/* Compute the intersected (2 x 2) metric between metrics m and n, PRESERVING the directions
of m. Result is stored in mr*/
int intmetsavedir(MMG5_pMesh mesh, double *m,double *n,double *mr) {
int i;
double lambda[2],vp[2][2],siz,isqhmin;
isqhmin = 1.0 / (mesh->info.hmin * mesh->info.hmin);
_MMG5_eigensym(m,lambda,vp);
for (i=0; i<2; i++) {
siz = n[0]*vp[i][0]*vp[i][0] + 2.0*n[1]*vp[i][0]*vp[i][1] + n[2]*vp[i][1]*vp[i][1];
lambda[i] = MG_MAX(lambda[i],siz);
lambda[i] = MG_MIN(lambda[i],isqhmin);
}
mr[0] = lambda[0]*vp[0][0]*vp[0][0] + lambda[1]*vp[1][0]*vp[1][0];
mr[1] = lambda[0]*vp[0][0]*vp[0][1] + lambda[1]*vp[1][0]*vp[1][1];
mr[2] = lambda[0]*vp[0][1]*vp[0][1] + lambda[1]*vp[1][1]*vp[1][1];
return(1);
}
/**
* \param mesh pointer toward the mesh structure.
* \param met pointer toward the metric structure.
* \param nump index of point in which the size must be computed.
* \param lists pointer toward the surfacic ball of \a nump.
* \param ilists size of surfacic ball of \a nump.
* \param hmin minimal edge size.
* \param hmax maximal edge size.
* \param hausd hausdorff value.
* \return the isotropic size at the point.
*
* Define isotropic size at regular point nump, whose surfacic ball is provided.
*
*/
static double
_MMG5_defsizreg(MMG5_pMesh mesh,MMG5_pSol met,int nump,int *lists,
int ilists, double hmin,double hmax,double hausd) {
MMG5_pTetra pt;
MMG5_pxTetra pxt;
MMG5_pPoint p0,p1;
MMG5_Tria tt;
_MMG5_Bezier b;
double ux,uy,uz,det2d,h,isqhmin,isqhmax,ll,lmin,lmax,hnm,s;
double *n,*t,r[3][3],lispoi[3*MMG3D_LMAX+1],intm[3],b0[3],b1[3],c[3],tAA[6],tAb[3],d[3];
double kappa[2],vp[2][2];
int k,na,nb,ntempa,ntempb,iel,ip0;
char iface,i,j,i0;
p0 = &mesh->point[nump];
if ( !p0->xp || MG_EDG(p0->tag) || (p0->tag & MG_NOM) || (p0->tag & MG_REQ)) {
fprintf(stdout," ## Func. _MMG5_defsizreg : wrong point qualification : xp ? %d\n",p0->xp);
return(0);
}
isqhmin = 1.0 / (hmin*hmin);
isqhmax = 1.0 / (hmax*hmax);
n = &mesh->xpoint[p0->xp].n1[0];
/* Step 1 : rotation matrix that sends normal n to the third coordinate vector of R^3 */
if ( !_MMG5_rotmatrix(n,r) ) {
fprintf(stdout,"%s:%d: Error: function _MMG5_rotmatrix return 0\n",
__FILE__,__LINE__);
exit(EXIT_FAILURE);
}
/* Step 2 : rotation of the oriented surfacic ball with r : lispoi[k] is the common edge
between faces lists[k-1] and lists[k] */
iel = lists[0] / 4;
