/** compute iso size map */
int _MMG5_DoSol(MMG5_pMesh mesh,MMG5_pSol met) {
MMG5_pTetra pt;
MMG5_pPoint p1,p2;
double ux,uy,uz,dd;
int i,k,ia,ib,ipa,ipb;
int *mark;
_MMG5_SAFE_CALLOC(mark,mesh->np+1,int);
/* Memory alloc */
met->np = mesh->np;
met->npmax = mesh->npmax;
met->size = 1;
met->dim = mesh->dim;
_MMG5_ADD_MEM(mesh,(met->npmax*met->size+1)*sizeof(double),"solution",return(0));
_MMG5_SAFE_CALLOC(met->m,met->npmax*met->size+1,double);
/* internal edges */
for (k=1; k<=mesh->ne; k++) {
pt = &mesh->tetra[k];
if ( !pt->v[0] ) continue;
/* internal edges */
for (i=0; i<6; i++) {
ia = _MMG5_iare[i][0];
ib = _MMG5_iare[i][1];
ipa = pt->v[ia];
ipb = pt->v[ib];
p1 = &mesh->point[ipa];
p2 = &mesh->point[ipb];
ux = p1->c[0] - p2->c[0];
uy = p1->c[1] - p2->c[1];
uz = p1->c[2] - p2->c[2];
dd = sqrt(ux*ux + uy*uy + uz*uz);
met->m[ipa] += dd;
mark[ipa]++;
met->m[ipb] += dd;
mark[ipb]++;
}
}
/* vertex size */
for (k=1; k<=mesh->np; k++) {
p1 = &mesh->point[k];
if ( !mark[k] ) {
met->m[k] = mesh->info.hmax;
continue;
}
else
met->m[k] = MG_MIN(mesh->info.hmax,MG_MAX(mesh->info.hmin,met->m[k] / (double)mark[k]));
}
_MMG5_SAFE_FREE(mark);
return(1);
}
/* 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 n pointer toward the vector that we want to send on the third vector
* of canonical basis.
* \param r computed rotation matrix.
*
* Compute rotation matrix that sends vector \a n to the third vector of
* canonical basis.
*
*/
inline int _MMG5_rotmatrix(double n[3],double r[3][3]) {
double aa,bb,ab,ll,l,cosalpha,sinalpha;
aa = n[0]*n[0];
bb = n[1]*n[1];
ab = n[0]*n[1];
ll = aa+bb;
cosalpha = n[2];
sinalpha = sqrt(1.0- MG_MIN(1.0,cosalpha*cosalpha));
/* No rotation needed in this case */
if ( ll < _MMG5_EPS ) {
if ( n[2] > 0.0 ) {
r[0][0] = 1.0 ; r[0][1] = 0.0 ; r[0][2] = 0.0;
r[1][0] = 0.0 ; r[1][1] = 1.0 ; r[1][2] = 0.0;
r[2][0] = 0.0 ; r[2][1] = 0.0 ; r[2][2] = 1.0;
}
else {
r[0][0] = -1.0 ; r[0][1] = 0.0 ; r[0][2] = 0.0;
r[1][0] = 0.0 ; r[1][1] = 1.0 ; r[1][2] = 0.0;
r[2][0] = 0.0 ; r[2][1] = 0.0 ; r[2][2] = -1.0;
}
}
else {
l = sqrt(ll);
r[0][0] = (aa*cosalpha + bb)/ll;
r[0][1] = ab*(cosalpha-1)/ll;
r[0][2] = -n[0]*sinalpha/l;
r[1][0] = r[0][1];
r[1][1] = (bb*cosalpha + aa)/ll;
r[1][2] = -n[1]*sinalpha/l;
r[2][0] = n[0]*sinalpha/l;
r[2][1] = n[1]*sinalpha/l;
r[2][2] = cosalpha;
}
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);
}
/* collapse edge i of k, i1->i2 */
int litcol(MMG5_pMesh mesh,int k,char i,double kali) {
MMG5_pTria pt,pt0,pt1;
MMG5_pPoint p1,p2;
double kal,ps,cosnold,cosnnew,n0old[3],n0new[3],n1old[3],n1new[3],n00old[3],n00new[3];
int *adja,list[_MMG5_LMAX+2],jel,ip2,l,ilist;
char i1,i2,j,jj,j2,open;
pt0 = &mesh->tria[0];
pt = &mesh->tria[k];
