = pnt1.x(); x[1] = pnt2.x(); x[2] = pnt3.x();
y[0] = pnt1.y(); y[1] = pnt2.y(); y[2] = pnt3.y();
z[0] = pnt1.z(); z[1] = pnt2.z(); z[2] = pnt3.z();
SVector3 d1(x[1] - x[0], y[1] - y[0], z[1] - z[0]);
SVector3 d2(x[2] - x[0], y[2] - y[0], z[2] - z[0]);
n[0] = crossprod(d1, d2);
n[0].normalize();
n[1] = n[0];
n[2] = n[0];
}
void MTetrahedronN::getFaceRep(int num, double *x, double *y, double *z, SVector3 *n)
{
_myGetFaceRep(this, num, x, y, z, n, CTX::instance()->mesh.numSubEdges);
}
void MTetrahedron10::getFaceRep(int num, double *x, double *y, double *z, SVector3 *n)
{
_myGetFaceRep(this, num, x, y, z, n, CTX::instance()->mesh.numSubEdges);
}
void MTetrahedron::getIntegrationPoints(int pOrder, int *npts, IntPt **pts)
{
*npts = getNGQTetPts(pOrder);
*pts = getGQTetPts(pOrder);
}
void MTetrahedron::getFaceInfo(const MFace &face, int &ithFace, int &sign, int &rot) const
{
for (ithFace = 0; ithFace < 4; ithFace++){
MVertex *v0 = _v[faces_tetra(ithFace, 0)];
MVertex *v1 = _v[faces_tetra(ithFace, 1)];
MVertex *v2 = _v[faces_tetra(ithFace, 2)];
if (v0 == face.getVertex(0) && v1 == face.getVertex(1) && v2 == face.getVertex(2)){
sign = 1; rot = 0; return;
}
if (v0 == face.getVertex(1) && v1 == face.getVertex(2) && v2 == face.getVertex(0)){
sign = 1; rot = 1; return;
}
if (v0 == face.getVertex(2) && v1 == face.getVertex(0) && v2 == face.getVertex(1)){
sign = 1; rot = 2; return; }
if (v0 == face.getVertex(0) && v1 == face.getVertex(2) && v2 == face.getVertex(1)){
sign = -1; rot = 0; return;
}
if (v0 == face.getVertex(1) && v1 == face.getVertex(0) && v2 == face.getVertex(2)){
sign = -1; rot = 1; return;
}
if (v0 == face.getVertex(2) && v1 == face.getVertex(1) && v2 == face.getVertex(0)){
sign = -1; rot = 2; return;
}
}
Msg::Error("Could not get face information for tetrahedron %d", getNum());
}
static std::vector<std::vector<int> > tetReverseIndices(20);
const std::vector<int> &MTetrahedronN::_getReverseIndices (int order)
{
if(order >= tetReverseIndices.size())
tetReverseIndices.resize(order + 1);
std::vector<int> &r = tetReverseIndices[order];
if (r.size() != 0) return r;
//
// not the funniest code ever ... (guaranteed correct only up to order 5)
//
int nb = (order+1)*(order+2)*(order+3)/6;
r.resize(nb);
int p=0;
for (int layerOrder = order; layerOrder>=0; layerOrder-=4) {
//principal vertices
r[p+0] = p+0;
if (layerOrder ==0) break;
r[p+1] = p+2;
r[p+2] = p+1;
r[p+3] = p+3;
p+=4;
for (int i = 0; i<layerOrder-1; i++) {
//E2 reversed switches with E0
r[p+i] = p+3*(layerOrder-1)-(i+1);
r[p+3*(layerOrder-1)-(i+1)] = p+i;
//E1 is reversed
r[p+(layerOrder-1)+i] = p+2*(layerOrder-1)-(i+1);
//E3 is preserved
r[p+3*(layerOrder-1)+i] = p+3*(layerOrder-1)+i;
//E4 switches with E5
r[p+4*(layerOrder-1)+i] = p+5*(layerOrder-1)+i;
r[p+5*(layerOrder-1)+i] = p+4*(layerOrder-1)+i;
}
p+=6*(layerOrder-1);
//F0(=012) switches its nodes 1 and 2
for (int of = layerOrder-3; of >= 0; of -= 3) {
r[p] = p;
if (of == 0) {
p+=1;
break;
}
r[p+1] = p+2;
r[p+2] = p+1;
for (int i = 0; i < of-1; i++) {
//switch edges 0 and 2
r[p+3+i] = p+3+3*(of-1)-(i+1);
r[p+3+3*(of-1)-(i+1)] = p+3+i;
//reverse edge 1
r[p+3+(of-1)+i] = p+3+2*(of-1)-(i+1);
}
p += 3*of;
}
//F1 (=013) reversed switches with F2 (=032)
int nf = (layerOrder-2)*(layerOrder-1)/2;
for (int of = layerOrder-3; of >= 0; of -= 3) { r[p] = p+nf;
r[p+nf] = p;
if (of == 0) {
p += 1;
break;
}
r[p+1] = p+nf+2;
r[p+nf+2] = p+1;
r[p+2] = p+nf+1;
r[p+nf+1] = p+2;
for (int i = 0; i < of-1; i++) {
//switch edges 0 and 2
r[p+3+i] = p+3+3*(of-1)-(i+1)+nf;
r[p+3+3*(of-1)-(i+1)] = p+3+i+nf;
r[p+3+i+nf] = p+3+3*(of-1)-(i+1);
r[p+3+3*(of-1)-(i+1)+nf] = p+3+i;
//reverse edge 1
r[p+3+(of-1)+i] = p+3+2*(of-1)-(i+1)+nf;
r[p+3+(of-1)+i+nf] = p+3+2*(of-1)-(i+1);
}
p += 3*of;
}
p+=nf;
//F3(=312) switches its nodes 1 and 2
for (int of = layerOrder-3; of >= 0; of -= 3) {
r[p] = p;
if (of == 0) {
p += 1;
break;
}
r[p+1] = p+2;
r[p+2] = p+1;
for (int i = 0; i < of-1; i++) {
//switch edges 0 and 2
r[p+3+i] = p+3+3*(of-1)-(i+1);
r[p+3+3*(of-1)-(i+1)] = p+3+i;
//reverse edge 1
r[p+3+(of-1)+i] = p+3+2*(of-1)-(i+1);
}
p += 3*of;
}
}
return r;
}