iface = lists[0] % 4;
pt = &mesh->tetra[iel];
lmin = MAXLEN;
lmax = 0.0;
na = nb = 0;
for (i=0; i<3; i++) {
if ( pt->v[_MMG5_idir[iface][i]] != nump ) {
if ( !na )
na = pt->v[_MMG5_idir[iface][i]];
else
nb = pt->v[_MMG5_idir[iface][i]];
}
}
for (k=1; k<ilists; k++) {
iel = lists[k] / 4;
iface = lists[k] % 4;
pt = &mesh->tetra[iel];
ntempa = ntempb = 0;
for (i=0; i<3; i++) {
if ( pt->v[_MMG5_idir[iface][i]] != nump ) {
if ( !ntempa )
ntempa = pt->v[_MMG5_idir[iface][i]];
else
ntempb = pt->v[_MMG5_idir[iface][i]];
}
}
if ( ntempa == na )
p1 = &mesh->point[na];
else if ( ntempa == nb )
p1 = &mesh->point[nb];
else if ( ntempb == na )
p1 = &mesh->point[na];
else {
assert(ntempb == nb);
p1 = &mesh->point[nb];
}
ux = p1->c[0] - p0->c[0];
uy = p1->c[1] - p0->c[1];
uz = p1->c[2] - p0->c[2];
lispoi[3*k+1] = r[0][0]*ux + r[0][1]*uy + r[0][2]*uz;
lispoi[3*k+2] = r[1][0]*ux + r[1][1]*uy + r[1][2]*uz;
lispoi[3*k+3] = r[2][0]*ux + r[2][1]*uy + r[2][2]*uz;
ll = lispoi[3*k+1]*lispoi[3*k+1] + lispoi[3*k+2]*lispoi[3*k+2] + lispoi[3*k+3]*lispoi[3*k+3];
lmin = MG_MIN(lmin,ll);
lmax = MG_MAX(lmax,ll);
na = ntempa;
nb = ntempb;
}
/* Finish with point 0 */
iel = lists[0] / 4;
iface = lists[0] % 4;
pt = &mesh->tetra[iel];
ntempa = ntempb = 0;
for (i=0; i<3; i++) {
if ( pt->v[_MMG5_idir[iface][i]] != nump ) {
if ( !ntempa )
ntempa = pt->v[_MMG5_idir[iface][i]];
else
ntempb = pt->v[_MMG5_idir[iface][i]];
}
}
if ( ntempa == na )
p1 = &mesh->point[na];
else if ( ntempa == nb )
p1 = &mesh->point[nb];
else if ( ntempb == na )
p1 = &mesh->point[na];
else {
assert(ntempb == nb);
p1 = &mesh->point[nb];
}
ux = p1->c[0] - p0->c[0];
uy = p1->c[1] - p0->c[1];
uz = p1->c[2] - p0->c[2];
lispoi[1] = r[0][0]*ux + r[0][1]*uy + r[0][2]*uz;
lispoi[2] = r[1][0]*ux + r[1][1]*uy + r[1][2]*uz;
lispoi[3] = r[2][0]*ux + r[2][1]*uy + r[2][2]*uz;
ll = lispoi[1]*lispoi[1] + lispoi[2]*lispoi[2] + lispoi[3]*lispoi[3];
lmin = MG_MIN(lmin,ll);
lmax = MG_MAX(lmax,ll);
/* list goes modulo ilist */
lispoi[3*ilists+1] = lispoi[1];
lispoi[3*ilists+2] = lispoi[2];
lispoi[3*ilists+3] = lispoi[3];
/* At this point, lispoi contains the oriented surface ball of point p0, that has been rotated
through r, with the convention that triangle l has edges lispoi[l]; lispoi[l+1] */
if ( lmax/lmin > 4.0*hmax*hmax/
(hmin*hmin) ) return(hmax);
/* Check all projections over tangent plane. */
