diff --git a/Adapt/dsvdcmp.cpp b/Adapt/dsvdcmp.cpp
index d143484240e1132eef4259f6a4a8360b8bd018d9..3a6c849a3611307efce2d59ff49851e7994b2f0b 100644
--- a/Adapt/dsvdcmp.cpp
+++ b/Adapt/dsvdcmp.cpp
@@ -1,6 +1,6 @@
-// $Id: dsvdcmp.cpp,v 1.4 2001-01-08 08:05:39 geuzaine Exp $
-#include <math.h>
+// $Id: dsvdcmp.cpp,v 1.5 2001-11-01 09:36:59 geuzaine Exp $
+#include "Gmsh.h"
#include "nrutil.h"
double dpythag(double a, double b)
@@ -136,7 +136,9 @@ void dsvdcmp(double **a, int m, int n, double w[], double **v)
}
break;
}
- if (its == 30) nrerror("no convergence in 30 dsvdcmp iterations");
+ if (its == 1000){
+ Msg(GERROR, "SVD decomposition: no convergence in 1000 iterations");
+ }
x=w[l];
nm=k-1;
y=w[nm];
@@ -190,51 +192,24 @@ void dsvdcmp(double **a, int m, int n, double w[], double **v)
free_dvector(rv1,1,n);
}
+void dsvbksb(double **u, double w[], double **v, int m, int n, double b[], double x[])
+{
+ int jj,j,i;
+ double s,*tmp;
-/* cf. Numerical Recipes in C, p. 62 */
-
-#define PREC 1.e-16
-
-void invert_singular_matrix(double **M, int n, double **I){
- double **V, **T, *W;
- int i, j, k;
-
- V = dmatrix(1,n,1,n);
- T = dmatrix(1,n,1,n);
- W = dvector(1,n);
-
- dsvdcmp(M, n, n, W, V);
-
- for(i=1 ; i<=n ; i++){
- for(j=1 ; j<=n ; j++){
- I[i][j] = 0.0 ;
- T[i][j] = 0.0 ;
- }
- }
-
- for(i=1 ; i<=n ; i++){
- for(j=1 ; j<=n ; j++){
- if(fabs(W[i]) > PREC){
- T[i][j] += M[j][i] / W[i] ;
- }
- /*
- else{
- T[i][j] += 0.0 ;
- }
- */
- }
- }
- for(i=1 ; i<=n ; i++){
- for(j=1 ; j<=n ; j++){
- for(k=1 ; k<=n ; k++){
- I[i][j] += V[i][k] * T[k][j] ;
- }
- }
- }
-
- free_dmatrix(V,1,n,1,n);
- free_dmatrix(T,1,n,1,n);
- free_dvector(W,1,n);
+ tmp=dvector(1,n);
+ for (j=1;j<=n;j++) {
+ s=0.0;
+ if (w[j]) {
+ for (i=1;i<=m;i++) s += u[i][j]*b[i];
+ s /= w[j];
+ }
+ tmp[j]=s;
+ }
+ for (j=1;j<=n;j++) {
+ s=0.0;
+ for (jj=1;jj<=n;jj++) s += v[j][jj]*tmp[jj];
+ x[j]=s;
+ }
+ free_dvector(tmp,1,n);
}
-
-#undef PREC
diff --git a/Mesh/Utils.cpp b/Mesh/Utils.cpp
index 7c0deec3f3dad83feaafa8f64f82be2558d218f7..c4a9887c82440763db7003cca96b4d7eddfe7202 100644
--- a/Mesh/Utils.cpp
+++ b/Mesh/Utils.cpp
@@ -1,4 +1,4 @@
-// $Id: Utils.cpp,v 1.2 2001-08-12 20:45:58 geuzaine Exp $
+// $Id: Utils.cpp,v 1.3 2001-11-01 09:36:59 geuzaine Exp $
#include "Gmsh.h"
#include "Numeric.h"
@@ -11,6 +11,9 @@
extern Context_T CTX;
+void dsvdcmp(double **a, int m, int n, double w[], double **v);
+void dsvbksb(double **u, double w[], double **v, int m, int n, double b[], double x[]);
+
void direction (Vertex * v1, Vertex * v2, double d[3]){