i1 = _MMG5_inxt2[i];
i2 = _MMG5_iprv2[i];
ip2 = pt->v[i2];
/* collect all triangles around vertex i1 */
ilist = boulet(mesh,k,i1,list);
/* check for open ball */
adja = &mesh->adja[3*(k-1)+1];
open = adja[i] == 0;
if ( ilist > 3 ) {
/* check references */
jel = list[1] / 3;
pt1 = &mesh->tria[jel];
if ( abs(pt->ref) != abs(pt1->ref) ) return(0);
/* analyze ball */
for (l=1; l<ilist-1+open; l++) {
jel = list[l] / 3;
j = list[l] % 3;
jj = _MMG5_inxt2[j];
j2 = _MMG5_iprv2[j];
pt1 = &mesh->tria[jel];
/* check normal flipping */
if ( !_MMG5_nortri(mesh,pt1,n1old) ) return(0);
memcpy(pt0,pt1,sizeof(MMG5_Tria));
pt0->v[j] = ip2;
if ( !_MMG5_nortri(mesh,pt0,n1new) ) return(0);
ps = n1new[0]*n1old[0] + n1new[1]*n1old[1] + n1new[2]*n1old[2];
if ( ps < 0.0 ) return(0);
/* keep normals at 1st triangles */
if ( l == 1 && !open ) {
memcpy(n00old,n1old,3*sizeof(double));
memcpy(n00new,n1new,3*sizeof(double));
}
/* check normals deviation */
if ( !(pt1->tag[j2] & MG_GEO) ) {
if ( l > 1 ) {
cosnold = n0old[0]*n1old[0] + n0old[1]*n1old[1] + n0old[2]*n1old[2];
cosnnew = n0new[0]*n1new[0] + n0new[1]*n1new[1] + n0new[2]*n1new[2];
if ( cosnold < _MMG5_ANGEDG ) {
if ( cosnnew < MG_MIN(0.0,cosnold) ) return(0);
}
else if ( cosnnew < _MMG5_ANGEDG ) return(0);
}
memcpy(n0old,n1old,3*sizeof(double));
memcpy(n0new,n1new,3*sizeof(double));
}
/* check quality */
kal = ALPHAD*_MMG5_caltri_iso(mesh,NULL,pt0);
if ( kal < NULKAL ) return(0);
}
/* check angle between 1st and last triangles */
if ( !open ) {
cosnold = n00old[0]*n1old[0] + n00old[1]*n1old[1] + n00old[2]*n1old[2];
cosnnew = n00new[0]*n1new[0] + n00new[1]*n1new[1] + n00new[2]*n1new[2];
if ( cosnold < _MMG5_ANGEDG ) {
if ( cosnnew < MG_MIN(0.0,cosnold) ) return(0);
}
else if ( cosnnew < _MMG5_ANGEDG ) return(0);
/* other reference checks */
jel = list[ilist-1] / 3;
pt = &mesh->tria[jel];
jel = list[ilist-2] / 3;
pt1 = &mesh->tria[jel];
if ( abs(pt->ref) != abs(pt1->ref) ) return(0);
}
return(colver(mesh,list,ilist));
}
/* specific test: no collapse if any interior edge is EDG */
else if ( ilist == 3 ) {
p1 = &mesh->point[pt->v[i1]];
if ( MS_SIN(p1->tag) ) return(0);
else if ( MG_EDG(pt->tag[i2]) && !MG_EDG(pt->tag[i]) ) return(0);
else if ( !MG_EDG(pt->tag[i2]) && MG_EDG(pt->tag[i]) ) return(0);
else if ( MG_EDG(pt->tag[i2]) && MG_EDG(pt->tag[i]) && MG_EDG(pt->tag[i1]) ) return(0);
return(colver3(mesh,list));
}
/* for specific configurations along open ridge */
else if ( ilist == 2 ) {
if ( !open ) return(0);
jel = list[1] / 3;
j = list[1] % 3;
jj = _MMG5_inxt2[j];
pt1 = &mesh->tria[jel];
if ( abs(pt->ref) != abs(pt1->ref) ) return(0);
else if ( !(pt1->tag[jj] & MG_GEO) ) return(0);
p1 = &mesh->point[pt->v[i1]];
p2 = &mesh->point[pt1->v[jj]];