for (k=0; k<ilists-1; k++) {
det2d = lispoi[3*k+1]*lispoi[3*(k+1)+2] - lispoi[3*k+2]*lispoi[3*(k+1)+1];
if ( det2d < 0.0 ) return(hmax);
}
det2d = lispoi[3*(ilists-1)+1]*lispoi[3*0+2] - lispoi[3*(ilists-1)+2]*lispoi[3*0+1];
if ( det2d < 0.0 ) return(hmax);
/* Reconstitution of the curvature tensor at p0 in the tangent plane,
with a quadric fitting approach */
memset(intm,0.0,3*sizeof(double));
memset(tAA,0.0,6*sizeof(double));
memset(tAb,0.0,3*sizeof(double));
for (k=0; k<ilists; k++) {
iel = lists[k] / 4;
iface = lists[k] % 4;
_MMG5_tet2tri(mesh,iel,iface,&tt);
pxt = &mesh->xtetra[mesh->tetra[iel].xt];
if ( !_MMG5_bezierCP(mesh,&tt,&b,MG_GET(pxt->ori,iface)) ) {
fprintf(stdout,"%s:%d: Error: function _MMG5_bezierCP return 0\n",
__FILE__,__LINE__);
exit(EXIT_FAILURE);
}
for (i0=0; i0<3; i0++) {
if ( tt.v[i0] == nump ) break;
}
assert(i0 < 3);
for (j=0; j<10; j++) {
c[0] = b.b[j][0] - p0->c[0];
c[1] = b.b[j][1] - p0->c[1];
c[2] = b.b[j][2] - p0->c[2];
b.b[j][0] = r[0][0]*c[0] + r[0][1]*c[1] + r[0][2]*c[2];
b.b[j][1] = r[1][0]*c[0] + r[1][1]*c[1] + r[1][2]*c[2];
b.b[j][2] = r[2][0]*c[0] + r[2][1]*c[1] + r[2][2]*c[2];
}
/* Mid-point along left edge and endpoint in the rotated frame */
if ( i0 == 0 ) {
memcpy(b0,&(b.b[7][0]),3*sizeof(double));
memcpy(b1,&(b.b[8][0]),3*sizeof(double));
}
else if ( i0 == 1 ) {
memcpy(b0,&(b.b[3][0]),3*sizeof(double));
memcpy(b1,&(b.b[4][0]),3*sizeof(double));
}
else {
memcpy(b0,&(b.b[5][0]),3*sizeof(double));
memcpy(b1,&(b.b[6][0]),3*sizeof(double));
}
s = 0.5;
/* At this point, the two control points are expressed in the rotated frame */
c[0] = 3.0*s*(1.0-s)*(1.0-s)*b0[0] + 3.0*s*s*(1.0-s)*b1[0] + s*s*s*lispoi[3*k+1];
c[1] = 3.0*s*(1.0-s)*(1.0-s)*b0[1] + 3.0*s*s*(1.0-s)*b1[1] + s*s*s*lispoi[3*k+2];
c[2] = 3.0*s*(1.0-s)*(1.0-s)*b0[2] + 3.0*s*s*(1.0-s)*b1[2] + s*s*s*lispoi[3*k+3];
/* Fill matric tAA and second member tAb*/
tAA[0] += c[0]*c[0]*c[0]*c[0];
tAA[1] += c[0]*c[0]*c[1]*c[1];
tAA[2] += c[0]*c[0]*c[0]*c[1];
tAA[3] += c[1]*c[1]*c[1]*c[1];
tAA[4] += c[0]*c[1]*c[1]*c[1];
tAA[5] += c[0]*c[0]*c[1]*c[1];
tAb[0] += c[0]*c[0]*c[2];
tAb[1] += c[1]*c[1]*c[2];
tAb[2] += c[0]*c[1]*c[2];
s = 1.0;
/* At this point, the two control points are expressed in the rotated frame */
c[0] = 3.0*s*(1.0-s)*(1.0-s)*b0[0] + 3.0*s*s*(1.0-s)*b1[0] + s*s*s*lispoi[3*k+1];
c[1] = 3.0*s*(1.0-s)*(1.0-s)*b0[1] + 3.0*s*s*(1.0-s)*b1[1] + s*s*s*lispoi[3*k+2];
