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qualityMeasures.cpp
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qualityMeasures.cpp 8.88 KiB
// Gmsh - Copyright (C) 1997-2008 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// bugs and problems to <gmsh@geuz.org>.
#include "qualityMeasures.h"
#include "BDS.h"
#include "MVertex.h"
#include "MElement.h"
#include "Numeric.h"
#include "Message.h"
double qmTriangle(const BDS_Point *p1, const BDS_Point *p2, const BDS_Point *p3,
const gmshQualityMeasure4Triangle &cr)
{
return qmTriangle(p1->X, p1->Y, p1->Z, p2->X, p2->Y, p2->Z, p3->X, p3->Y, p3->Z, cr);
}
double qmTriangle(BDS_Face *t, const gmshQualityMeasure4Triangle &cr)
{
BDS_Point *n[4];
t->getNodes(n);
return qmTriangle(n[0], n[1], n[2], cr);
}
double qmTriangle(MTriangle*t, const gmshQualityMeasure4Triangle &cr)
{
return qmTriangle(t->getVertex(0), t->getVertex(1), t->getVertex(2), cr);
}
double qmTriangle(const MVertex *v1, const MVertex *v2, const MVertex *v3,
const gmshQualityMeasure4Triangle &cr)
{
return qmTriangle(v1->x(), v1->y(), v1->z(), v2->x(), v2->y(), v2->z(),
v3->x(), v3->y(), v3->z(), cr);
}
// Triangle abc
// quality is between 0 and 1
double qmTriangle(const double &xa, const double &ya, const double &za,
const double &xb, const double &yb, const double &zb,
const double &xc, const double &yc, const double &zc,
const gmshQualityMeasure4Triangle &cr)
{
double quality;
switch(cr){
case QMTRI_RHO:
{
// quality = rho / R = 2 * inscribed radius / circumradius
double a [3] = {xc - xb, yc - yb, zc - zb};
double b [3] = {xa - xc, ya - yc, za - zc};
double c [3] = {xb - xa, yb - ya, zb - za};
norme(a);
norme(b);
norme(c);
double pva [3]; prodve(b, c, pva); const double sina = norm3(pva);
double pvb [3]; prodve(c, a, pvb); const double sinb = norm3(pvb);
double pvc [3]; prodve(a, b, pvc); const double sinc = norm3(pvc);
if (sina == 0.0 && sinb == 0.0 && sinc == 0.0) quality = 0.0;
else quality = 2 * (2 * sina * sinb * sinc / (sina + sinb + sinc));
}
break;
// condition number
case QMTRI_COND:
{
double a [3] = {xc - xa, yc - ya, zc - za};
double b [3] = {xb - xa, yb - ya, zb - za};
double c [3] ; prodve(a, b, c); norme(c);
double A[3][3] = {{a[0] , b[0] , c[0]} ,
{a[1] , b[1] , c[1]} ,
{a[2] , b[2] , c[2]}};
quality = -1;
}
break;
default:
Msg::Error("Unknown quality measure");
return 0.;
}
return quality;
}
double qmTet(MTetrahedron *t, const gmshQualityMeasure4Tet &cr, double *volume)
{
return qmTet(t->getVertex(0), t->getVertex(1), t->getVertex(2), t->getVertex(3),
cr, volume);
}
double qmTet(const MVertex *v1, const MVertex *v2, const MVertex *v3,
const MVertex *v4, const gmshQualityMeasure4Tet &cr, double *volume)
{
return qmTet(v1->x(), v1->y(), v1->z(), v2->x(), v2->y(), v2->z(),
v3->x(), v3->y(), v3->z(), v4->x(), v4->y(), v4->z(), cr, volume);
}
double qmTet(const double &x1, const double &y1, const double &z1,
const double &x2, const double &y2, const double &z2,
const double &x3, const double &y3, const double &z3,
const double &x4, const double &y4, const double &z4,
const gmshQualityMeasure4Tet &cr, double *volume)
{
double quality;
switch(cr){
case QMTET_ONE:
return 1.0;
case QMTET_3:
{
double mat[3][3];
mat[0][0] = x2 - x1;
mat[0][1] = x3 - x1;
mat[0][2] = x4 - x1;
mat[1][0] = y2 - y1;
mat[1][1] = y3 - y1;
mat[1][2] = y4 - y1;
mat[2][0] = z2 - z1;
mat[2][1] = z3 - z1;
mat[2][2] = z4 - z1;
*volume = fabs(det3x3(mat)) / 6.;
double l = ((x2 - x1) * (x2 - x1) +
(y2 - y1) * (y2 - y1) +
(z2 - z1) * (z2 - z1));
l += ((x3 - x1) * (x3 - x1) + (y3 - y1) * (y3 - y1) + (z3 - z1) * (z3 - z1));
l += ((x4 - x1) * (x4 - x1) + (y4 - y1) * (y4 - y1) + (z4 - z1) * (z4 - z1));
l += ((x3 - x2) * (x3 - x2) + (y3 - y2) * (y3 - y2) + (z3 - z2) * (z3 - z2));
l += ((x4 - x2) * (x4 - x2) + (y4 - y2) * (y4 - y2) + (z4 - z2) * (z4 - z2));
l += ((x3 - x4) * (x3 - x4) + (y3 - y4) * (y3 - y4) + (z3 - z4) * (z3 - z4));
return 12. * pow(3 * fabs(*volume), 2. / 3.) / l;
}
case QMTET_2:
{
double mat[3][3];