d[0] = v2->Pos.X - v1->Pos.X;
d[1] = v2->Pos.Y - v1->Pos.Y;
@@ -28,242 +31,149 @@ void Projette (Vertex * v, double mat[3][3]){
v->Pos.Z = Z;
}
-void MeanPlane(List_T *points, Surface *s){
- int i, j, ix, iy, iz, N;
- double det,sys[3][3],b[3],res[3],mod,t1[3],t2[3],ex[3],s2s[2][2],r2[2],X,Y,Z;
- Vertex *v;
-
- N = List_Nbr (points);
-
- for (i = 0; i < 3; i++){
- b[i] = 0.0;
- for (j = 0; j < 3; j++){
- sys[i][j] = 0.0;
- }
- }
-
- /* ax + by + cz = 1 */
-
- ix = iy = iz = 0;
-
- // TOLERANCE ! WARNING WARNING
- double eps = 1.e-6 * CTX.lc;
+/*
+ Le concept d'un plan moyen calcule au sens des moidres carres n'est
+ pas le bon. Imagine un quart de cercle extrude d'une faible
+ hauteur. Le plan moyen sera dans le plan du cercle! En attendant
+ mieux, il y a un test de coherence pour les surfaces non-planes. */
- for (i = 0; i < N; i++){
- List_Read (points, i, &v);
-
- if (!i){
- X = v->Pos.X;
- Y = v->Pos.Y;
- Z = v->Pos.Z;
- }
- else{
- if(fabs(X-v->Pos.X) > eps) ix = 1;
- if(fabs(Y-v->Pos.Y) > eps) iy = 1;
- if(fabs(Z-v->Pos.Z) > eps) iz = 1;
- }
-
- sys[0][0] += v->Pos.X * v->Pos.X;
- sys[1][1] += v->Pos.Y * v->Pos.Y;
- sys[2][2] += v->Pos.Z * v->Pos.Z;
- sys[0][1] += v->Pos.X * v->Pos.Y;
- sys[0][2] += v->Pos.X * v->Pos.Z;
- sys[1][2] += v->Pos.Y * v->Pos.Z;
- sys[2][1] = sys[1][2];
- sys[1][0] = sys[0][1];
- sys[2][0] = sys[0][2];
- b[0] += v->Pos.X;
- b[1] += v->Pos.Y;
- b[2] += v->Pos.Z;
- }
-
- s->d = 1.0;
-
- /* x = X */
-
- if (!ix){
- s->d = X;
- res[0] = 1.;
- res[1] = res[2] = 0.0;
- Msg(DEBUG, "Mean plane of type 'x = c'");
+void MeanPlane(List_T *points, Surface *s){
+ int i, j, min, ndata, na;
+ double **U, **V, *W, res[4], ex[3], t1[3], t2[3];
+ Vertex *v;
+ double xm=0., ym=0., zm=0.;
+
+ ndata = List_Nbr(points);
+ na = 3;
+
+ U = dmatrix(1,ndata,1,na);
+ V = dmatrix(1,ndata,1,ndata);
+ W = dvector(1,na);
+
+ for (i=0; i<ndata; i++){
+ List_Read(points, i, &v);
+ xm += v->Pos.X;
+ ym += v->Pos.Y;
+ zm += v->Pos.Z;
}
-
- /* y = Y */
-
- else if (!iy){
- s->d = Y;
- res[1] = 1.;
- res[0] = res[2] = 0.0;
- Msg(DEBUG, "Mean plane of type 'y = c'");
+ xm/=(double)ndata;
+ ym/=(double)ndata;
+ zm/=(double)ndata;
+
+ for (i=0; i<ndata; i++){
+ List_Read(points, i, &v);
+ U[i+1][1] = v->Pos.X-xm;
+ U[i+1][2] = v->Pos.Y-ym;
+ U[i+1][3] = v->Pos.Z-zm;
}
-
- /* z = Z */
-
- else if (!iz){
- s->d = Z;
- res[2] = 1.;
- res[1] = res[0] = 0.0;
- Msg(DEBUG, "Mean plane of type 'z = c'");
- }
-
- /* by + cz = -x */
-
- else if (!sys3x3_with_tol (sys, b, res, &det)){