c[2] = 3.0*s*(1.0-s)*(1.0-s)*b0[2] + 3.0*s*s*(1.0-s)*b1[2] + s*s*s*lispoi[3*k+3];
/* Fill matric tAA and second member tAb*/
tAA[0] += c[0]*c[0]*c[0]*c[0];
tAA[1] += c[0]*c[0]*c[1]*c[1];
tAA[2] += c[0]*c[0]*c[0]*c[1];
tAA[3] += c[1]*c[1]*c[1]*c[1];
tAA[4] += c[0]*c[1]*c[1]*c[1];
tAA[5] += c[0]*c[0]*c[1]*c[1];
tAb[0] += c[0]*c[0]*c[2];
tAb[1] += c[1]*c[1]*c[2];
tAb[2] += c[0]*c[1]*c[2];
/* Mid-point along median edge and endpoint in the rotated frame */
if ( i0 == 0 ) {
c[0] = A64TH*(b.b[1][0] + b.b[2][0] + 3.0*(b.b[3][0] + b.b[4][0])) \
+ 3.0*A16TH*(b.b[6][0] + b.b[7][0] + b.b[9][0]) + A32TH*(b.b[5][0] + b.b[8][0]);
c[1] = A64TH*(b.b[1][1] + b.b[2][1] + 3.0*(b.b[3][1] + b.b[4][1])) \
+ 3.0*A16TH*(b.b[6][1] + b.b[7][1] + b.b[9][1]) + A32TH*(b.b[5][1] + b.b[8][1]);
c[2] = A64TH*(b.b[1][2] + b.b[2][2] + 3.0*(b.b[3][2] + b.b[4][2])) \
+ 3.0*A16TH*(b.b[6][2] + b.b[7][2] + b.b[9][2]) + A32TH*(b.b[5][2] + b.b[8][2]);
d[0] = 0.125*b.b[1][0] + 0.375*(b.b[3][0] + b.b[4][0]) + 0.125*b.b[2][0];
d[1] = 0.125*b.b[1][1] + 0.375*(b.b[3][1] + b.b[4][1]) + 0.125*b.b[2][1];
d[2] = 0.125*b.b[1][2] + 0.375*(b.b[3][2] + b.b[4][2]) + 0.125*b.b[2][2];
}
else if (i0 == 1) {
c[0] = A64TH*(b.b[0][0] + b.b[2][0] + 3.0*(b.b[5][0] + b.b[6][0])) \
+ 3.0*A16TH*(b.b[3][0] + b.b[8][0] + b.b[9][0]) + A32TH*(b.b[4][0] + b.b[7][0]);
c[1] = A64TH*(b.b[0][1] + b.b[2][1] + 3.0*(b.b[5][1] + b.b[6][1])) \
+ 3.0*A16TH*(b.b[3][1] + b.b[8][1] + b.b[9][1]) + A32TH*(b.b[4][1] + b.b[7][1]);
c[2] = A64TH*(b.b[0][2] + b.b[2][2] + 3.0*(b.b[5][2] + b.b[6][2])) \
+ 3.0*A16TH*(b.b[3][2] + b.b[8][2] + b.b[9][2]) + A32TH*(b.b[4][2] + b.b[7][2]);
d[0] = 0.125*b.b[2][0] + 0.375*(b.b[5][0] + b.b[6][0]) + 0.125*b.b[0][0];
d[1] = 0.125*b.b[2][1] + 0.375*(b.b[5][1] + b.b[6][1]) + 0.125*b.b[0][1];
d[2] = 0.125*b.b[2][2] + 0.375*(b.b[5][2] + b.b[6][2]) + 0.125*b.b[0][2];
}
else {
c[0] = A64TH*(b.b[0][0] + b.b[1][0] + 3.0*(b.b[7][0] + b.b[8][0])) \
+ 3.0*A16TH*(b.b[4][0] + b.b[5][0] + b.b[9][0]) + A32TH*(b.b[3][0] + b.b[6][0]);
c[1] = A64TH*(b.b[0][1] + b.b[1][1] + 3.0*(b.b[7][1] + b.b[8][1])) \
+ 3.0*A16TH*(b.b[4][1] + b.b[5][1] + b.b[9][1]) + A32TH*(b.b[3][1] + b.b[6][1]);
c[2] = A64TH*(b.b[0][2] + b.b[1][2] + 3.0*(b.b[7][2] + b.b[8][2])) \
+ 3.0*A16TH*(b.b[4][2] + b.b[5][2] + b.b[9][2]) + A32TH*(b.b[3][2] + b.b[6][2]);
