Select Git revision
qualityMeasures.cpp
Forked from
gmsh / gmsh
Source project has a limited visibility.
qualityMeasures.cpp 10.80 KiB
// Gmsh - Copyright (C) 1997-2013 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// bugs and problems to the public mailing list <gmsh@geuz.org>.
#include "qualityMeasures.h"
#include "BDS.h"
#include "MVertex.h"
#include "MTriangle.h"
#include "MQuadrangle.h"
#include "MTetrahedron.h"
#include "Numeric.h"
#include "polynomialBasis.h"
#include "GmshMessage.h"
#include <limits>
#include <string.h>
double qmTriangle(const BDS_Point *p1, const BDS_Point *p2, const BDS_Point *p3,
const qualityMeasure4Triangle &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 qualityMeasure4Triangle &cr)
{
BDS_Point *n[4];
t->getNodes(n);
return qmTriangle(n[0], n[1], n[2], cr);
}
double qmTriangle(MTriangle*t, const qualityMeasure4Triangle &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 qualityMeasure4Triangle &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 qualityMeasure4Triangle &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 qualityMeasure4Tet &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 qualityMeasure4Tet &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 qualityMeasure4Tet &cr, double *volume)
{
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;
case QMTET_COND:
{
/// condition number is defined as (see Knupp & Freitag in IJNME)
double INVW[3][3] = {{1,-1./sqrt(3.),-1./sqrt(6.)},{0,2/sqrt(3.),-1./sqrt(6.)},{0,0,sqrt(1.5)}};
double A[3][3] = {{x2-x1,y2-y1,z2-z1},{x3-x1,y3-y1,z3-z1},{x4-x1,y4-y1,z4-z1}};
double S[3][3],INVS[3][3];
matmat(A,INVW,S);
*volume = inv3x3(S,INVS) * 0.70710678118654762;//2/sqrt(2);
double normS = norm2 (S);
double normINVS = norm2 (INVS);
return normS * normINVS;
}
default:
Msg::Error("Unknown quality measure");
return 0.;
}
}
/*
double conditionNumberAndDerivativeOfTet(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){
double INVW[3][3] = {{1,-1./sqrt(3.),-1./sqrt(6.)},{0,2/sqrt(3.),-1./sqrt(6.)},{0,0,sqrt(1.5)}};
double A[3][3] = {{x2-x1,y2-y1,z2-z1},{x3-x1,y3-y1,z3-z1},{x4-x1,y4-y1,z4-z1}};
double S[3][3],INVS[3][3];
matmat(A,INVW,S);
double sigma = inv3x3(S,INVS);
double normS = norm2 (S);
double normINVS = norm2 (INVS);
conditionNumber = normS * normINVS;
}
*/
double qmTriangleAngles (MTriangle *e) {
double a = 500;
double worst_quality = std::numeric_limits<double>::max();
double mat[3][3];
double mat2[3][3];
double den = atan(a*(M_PI/9)) + atan(a*(M_PI/9));
// This matrix is used to "rotate" the triangle to get each vertex
// as the "origin" of the mapping in turn
double rot[3][3];
rot[0][0]=-1; rot[0][1]=1; rot[0][2]=0;
rot[1][0]=-1; rot[1][1]=0; rot[1][2]=0;
rot[2][0]= 0; rot[2][1]=0; rot[2][2]=1;
double tmp[3][3];
//double minAngle = 120.0;
for (int i = 0; i < e->getNumPrimaryVertices(); i++) {
const double u = i == 1 ? 1 : 0;
const double v = i == 2 ? 1 : 0;
const double w = 0;
e->getJacobian(u, v, w, mat);
e->getPrimaryJacobian(u,v,w,mat2);
for (int j = 0; j < i; j++) {
matmat(rot,mat,tmp);
memcpy(mat, tmp, sizeof(mat));
}
//get angle
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 v3[3] = {mat2[0][0], mat2[0][1], mat2[0][2] };
double v4[3] = {mat2[1][0], mat2[1][1], mat2[1][2] };
norme(v1);
norme(v2);
norme(v3);
norme(v4);
double v12[3], v34[3];
prodve(v1,v2,v12);
prodve(v3,v4,v34);
norme(v12);
norme(v34);
double orientation;
prosca(v12,v34,&orientation);
// If the triangle is "flipped" it's no good
if (orientation < 0)
return -std::numeric_limits<double>::max();
double c;
prosca(v1,v2,&c);
double x = acos(c)-M_PI/3;
//double angle = (x+M_PI/3)/M_PI*180;
double quality = (atan(a*(x+M_PI/9)) + atan(a*(M_PI/9-x)))/den;
worst_quality = std::min(worst_quality, quality);
//minAngle = std::min(angle, minAngle);
//printf("Angle %g ", angle);
// printf("Quality %g\n",quality);
}
//printf("MinAngle %g \n", minAngle);
//return minAngle;
return worst_quality;
}
double qmQuadrangleAngles (MQuadrangle *e) {
double a = 100;
double worst_quality = std::numeric_limits<double>::max();
double mat[3][3];
double mat2[3][3];
double den = atan(a*(M_PI/4)) + atan(a*(2*M_PI/4 - (M_PI/4)));
// This matrix is used to "rotate" the triangle to get each vertex
// as the "origin" of the mapping in turn
//double rot[3][3];
//rot[0][0]=-1; rot[0][1]=1; rot[0][2]=0;
//rot[1][0]=-1; rot[1][1]=0; rot[1][2]=0;
//rot[2][0]= 0; rot[2][1]=0; rot[2][2]=1;
//double tmp[3][3];
const double u[9] = {-1,-1, 1, 1, 0,0,1,-1,0};
const double v[9] = {-1, 1, 1,-1, -1,1,0,0,0};
for (int i = 0; i < 9; i++) {
e->getJacobian(u[i], v[i], 0, mat);
e->getPrimaryJacobian(u[i],v[i],0,mat2);
//for (int j = 0; j < i; j++) {
// matmat(rot,mat,tmp);
// memcpy(mat, tmp, sizeof(mat));
//}
//get angle
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 v3[3] = {mat2[0][0], mat2[0][1], mat2[0][2] };
double v4[3] = {mat2[1][0], mat2[1][1], mat2[1][2] };
norme(v1);
norme(v2);
norme(v3);
norme(v4);
double v12[3], v34[3];
prodve(v1,v2,v12);
prodve(v3,v4,v34);
norme(v12);
norme(v34);
double orientation;
prosca(v12,v34,&orientation);
// If the if the triangle is "flipped" it's no good
// if (orientation < 0)
// return -std::numeric_limits<double>::max();
double c;
prosca(v1,v2,&c);
double x = fabs(acos(c))-M_PI/2;
//double angle = fabs(acos(c))*180/M_PI;
double quality = (atan(a*(x+M_PI/4)) + atan(a*(2*M_PI/4 - (x+M_PI/4))))/den;
worst_quality = std::min(worst_quality, quality);
}
return worst_quality;
}