if ( p2->tag > p1->tag || p2->ref != p1->ref ) return(0);
return(colver2(mesh,list));
}
return(0);
}
/* check if geometry preserved by collapsing edge i */
int chkcol(MMG5_pMesh mesh,MMG5_pSol met,int k,char i,int *list,char typchk) {
MMG5_pTria pt,pt0,pt1,pt2;
MMG5_pPoint p1,p2;
double len,lon,ps,cosnold,cosnnew,kal,n0old[3],n1old[3],n00old[3];
double n0new[3],n1new[3],n00new[3];
int *adja,jel,kel,ip1,ip2,l,ll,ilist;
char i1,i2,j,jj,j2,lj,open,voy;
pt0 = &mesh->tria[0];
pt = &mesh->tria[k];
i1 = _MMG5_inxt2[i];
i2 = _MMG5_iprv2[i];
ip1 = pt->v[i1];
ip2 = pt->v[i2];
if ( typchk == 2 && met->m ) {
lon = _MMG5_lenedg(mesh,met,ip1,ip2,0);
lon = MG_MIN(lon,LSHRT);
lon = MG_MAX(1.0/lon,LLONG);
}
/* collect all triangles around vertex i1 */
ilist = boulechknm(mesh,k,i1,list);
if ( ilist <= 0 ) return(0);
/* check for open ball */
adja = &mesh->adja[3*(k-1)+1];
open = adja[i] == 0;
if ( ilist > 3 ) {
/* check references */
if ( MG_EDG(pt->tag[i2]) ) {
jel = list[1] / 3;
pt1 = &mesh->tria[jel];
if ( abs(pt->ref) != abs(pt1->ref) ) return(0);
}
/* analyze ball */
for (l=1; l<ilist-1+open; l++) {
jel = list[l] / 3;
j = list[l] % 3;
jj = _MMG5_inxt2[j];
j2 = _MMG5_iprv2[j];
pt1 = &mesh->tria[jel];
/* check length */
if ( typchk == 2 && met->m && !MG_EDG(mesh->point[ip2].tag) ) {
ip1 = pt1->v[j2];
len = _MMG5_lenedg(mesh,met,ip1,ip2,0);
if ( len > lon ) return(0);
}
/* check normal flipping */
if ( !_MMG5_nortri(mesh,pt1,n1old) ) return(0);
memcpy(pt0,pt1,sizeof(MMG5_Tria));
pt0->v[j] = ip2;
if ( !_MMG5_nortri(mesh,pt0,n1new) ) return(0);
ps = n1new[0]*n1old[0] + n1new[1]*n1old[1] + n1new[2]*n1old[2];
if ( ps < 0.0 ) return(0);
/* keep normals at 1st triangles */
if ( l == 1 && !open ) {
memcpy(n00old,n1old,3*sizeof(double));
memcpy(n00new,n1new,3*sizeof(double));
}
/* check normals deviation */
if ( !(pt1->tag[j2] & MG_GEO) ) {
if ( l > 1 ) {
cosnold = n0old[0]*n1old[0] + n0old[1]*n1old[1] + n0old[2]*n1old[2];
cosnnew = n0new[0]*n1new[0] + n0new[1]*n1new[1] + n0new[2]*n1new[2];
if ( cosnold < _MMG5_ANGEDG ) {
if ( cosnnew < cosnold ) return(0);
}
else if ( cosnnew < _MMG5_ANGEDG ) return(0);
}
}
/* check geometric support */
if ( l == 1 ) {
pt0->tag[j2] = MG_MAX(pt0->tag[j2],pt->tag[i1]);
}
else if ( l == ilist-2+open ) {
ll = list[ilist-1+open] / 3;
if ( ll > mesh->nt ) return(0);
lj = list[ilist-1+open] % 3;
pt0->tag[jj] = MG_MAX(pt0->tag[jj],mesh->tria[ll].tag[lj]);
}
if ( chkedg(mesh,0) ) return(0);
/* check quality */
if ( typchk == 2 && met->m )
kal = ALPHAD*_MMG5_calelt(mesh,met,pt0);
else
kal = ALPHAD*_MMG5_caltri_iso(mesh,NULL,pt0);
if ( kal < NULKAL ) return(0);
memcpy(n0old,n1old,3*sizeof(double));
memcpy(n0new,n1new,3*sizeof(double));
}
