/** Compute point located at parameter value step from point ip0, as well as interpolate
of normals, tangent for a regular edge ; v = ref vector (normal) for choice of normals if need be */
inline int _MMG5_BezierReg(MMG5_pMesh mesh,int ip0, int ip1, double s, double v[3], double *o, double *no){
MMG5_pPoint p0,p1;
double b0[3],b1[3],bn[3],t0[3],t1[3],np0[3],np1[3],alpha,ux,uy,uz,ps1,ps2,ll,il,dd,*n1,*n2;
p0 = &mesh->point[ip0];
p1 = &mesh->point[ip1];
ux = p1->c[0] - p0->c[0];
uy = p1->c[1] - p0->c[1];
uz = p1->c[2] - p0->c[2];
ll = ux*ux + uy*uy + uz*uz;
/* Pathological case : don't move in that case ! */
if(((MG_SIN(p0->tag)||(p0->tag & MG_NOM)) && (MG_SIN(p1->tag) || (p1->tag & MG_NOM)))||(ll<_MMG5_EPSD)){
o[0] = 0.5*( p0->c[0] + p1->c[0] );
o[1] = 0.5*( p0->c[1] + p1->c[1] );
o[2] = 0.5*( p0->c[2] + p1->c[2] );
memcpy(no,v,3*sizeof(double));
return(1);
}
il = 1.0 /sqrt(ll);
/* Coordinates of the new tangent and normal */
if(MG_SIN(p0->tag)||(p0->tag & MG_NOM)){
if(p1->tag & MG_GEO){
n1 = &mesh->xpoint[p1->xp].n1[0];
n2 = &mesh->xpoint[p1->xp].n2[0];
ps1 = n1[0]*v[0] + n1[1]*v[1] + n1[2]*v[2];
ps2 = n2[0]*v[0] + n2[1]*v[1] + n2[2]*v[2];
if(fabs(ps1) < fabs(ps2)){
memcpy(np1,&mesh->xpoint[p1->xp].n2[0],3*sizeof(double));
}
else{
memcpy(np1,&mesh->xpoint[p1->xp].n1[0],3*sizeof(double));
}
}
else{
memcpy(np1,&mesh->xpoint[p1->xp].n1[0],3*sizeof(double));
}
memcpy(np0,np1,3*sizeof(double));
}
else if(MG_SIN(p1->tag) || (p1->tag & MG_NOM)){
if(p0->tag & MG_GEO){
n1 = &mesh->xpoint[p0->xp].n1[0];
n2 = &mesh->xpoint[p0->xp].n2[0];
ps1 = n1[0]*v[0] + n1[1]*v[1] + n1[2]*v[2];
ps2 = n2[0]*v[0] + n2[1]*v[1] + n2[2]*v[2];
if(fabs(ps1) < fabs(ps2)){
memcpy(np0,&mesh->xpoint[p0->xp].n2[0],3*sizeof(double));
}
else{
memcpy(np0,&mesh->xpoint[p0->xp].n1[0],3*sizeof(double));
}
}
else{
memcpy(np0,&mesh->xpoint[p0->xp].n1[0],3*sizeof(double));
}
memcpy(np1,np0,3*sizeof(double));
}
else{
if(p0->tag & MG_GEO){
n1 = &mesh->xpoint[p0->xp].n1[0];
n2 = &mesh->xpoint[p0->xp].n2[0];
ps1 = n1[0]*v[0] + n1[1]*v[1] + n1[2]*v[2];
ps2 = n2[0]*v[0] + n2[1]*v[1] + n2[2]*v[2];
if(fabs(ps1) < fabs(ps2)){
memcpy(np0,&mesh->xpoint[p0->xp].n2[0],3*sizeof(double));
}
else{
memcpy(np0,&mesh->xpoint[p0->xp].n1[0],3*sizeof(double));
}
}
else{
memcpy(np0,&mesh->xpoint[p0->xp].n1[0],3*sizeof(double));
}
if(p1->tag & MG_GEO){
n1 = &mesh->xpoint[p1->xp].n1[0];
n2 = &mesh->xpoint[p1->xp].n2[0];
ps1 = n1[0]*v[0] + n1[1]*v[1] + n1[2]*v[2];
ps2 = n2[0]*v[0] + n2[1]*v[1] + n2[2]*v[2];
if(fabs(ps1) < fabs(ps2)){
memcpy(np1,&mesh->xpoint[p1->xp].n2[0],3*sizeof(double));
}
else{
memcpy(np1,&mesh->xpoint[p1->xp].n1[0],3*sizeof(double));
}
}
else{
memcpy(np1,&mesh->xpoint[p1->xp].n1[0],3*sizeof(double));
}
}
/* Normal interpolation */
ps1 = ux*(np0[0] + np1[0]) + uy*(np0[1] + np1[1]) + uz*(np0[2] + np1[2]);