- s->d = 0.0;
- s2s[0][0] = sys[1][1];
- s2s[0][1] = sys[1][2];
- s2s[1][0] = sys[1][2];
- s2s[1][1] = sys[2][2];
- b[0] = -sys[0][1];
- b[1] = -sys[0][2];
- if (sys2x2 (s2s, b, r2)){
- res[0] = 1.;
- res[1] = r2[0];
- res[2] = r2[1];
- Msg(DEBUG, "Mean plane of type 'by + cz = -x'");
- }
-
- /* ax + cz = -y */
-
- else{
- s->d = 0.0;
- s2s[0][0] = sys[0][0];
- s2s[0][1] = sys[0][2];
- s2s[1][0] = sys[0][2];
- s2s[1][1] = sys[2][2];
- b[0] = -sys[0][1];
- b[1] = -sys[1][2];
- if (sys2x2 (s2s, b, r2)){
- res[0] = r2[0];
- res[1] = 1.;
- res[2] = r2[1];
- Msg(DEBUG, "Mean plane of type 'ax + cz = -y'");
- }
-
- /* ax + by = -z */
-
- else{
- s->d = 1.0;
- s2s[0][0] = sys[0][0];
- s2s[0][1] = sys[0][1];
- s2s[1][0] = sys[0][1];
- s2s[1][1] = sys[1][1];
- b[0] = -sys[0][2];
- b[1] = -sys[1][2];
- if (sys2x2 (s2s, b, r2)){
- res[0] = r2[0];
- res[1] = r2[1];
- res[2] = 1.;
- Msg(DEBUG, "Mean plane of type 'ax + by = -z'");
- }
- else{
- Msg(GERROR, "Problem in mean plane computation");
- }
- }
+ dsvdcmp(U,ndata,na,W,V);
+ if(W[1]<W[2] && W[1]<W[3]) min=1;
+ else if(W[2]<W[1] && W[2]<W[3]) min=2;
+ else min=3;
+ res[0] = V[1][min];
+ res[1] = V[2][min];
+ res[2] = V[3][min];
+ norme(res);
+
+ free_dmatrix(U,1,ndata,1,na);
+ free_dmatrix(V,1,ndata,1,ndata);
+ free_dvector(W,1,na);
+
+ // check coherence of results for non-plane surfaces
+ if(s->Typ != MSH_SURF_PLAN){
+ double res2[3], c[3], cosc, sinc, angplan;
+ double eps=1.e-3;
+ Vertex v1, v2, v3;
+ v1 = InterpolateSurface(s,0.5,0.5,0,0);
+ v2 = InterpolateSurface(s,0.5+eps,0.5,0,0);
+ v3 = InterpolateSurface(s,0.5,0.5+eps,0,0);
+ t1[0] = v2.Pos.X-v1.Pos.X;
+ t1[1] = v2.Pos.Y-v1.Pos.Y;
+ t1[2] = v2.Pos.Z-v1.Pos.Z;
+ t2[0] = v3.Pos.X-v1.Pos.X;
+ t2[1] = v3.Pos.Y-v1.Pos.Y;
+ t2[2] = v3.Pos.Z-v1.Pos.Z;
+ norme(t1);
+ norme(t2);
+ prodve(t1, t2, res2);
+ norme(res2);
+ prodve (res, res2, c);
+ prosca (res, res2, &cosc);
+ sinc = sqrt (c[0] * c[0] + c[1] * c[1] + c[2] * c[2]);
+ angplan = myatan2 (sinc, cosc);
+ angplan = angle_02pi(angplan)*180./Pi;
+ if((angplan>70 && angplan<110) ||
+ (angplan>260 && angplan<280)){
+ Msg(WARNING, "SVD failed (angle=%g): using rough algo...", angplan);
+ res[0]=res2[0];
+ res[1]=res2[1];
+ res[2]=res2[2];
+ goto end;
}
}
-
- s->a = res[0];
- s->b = res[1];
- s->c = res[2];
- mod = sqrt (res[0] * res[0] + res[1] * res[1] + res[2] * res[2]);
- for (i = 0; i < 3; i++)
- res[i] /= mod;
-
- /* L'axe n'est pas l'axe des x */
-
+
ex[0] = ex[1] = ex[2] = 0.0;
- if(res[0] == 0.0)
+ if(res[0]==0.)