/* check angle between 1st and last triangles */
if ( !open && !(pt->tag[i] & MG_GEO) ) {
cosnold = n00old[0]*n1old[0] + n00old[1]*n1old[1] + n00old[2]*n1old[2];
cosnnew = n00new[0]*n1new[0] + n00new[1]*n1new[1] + n00new[2]*n1new[2];
if ( cosnold < _MMG5_ANGEDG ) {
if ( cosnnew < cosnold ) return(0);
}
else if ( cosnnew < _MMG5_ANGEDG ) return(0);
/* other checks for reference collapse */
jel = list[ilist-1] / 3;
j = list[ilist-1] % 3;
j = _MMG5_iprv2[j];
pt = &mesh->tria[jel];
if ( MG_EDG(pt->tag[j]) ) {
jel = list[ilist-2] / 3;
pt1 = &mesh->tria[jel];
if ( abs(pt->ref) != abs(pt1->ref) ) return(0);
}
}
}
/* specific test: no collapse if any interior edge is EDG */
else if ( ilist == 3 ) {
p1 = &mesh->point[pt->v[i1]];
if ( MS_SIN(p1->tag) ) return(0);
else if ( MG_EDG(pt->tag[i2]) && !MG_EDG(pt->tag[i]) ) return(0);
else if ( !MG_EDG(pt->tag[i2]) && MG_EDG(pt->tag[i]) ) return(0);
else if ( MG_EDG(pt->tag[i2]) && MG_EDG(pt->tag[i]) && MG_EDG(pt->tag[i1]) ) return(0);
/* Check geometric approximation */
jel = list[1] / 3;
j = list[1] % 3;
jj = _MMG5_inxt2[j];
j2 = _MMG5_iprv2[j];
pt0 = &mesh->tria[0];
pt1 = &mesh->tria[jel];
memcpy(pt0,pt1,sizeof(MMG5_Tria));
pt0->v[j] = ip2;
jel = list[2] / 3;
j = list[2] % 3;
pt1 = &mesh->tria[jel];
pt0->tag[jj] |= pt1->tag[j];
pt0->tag[j2] |= pt1->tag[_MMG5_inxt2[j]];
if ( chkedg(mesh,0) ) return(0);
}
/* for specific configurations along open ridge */
else if ( ilist == 2 ) {
if ( !open ) return(0);
jel = list[1] / 3;
j = list[1] % 3;
/* Topological test */
adja = &mesh->adja[3*(jel-1)+1];
kel = adja[j] / 3;
voy = adja[j] % 3;
pt2 = &mesh->tria[kel];
if ( pt2->v[voy] == ip2) return(0);
jj = _MMG5_inxt2[j];
pt1 = &mesh->tria[jel];
if ( abs(pt->ref) != abs(pt1->ref) ) return(0);
else if ( !(pt1->tag[jj] & MG_GEO) ) return(0);
p1 = &mesh->point[pt->v[i1]];
p2 = &mesh->point[pt1->v[jj]];
if ( p2->tag > p1->tag || p2->ref != p1->ref ) return(0);
/* Check geometric approximation */
j2 = _MMG5_iprv2[j];
pt0 = &mesh->tria[0];
memcpy(pt0,pt,sizeof(MMG5_Tria));
pt0->v[i1] = pt1->v[j2];
if ( chkedg(mesh,0) ) return(0);
}
return(ilist);
}
/**
* \param mesh pointer toward the mesh structure
* \param start tetrahedra in which the swap should be performed
* \param ia edge that we want to swap
* \param ilist pointer to store the size of the shell of the edge
* \param list pointer to store the shell of the edge
* \param crit improvment coefficient
* \return 0 if fail, the index of point corresponding to the swapped
* configuration otherwise (\f$4*k+i\f$).
*
* Check whether swap of edge \a ia in \a start should be performed, and
* return \f$4*k+i\f$ the index of point corresponding to the swapped
* configuration. The shell of edge is built during the process.