ps1 = 2.0*ps1/ll;
bn[0] = np0[0] + np1[0] -ps1*ux;
bn[1] = np0[1] + np1[1] -ps1*uy;
bn[2] = np0[2] + np1[2] -ps1*uz;
dd = bn[0]*bn[0] + bn[1]*bn[1] + bn[2]*bn[2];
if(dd > _MMG5_EPSD){
dd = 1.0/sqrt(dd);
bn[0] *= dd;
bn[1] *= dd;
bn[2] *= dd;
}
no[0] = (1.0-s)*(1.0-s)*np0[0] + 2.0*s*(1.0-s)*bn[0] + s*s*np1[0];
no[1] = (1.0-s)*(1.0-s)*np0[1] + 2.0*s*(1.0-s)*bn[1] + s*s*np1[1];
no[2] = (1.0-s)*(1.0-s)*np0[2] + 2.0*s*(1.0-s)*bn[2] + s*s*np1[2];
dd = no[0]*no[0] + no[1]*no[1] + no[2]*no[2];
if(dd > _MMG5_EPSD){
dd = 1.0/sqrt(dd);
no[0] *= dd;
no[1] *= dd;
no[2] *= dd;
}
/* vertex position interpolation */
if(!_MMG5_BezierTgt(p0->c,p1->c,np0,np1,t0,t1)){
t0[0] = ux * il;
t0[1] = uy * il;
t0[2] = uz * il;
t1[0] = - ux * il;
t1[1] = - uy * il;
t1[2] = - uz * il;
}
alpha = _MMG5_BezierGeod(p0->c,p1->c,t0,t1);
b0[0] = p0->c[0] + alpha * t0[0];
b0[1] = p0->c[1] + alpha * t0[1];
b0[2] = p0->c[2] + alpha * t0[2];
b1[0] = p1->c[0] + alpha * t1[0];
b1[1] = p1->c[1] + alpha * t1[1];
b1[2] = p1->c[2] + alpha * t1[2];
o[0] = (1.0-s)*(1.0-s)*(1.0-s)*p0->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*p1->c[0];
o[1] = (1.0-s)*(1.0-s)*(1.0-s)*p0->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*p1->c[1];
o[2] = (1.0-s)*(1.0-s)*(1.0-s)*p0->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*p1->c[2];
return(1);
}
/** Compute point located at parameter value step from point ip0, as well as interpolate
of normals, tangent for a REF edge */
inline int _MMG5_BezierRef(MMG5_pMesh mesh,int ip0,int ip1,double s,double *o,double *no,double *to) {
MMG5_pPoint p0,p1;
double ux,uy,uz,n01[3],n02[3],n11[3],n12[3],ntemp[3],t0[3],t1[3];
double ps,b0[3],b1[3],bn[3],ll,il,dd,alpha,ps2;
p0 = &mesh->point[ip0]; /* Ref point, from which step is counted */
p1 = &mesh->point[ip1];
ux = p1->c[0] - p0->c[0];
uy = p1->c[1] - p0->c[1];
uz = p1->c[2] - p0->c[2];
ll = ux*ux + uy*uy + uz*uz;
if ( ll < _MMG5_EPSD2 ) return(0);
il = 1.0 / sqrt(ll);
assert( (MG_REF & p0->tag) && (MG_REF & p1->tag) );
/* Coordinates of the new point */
if ( MG_SIN(p0->tag) ) {
t0[0] = ux * il;
t0[1] = uy * il;
t0[2] = uz * il;
}
else {
memcpy(t0,&(mesh->xpoint[p0->xp].t[0]),3*sizeof(double));
ps = t0[0]*ux + t0[1]*uy + t0[2]*uz;
if ( ps < 0.0 ) {
t0[0] *= -1.0;
t0[1] *= -1.0;
t0[2] *= -1.0;
}
}
if ( MG_SIN(p1->tag) ) {
t1[0] = -ux * il;
t1[1] = -uy * il;
t1[2] = -uz * il;
}
else {
memcpy(t1,&(mesh->xpoint[p1->xp].t[0]),3*sizeof(double));
ps = - ( t1[0]*ux + t1[1]*uy + t1[2]*uz );
if ( ps < 0.0 ) {
t1[0] *= -1.0;
t1[1] *= -1.0;
t1[2] *= -1.0;
}
}
alpha = _MMG5_BezierGeod(p0->c,p1->c,t0,t1);
b0[0] = p0->c[0] + alpha * t0[0];
b0[1] = p0->c[1] + alpha * t0[1];
b0[2] = p0->c[2] + alpha * t0[2];
b1[0] = p1->c[0] + alpha * t1[0];
b1[1] = p1->c[1] + alpha * t1[1];
b1[2] = p1->c[2] + alpha * t1[2];