ex[0] = 1.0;
- else if(res[1] == 0.0)
+ else if(res[1]==0.)
ex[1] = 1.0;
else
ex[2] = 1.0;
- prodve (res, ex, t1);
-
- mod = sqrt (t1[0] * t1[0] + t1[1] * t1[1] + t1[2] * t1[2]);
- for (i = 0; i < 3; i++)
- t1[i] /= mod;
-
+ prodve(res, ex, t1);
+ norme(t1);
prodve (t1, res, t2);
+ norme(t2);
- mod = sqrt (t2[0] * t2[0] + t2[1] * t2[1] + t2[2] * t2[2]);
- for (i = 0; i < 3; i++)
- t2[i] /= mod;
-
- for (i = 0; i < 3; i++)
- s->plan[0][i] = t1[i];
- for (i = 0; i < 3; i++)
- s->plan[1][i] = t2[i];
- for (i = 0; i < 3; i++)
- s->plan[2][i] = res[i];
+end:
+ res[3] = (xm*res[0]+ym*res[1]+zm*res[2]);
- Msg(DEBUG1, "Plane : (%g x + %g y + %g z = %g)", s->a, s->b, s->c, s->d);
- Msg(DEBUG2, "Normal : (%g , %g , %g )", res[0], res[1], res[2]);
+ s->a = res[0];
+ s->b = res[1];
+ s->c = res[2];
+ s->d = res[3];
+ for(i=0; i<3; i++) s->plan[0][i] = t1[i];
+ for(i=0; i<3; i++) s->plan[1][i] = t2[i];
+ for(i=0; i<3; i++) s->plan[2][i] = res[i];
+
+ Msg(DEBUG1, "Surface: %d", s->Num);
+ Msg(DEBUG2, "SVD : %g,%g,%g (min=%d)", W[1],W[2],W[3],min);
+ Msg(DEBUG2, "Plane : (%g x + %g y + %g z = %g)", s->a, s->b, s->c, s->d);
+ Msg(DEBUG2, "Normal : (%g , %g , %g )", s->a, s->b, s->c);
Msg(DEBUG2, "t1 : (%g , %g , %g )", t1[0], t1[1], t1[2]);
Msg(DEBUG3, "t2 : (%g , %g , %g )", t2[0], t2[1], t2[2]);
- /* Matrice orthogonale */
-
- if (!iz){
- for (i = 0; i < 3; i++){
- for (j = 0; j < 3; j++){
- s->invplan[i][j] = (i == j) ? 1. : 0.;
- s->plan[i][j] = (i == j) ? 1. : 0.;
- }
+ for(i=0;i<3;i++){
+ for(j=0;j<3;j++){
+ s->invplan[i][j] = s->plan[j][i];
}
}
- else{
- for (i = 0; i < 3; i++){
- for (j = 0; j < 3; j++){
- s->invplan[i][j] = s->plan[j][i];
+
+ //check coherence for plane surfaces
+ if(s->Typ==MSH_SURF_PLAN){
+ Curve *c;
+ for(i=0;i<List_Nbr(s->Generatrices);i++) {
+ List_Read(s->Generatrices,i,&c);
+ if(c->Num>0){
+ List_Read(s->Generatrices,i,&c);
+ for(j=0;j<List_Nbr(c->Control_Points);j++){
+ List_Read(c->Control_Points,j,&v);
+ double d = s->a*v->Pos.X+s->b*v->Pos.Y+s->c*v->Pos.Z-s->d;
+ if(fabs(d)>CTX.lc*1.e-3){
+ Msg(GERROR1, "Plane surface %d (%gx+%gy+%gz+%g=0) is not plane!",