d[0] = 0.125*b.b[0][0] + 0.375*(b.b[7][0] + b.b[8][0]) + 0.125*b.b[1][0];
d[1] = 0.125*b.b[0][1] + 0.375*(b.b[7][1] + b.b[8][1]) + 0.125*b.b[1][1];
d[2] = 0.125*b.b[0][2] + 0.375*(b.b[7][2] + b.b[8][2]) + 0.125*b.b[1][2];
}
/* Fill matric tAA and second member tAb*/
tAA[0] += c[0]*c[0]*c[0]*c[0];
tAA[1] += c[0]*c[0]*c[1]*c[1];
tAA[2] += c[0]*c[0]*c[0]*c[1];
tAA[3] += c[1]*c[1]*c[1]*c[1];
tAA[4] += c[0]*c[1]*c[1]*c[1];
tAA[5] += c[0]*c[0]*c[1]*c[1];
tAb[0] += c[0]*c[0]*c[2];
tAb[1] += c[1]*c[1]*c[2];
tAb[2] += c[0]*c[1]*c[2];
tAA[0] += d[0]*d[0]*d[0]*d[0];
tAA[1] += d[0]*d[0]*d[1]*d[1];
tAA[2] += d[0]*d[0]*d[0]*d[1];
tAA[3] += d[1]*d[1]*d[1]*d[1];
tAA[4] += d[0]*d[1]*d[1]*d[1];
tAA[5] += d[0]*d[0]*d[1]*d[1];
tAb[0] += d[0]*d[0]*d[2];
tAb[1] += d[1]*d[1]*d[2];
tAb[2] += d[0]*d[1]*d[2];
}
/* solve now (a b c) = tAA^{-1} * tAb */
if ( !_MMG5_sys33sym(tAA,tAb,c) ) return(hmax);
intm[0] = 2.0*c[0];
intm[1] = c[2];
intm[2] = 2.0*c[1];
/* At this point, intm stands for the integral matrix of Taubin's approach : vp[0] and vp[1]
are the two pr. directions of curvature, and the two curvatures can be inferred from lambdas*/
if( !_MMG5_eigensym(intm,kappa,vp) ){
fprintf(stdout,"%s:%d: Error: function _MMG5_eigensym return 0\n",
__FILE__,__LINE__);
exit(EXIT_FAILURE);
}
/* h computation : h(x) = sqrt( 9*hausd / (2 * max(kappa1(x),kappa2(x)) ) */
kappa[0] = 2.0/9.0 * fabs(kappa[0]) / hausd;
kappa[0] = MG_MIN(kappa[0],isqhmin);
kappa[0] = MG_MAX(kappa[0],isqhmax);
kappa[1] = 2.0/9.0 * fabs(kappa[1]) / hausd;
kappa[1] = MG_MIN(kappa[1],isqhmin);
kappa[1] = MG_MAX(kappa[1],isqhmax);
kappa[0] = 1.0 / sqrt(kappa[0]);
kappa[1] = 1.0 / sqrt(kappa[1]);
h = MG_MIN(kappa[0],kappa[1]);
/* Travel surfacic ball one last time and update non manifold point metric */
for (k=0; k<ilists; k++) {
iel = lists[k] / 4;
iface = lists[k] % 4;
for (j=0; j<3; j++) {
i0 = _MMG5_idir[iface][j];
ip0 = pt->v[i0];
p1 = &mesh->point[ip0];
if( !(p1->tag & MG_NOM) || MG_SIN(p1->tag) ) continue;
assert(p1->xp);
t = &p1->n[0];
memcpy(c,t,3*sizeof(double));
d[0] = r[0][0]*c[0] + r[0][1]*c[1] + r[0][2]*c[2];
d[1] = r[1][0]*c[0] + r[1][1]*c[1] + r[1][2]*c[2];
hnm = intm[0]*d[0]*d[0] + 2.0*intm[1]*d[0]*d[1] + intm[2]*d[1]*d[1];
hnm = 2.0/9.0 * fabs(hnm) / hausd;
hnm = MG_MIN(hnm,isqhmin);
hnm = MG_MAX(hnm,isqhmax);
hnm = 1.0 / sqrt(hnm);
met->m[ip0] = MG_MIN(met->m[ip0],hnm);
}
}
return(h);
}