o[0] = (1.0-s)*(1.0-s)*(1.0-s)*p0->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*p1->c[0];
o[1] = (1.0-s)*(1.0-s)*(1.0-s)*p0->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*p1->c[1];
o[2] = (1.0-s)*(1.0-s)*(1.0-s)*p0->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*p1->c[2];
/* Coordinates of the new tangent and normal */
if ( MG_SIN(p0->tag) && MG_SIN(p1->tag) ) {
memcpy(to,t0,3*sizeof(double));
return(1);
}
else if ( MG_SIN(p0->tag) ) {
memcpy(n11,&(mesh->xpoint[p1->xp].n1[0]),3*sizeof(double));
memcpy(n01,&(mesh->xpoint[p1->xp].n1[0]),3*sizeof(double));
memcpy(n12,&(mesh->xpoint[p1->xp].n2[0]),3*sizeof(double));
memcpy(n02,&(mesh->xpoint[p1->xp].n2[0]),3*sizeof(double));
}
else if ( MG_SIN(p1->tag) ) {
memcpy(n01,&(mesh->xpoint[p0->xp].n1[0]),3*sizeof(double));
memcpy(n11,&(mesh->xpoint[p0->xp].n1[0]),3*sizeof(double));
memcpy(n02,&(mesh->xpoint[p0->xp].n2[0]),3*sizeof(double));
memcpy(n12,&(mesh->xpoint[p0->xp].n2[0]),3*sizeof(double));
}
else {
memcpy(n01,&(mesh->xpoint[p0->xp].n1[0]),3*sizeof(double));
memcpy(n11,&(mesh->xpoint[p1->xp].n1[0]),3*sizeof(double));
memcpy(n02,&(mesh->xpoint[p0->xp].n2[0]),3*sizeof(double));
memcpy(n12,&(mesh->xpoint[p1->xp].n2[0]),3*sizeof(double));
}
/* Switch normals of p1 for pairing */
ps = n01[0] * n11[0] + n01[1] * n11[1] + n01[2] * n11[2];
ps2 = n01[0] * n12[0] + n01[1] * n12[1] + n01[2] * n12[2];
if ( ps2 > ps ) {
memcpy(ntemp,n11,3*sizeof(double));
memcpy(n11,n12,3*sizeof(double));
memcpy(n12,ntemp,3*sizeof(double));
}
/* Normal interpolation */
ps = ux*(n01[0] + n11[0]) + uy*(n01[1] + n11[1]) + uz*(n01[2] + n11[2]);
ps = 2.0*ps/ll;
bn[0] = n01[0] + n11[0] -ps*ux;
bn[1] = n01[1] + n11[1] -ps*uy;
bn[2] = n01[2] + n11[2] -ps*uz;
dd = bn[0]*bn[0] + bn[1]*bn[1] + bn[2]*bn[2];
if ( dd > _MMG5_EPSD ) {
dd = 1.0 / sqrt(dd);
bn[0] *= dd;
bn[1] *= dd;
bn[2] *= dd;
}
no[0] = (1.0-s)*(1.0-s)*n01[0] + 2.0*s*(1.0-s)*bn[0] + s*s*n11[0];
no[1] = (1.0-s)*(1.0-s)*n01[1] + 2.0*s*(1.0-s)*bn[1] + s*s*n11[1];
no[2] = (1.0-s)*(1.0-s)*n01[2] + 2.0*s*(1.0-s)*bn[2] + s*s*n11[2];
dd = no[0]*no[0] + no[1]*no[1] + no[2]*no[2];
if ( dd > _MMG5_EPSD2 ) {
dd = 1.0/sqrt(dd);
no[0] *= dd;
no[1] *= dd;
no[2] *= dd;
}
/* Tangent interpolation : possibly flip (back) t1 */
ps = t0[0]*t1[0] + t0[1]*t1[1] + t0[2]*t1[2];
if ( ps < 0.0 ) {
t1[0] *= -1.0;
t1[1] *= -1.0;
t1[2] *= -1.0;
}
to[0] = (1.0-s)*t0[0] + s*t1[0];
to[1] = (1.0-s)*t0[1] + s*t1[1];
to[2] = (1.0-s)*t0[2] + s*t1[2];
/* Projection of the tangent in the tangent plane defined by no */
ps = to[0]*no[0] + to[1]*no[1] + to[2]*no[2];
to[0] = to[0] -ps*no[0];
to[1] = to[1] -ps*no[1];
to[2] = to[2] -ps*no[2];
dd = to[0]*to[0] + to[1]*to[1] + to[2]*to[2];
if ( dd > _MMG5_EPSD2) {
dd = 1.0 / sqrt(dd);
to[0] *= dd;
to[1] *= dd;
to[2] *= dd;
}
return(1);
}
/** Compute point located at parameter value step from point ip0, as well as interpolate