*
*/
int _MMG5_chkswpgen(MMG5_pMesh mesh,int start,int ia,int *ilist,int *list,double crit) {
MMG5_pTetra pt,pt0;
MMG5_pPoint p0;
double calold,calnew,caltmp;
int na,nb,np,adj,piv,npol,refdom,k,l,iel;
int *adja,pol[_MMG5_LMAX+2];
char i,ipa,ipb,ip,ier;
pt = &mesh->tetra[start];
refdom = pt->ref;
pt0 = &mesh->tetra[0];
na = pt->v[_MMG5_iare[ia][0]];
nb = pt->v[_MMG5_iare[ia][1]];
calold = pt->qual;
/* Store shell of ia in list, and associated pseudo polygon in pol */
(*ilist) = 0;
npol = 0;
list[(*ilist)] = 6*start+ia;
(*ilist)++;
adja = &mesh->adja[4*(start-1)+1];
adj = adja[_MMG5_ifar[ia][0]] / 4; // start travelling by face (ia,0)
piv = pt->v[_MMG5_ifar[ia][1]];
pol[npol] = 4*start + _MMG5_ifar[ia][1];
npol++;
while ( adj && adj != start ) {
pt = &mesh->tetra[adj];
if ( pt->tag & MG_REQ ) return(0);
/* Edge is on a boundary between two different domains */
if ( pt->ref != refdom ) return(0);
calold = MG_MIN(calold, pt->qual);
/* identification of edge number in tetra adj */
for (i=0; i<6; i++) {
ipa = _MMG5_iare[i][0];
ipb = _MMG5_iare[i][1];
if ( (pt->v[ipa] == na && pt->v[ipb] == nb) ||
(pt->v[ipa] == nb && pt->v[ipb] == na)) break;
}
assert(i<6);
list[(*ilist)] = 6*adj +i;
(*ilist)++;
/* overflow */
if ( (*ilist) > _MMG5_LMAX-3 ) return(0);
/* set new triangle for travel */
adja = &mesh->adja[4*(adj-1)+1];
if ( pt->v[ _MMG5_ifar[i][0] ] == piv ) {
pol[npol] = 4*adj + _MMG5_ifar[i][1];
npol++;
adj = adja[ _MMG5_ifar[i][0] ] / 4;
piv = pt->v[ _MMG5_ifar[i][1] ];
}
else {
assert(pt->v[ _MMG5_ifar[i][1] ] == piv);
pol[npol] = 4*adj + _MMG5_ifar[i][0];
npol++;
adj = adja[ _MMG5_ifar[i][1] ] /4;
piv = pt->v[ _MMG5_ifar[i][0] ];
}
}
//CECILE : je vois pas pourquoi ca ameliore de faire ce test
//plus rapide mais du coup on elimine des swap...
//4/01/14 commentaire
//if ( calold*_MMG5_ALPHAD > 0.5 ) return(0);
/* Prevent swap of an external boundary edge */
if ( !adj ) return(0);
assert(npol == (*ilist)); // du coup, apres on pourra virer npol
/* Find a configuration that enhances the worst quality within the shell */
for (k=0; k<npol; k++) {
iel = pol[k] / 4;
ip = pol[k] % 4;
np = mesh->tetra[iel].v[ip];
calnew = 1.0;
ier = 1;
if ( mesh->info.fem ) {
p0 = &mesh->point[np];
if ( p0->tag & MG_BDY ) {
for (l=0; l<npol;l++) {
if ( k < npol-1 ) {
if ( l == k || l == k+1 ) continue;
}
else {
if ( l == npol-1 || l == 0 ) continue;
}
iel = pol[l] / 4;
ip = pol[l] % 4;
pt = &mesh->tetra[iel];
p0 = &mesh->point[pt->v[ip]];
if ( p0->tag & MG_BDY ) {
ier = 0;
break;
}
}
}
if ( !ier ) continue;
ier = 1;
}
for (l=0; l<(*ilist); l++) {
/* Do not consider tets of the shell of collapsed edge */
if ( k < npol-1 ) {
if ( l == k || l == k+1 ) continue;
}
else {
if ( l == npol-1 || l == 0 ) continue;
}
iel = list[l] / 6;
i = list[l] % 6;
pt = &mesh->tetra[iel];
/* First tetra obtained from iel */
memcpy(pt0,pt,sizeof(MMG5_Tetra));
pt0->v[_MMG5_iare[i][0]] = np;
caltmp = _MMG5_orcal(mesh,0);
calnew = MG_MIN(calnew,caltmp);
/* Second tetra obtained from iel */
memcpy(pt0,pt,sizeof(MMG5_Tetra));
pt0->v[_MMG5_iare[i][1]] = np;
caltmp = _MMG5_orcal(mesh,0);
calnew = MG_MIN(calnew,caltmp);
ier = (calnew > crit*calold);
if ( !ier ) break;
}
if ( ier ) return(pol[k]);
}
return(0);
}