mat[0][0] = x2 - x1;
mat[0][1] = x3 - x1;
mat[0][2] = x4 - x1;
mat[1][0] = y2 - y1;
mat[1][1] = y3 - y1;
mat[1][2] = y4 - y1;
mat[2][0] = z2 - z1;
mat[2][1] = z3 - z1;
mat[2][2] = z4 - z1;
*volume = fabs(det3x3(mat)) / 6.;
double p0[3] = {x1, y1, z1};
double p1[3] = {x2, y2, z2};
double p2[3] = {x3, y3, z3};
double p3[3] = {x4, y4, z4};
double s1 = fabs(triangle_area(p0, p1, p2));
double s2 = fabs(triangle_area(p0, p2, p3));
double s3 = fabs(triangle_area(p0, p1, p3));
double s4 = fabs(triangle_area(p1, p2, p3));
double rhoin = 3. * fabs(*volume) / (s1 + s2 + s3 + s4);
double l = sqrt((x2 - x1) * (x2 - x1) +
(y2 - y1) * (y2 - y1) +
(z2 - z1) * (z2 - z1));
l = std::max(l, sqrt((x3 - x1) * (x3 - x1) + (y3 - y1) * (y3 - y1) +
(z3 - z1) * (z3 - z1)));
l = std::max(l, sqrt((x4 - x1) * (x4 - x1) + (y4 - y1) * (y4 - y1) +
(z4 - z1) * (z4 - z1)));
l = std::max(l, sqrt((x3 - x2) * (x3 - x2) + (y3 - y2) * (y3 - y2) +
(z3 - z2) * (z3 - z2)));
l = std::max(l, sqrt((x4 - x2) * (x4 - x2) + (y4 - y2) * (y4 - y2) +
(z4 - z2) * (z4 - z2)));
l = std::max(l, sqrt((x3 - x4) * (x3 - x4) + (y3 - y4) * (y3 - y4) +
(z3 - z4) * (z3 - z4)));
return 2. * sqrt(6.) * rhoin / l;
}
break;
default:
Msg::Error("Unknown quality measure");
return 0.;
}
}
static double mesh_functional_distorsion(MTriangle *t, double u, double v)
{
// compute uncurved element jacobian d_u x and d_v x
double mat[3][3];
// double d1 = t->getPrimaryJacobian(u,v,0,mat);
double d1 = t->getJacobian(u,v,0,mat);
double v1[3] = {mat[0][0], mat[0][1], mat[0][2]};
double v2[3] = {mat[1][0], mat[1][1], mat[1][2]};
double normal1[3];
prodve(v1, v2, normal1);
double nn = sqrt(normal1[0]*normal1[0] +
normal1[1]*normal1[1] +
normal1[2]*normal1[2]);
// compute uncurved element jacobian d_u x and d_v x
double d2 = t->getJacobian(u, v, 0, mat);
double v1b[3] = {mat[0][0], mat[0][1], mat[0][2]};
double v2b[3] = {mat[1][0], mat[1][1], mat[1][2]};
double normal[3];
prodve(v1b, v2b, normal);
double sign;
prosca(normal1, normal, &sign);
double det = norm3(normal) * (sign > 0 ? 1. : -1.) / nn;
// compute distorsion
double dist = std::min(1. / det, det);
return dist;
}
double qmDistorsionOfMapping (MTriangle *e)
{
if (e->getPolynomialOrder() == 1)return 1.0;
IntPt *pts;
int npts;
e->getIntegrationPoints(e->getPolynomialOrder(),&npts, &pts);
double dmin;
for (int i=0;i<npts;i++){
const double u = pts[i].pt[0];
const double v = pts[i].pt[1];
const double w = pts[i].pt[2];
const double di = mesh_functional_distorsion (e,u,v);
dmin = (i==0)? di : std::min(dmin,di);
}
double p[3][2] = {{0,0},{0,1},{1,0}};
for (int i=0;i<3;i++){
const double u = p[i][0];
const double v = p[i][1];
const double di = mesh_functional_distorsion (e,u,v);
dmin = std::min(dmin,di);
}
return dmin;
}
static double mesh_functional_distorsion(MTetrahedron *t, double u, double v, double w)
{
// compute uncurved element jacobian d_u x and d_v x
double mat[3][3];
// const double det1 = t->getPrimaryJacobian(u,v,w, mat);
const double det1 = t->getJacobian(u,v,w, mat);
// const double det1 = det3x3(mat);
const double detN = t->getJacobian(u, v, w, mat);
// const double detN = det3x3(mat);
// printf("%g %g %g = %g %g\n",u,v,w,det1,detN);
if (det1 == 0 || detN == 0) return 0;
double dist = std::min(detN/det1, det1/detN);
return dist;
}
double qmDistorsionOfMapping (MTetrahedron *e)
{
if (e->getPolynomialOrder() == 1)return 1.0;
IntPt *pts;
int npts;
e->getIntegrationPoints(e->getPolynomialOrder(),&npts, &pts);
double dmin;
for (int i=0;i<npts;i++){
const double u = pts[i].pt[0];
const double v = pts[i].pt[1];
const double w = pts[i].pt[2];
const double di = mesh_functional_distorsion (e,u,v,w);
dmin = (i==0)? di : std::min(dmin,di);
}
double p[4][3] = {{0,0,0},{0,1,0},{1,0,0},{0,0,1}};
for (int i=0;i<4;i++){
const double u = p[i][0];
const double v = p[i][1];
const double w = p[i][2];
const double di = mesh_functional_distorsion (e,u,v,w);
dmin = std::min(dmin,di);
}
// printf("DMIN = %g\n\n",dmin);
return dmin< 0 ? 0 :dmin;
}