+ s->Num, s->a, s->b, s->c, s->d);
+ Msg(GERROR3, "Control point %d = (%g,%g,%g), val=%g",
+ v->Num, v->Pos.X, v->Pos.Y, v->Pos.Z, d);
+ return;
+ }
+ }
}
}
}
-
-// this is the end of the algo as it was used for surface drawing:
-
-#if 0
- /* L'axe n'est pas l'axe des x */
- if(res[0] > res[1]){
- ex[0] = 0.;
- ex[1] = 1.;
- ex[2] = 0.;
- }
- else{
- ex[0] = 1.;
- ex[1] = 0.;
- ex[2] = 0.;
- }
-
- prodve(res,ex,t1);
-
- mod = sqrt (t1[0] * t1[0] + t1[1] * t1[1] + t1[2] * t1[2] ) ;
- for(i=0;i<3;i++) t1[i]/=mod;
-
- prodve(t1,res,t2);
-
- mod = sqrt (t2[0] * t2[0] + t2[1] * t2[1] + t2[2] * t2[2] ) ;
- for(i=0;i<3;i++) t2[i]/=mod;
-
- for(i=0;i<3;i++)s->plan[0][i] = t1[i];
- for(i=0;i<3;i++)s->plan[1][i] = t2[i];
- for(i=0;i<3;i++)s->plan[2][i] = res[i];
-
- /* Matrice orthogonale */
-
- for(i=0;i<3;i++){
- for(j=0;j<3;j++){
- s->invplan[i][j] = s->plan[j][i];
- }
- }
-#endif
}
-
#define Precision 1.e-10
#define MaxIter 20
@@ -300,7 +210,45 @@ void find_bestuv (Surface * s, double X, double Y,
*V = minv;
}
-void invert_singular_matrix(double **M, int n, double **I);
+// Numerical Recipes in C, p. 62
+void invert_singular_matrix(double **M, int n, double **I){
+ double **V, **T, *W;
+ int i, j, k;
+
+ V = dmatrix(1,n,1,n);
+ T = dmatrix(1,n,1,n);
+ W = dvector(1,n);
+
+ dsvdcmp(M, n, n, W, V);
+
+ for(i=1 ; i<=n ; i++){
+ for(j=1 ; j<=n ; j++){
+ I[i][j] = 0.0 ;
+ T[i][j] = 0.0 ;
+ }
+ }
+
+#define PREC 1.e-16 //singular value precision
+ for(i=1 ; i<=n ; i++){
+ for(j=1 ; j<=n ; j++){
+ if(fabs(W[i]) > PREC){
+ T[i][j] += M[j][i] / W[i] ;
+ }
+ }
+ }
+#undef PREC
+ for(i=1 ; i<=n ; i++){
+ for(j=1 ; j<=n ; j++){
+ for(k=1 ; k<=n ; k++){
+ I[i][j] += V[i][k] * T[k][j] ;
+ }
+ }
+ }
+
+ free_dmatrix(V,1,n,1,n);
+ free_dmatrix(T,1,n,1,n);
+ free_dvector(W,1,n);
+}
void XYZtoUV (Surface *s, double X, double Y, double Z, double *U, double *V) {
double Unew,Vnew,err;
@@ -529,7 +477,6 @@ double angle_plan (Vertex * V, Vertex * P1, Vertex * P2, double n[3]){
prosca (PA, PB, &cosc);
prosca (c, n, &sinc);
-
angplan = myatan2 (sinc, cosc);
return angplan;