of normals, tangent for a NOM edge */
inline int _MMG5_BezierNom(MMG5_pMesh mesh,int ip0,int ip1,double s,double *o,double *no,double *to) {
MMG5_pPoint p0,p1;
double ux,uy,uz,il,ll,ps,alpha,dd;
double t0[3],t1[3],b0[3],b1[3],n0[3],n1[3],bn[3];
p0 = &mesh->point[ip0];
p1 = &mesh->point[ip1];
ux = p1->c[0] - p0->c[0];
uy = p1->c[1] - p0->c[1];
uz = p1->c[2] - p0->c[2];
ll = ux*ux + uy*uy + uz*uz;
if(ll < _MMG5_EPSD2) return(0);
il = 1.0 / sqrt(ll);
assert(( p0->tag & MG_NOM ) && ( p1->tag & MG_NOM ));
/* Coordinates of the new point */
if ( MG_SIN(p0->tag) ) {
t0[0] = ux * il;
t0[1] = uy * il;
t0[2] = uz * il;
}
else {
memcpy(t0,&(mesh->xpoint[p0->xp].t[0]),3*sizeof(double));
ps = t0[0]*ux + t0[1]*uy + t0[2]*uz;
if ( ps < 0.0 ) {
t0[0] *= -1.0;
t0[1] *= -1.0;
t0[2] *= -1.0;
}
}
if ( MG_SIN(p1->tag) ) {
t1[0] = -ux * il;
t1[1] = -uy * il;
t1[2] = -uz * il;
}
else {
memcpy(t1,&(mesh->xpoint[p1->xp].t[0]),3*sizeof(double));
ps = - ( t1[0]*ux + t1[1]*uy + t1[2]*uz );
if ( ps < 0.0 ) {
t1[0] *= -1.0;
t1[1] *= -1.0;
t1[2] *= -1.0;
}
}
alpha = _MMG5_BezierGeod(p0->c,p1->c,t0,t1);
b0[0] = p0->c[0] + alpha * t0[0];
b0[1] = p0->c[1] + alpha * t0[1];
b0[2] = p0->c[2] + alpha * t0[2];
b1[0] = p1->c[0] + alpha * t1[0];
b1[1] = p1->c[1] + alpha * t1[1];
b1[2] = p1->c[2] + alpha * t1[2];
o[0] = (1.0-s)*(1.0-s)*(1.0-s)*p0->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*p1->c[0];
o[1] = (1.0-s)*(1.0-s)*(1.0-s)*p0->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*p1->c[1];
o[2] = (1.0-s)*(1.0-s)*(1.0-s)*p0->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*p1->c[2];
/* Coordinates of the new tangent and normal */
if ( MG_SIN(p0->tag) && MG_SIN(p1->tag) ) { // function should not be used in that case
memcpy(to,t0,3*sizeof(double));
return(1);
}
else if ( MG_SIN(p0->tag) ) {
memcpy(n1,&(mesh->xpoint[p1->xp].n1[0]),3*sizeof(double));
memcpy(n0,&(mesh->xpoint[p1->xp].n1[0]),3*sizeof(double));
}
else if ( MG_SIN(p1->tag) ) {
memcpy(n0,&(mesh->xpoint[p0->xp].n1[0]),3*sizeof(double));
memcpy(n1,&(mesh->xpoint[p0->xp].n1[0]),3*sizeof(double));
}
else {
memcpy(n0,&(mesh->xpoint[p0->xp].n1[0]),3*sizeof(double));
memcpy(n1,&(mesh->xpoint[p1->xp].n1[0]),3*sizeof(double));
}
/* Normal interpolation */
ps = ux*(n0[0] + n1[0]) + uy*(n0[1] + n1[1]) + uz*(n0[2] + n1[2]);
ps = 2.0*ps/ll;
bn[0] = n0[0] + n1[0] -ps*ux;
bn[1] = n0[1] + n1[1] -ps*uy;
bn[2] = n0[2] + n1[2] -ps*uz;
dd = bn[0]*bn[0] + bn[1]*bn[1] + bn[2]*bn[2];
if ( dd > _MMG5_EPSD ) {
dd = 1.0 / sqrt(dd);
bn[0] *= dd;
bn[1] *= dd;
bn[2] *= dd;
}
no[0] = (1.0-s)*(1.0-s)*n0[0] + 2.0*s*(1.0-s)*bn[0] + s*s*n1[0];
no[1] = (1.0-s)*(1.0-s)*n0[1] + 2.0*s*(1.0-s)*bn[1] + s*s*n1[1];
no[2] = (1.0-s)*(1.0-s)*n0[2] + 2.0*s*(1.0-s)*bn[2] + s*s*n1[2];
dd = no[0]*no[0] + no[1]*no[1] + no[2]*no[2];
if ( dd > _MMG5_EPSD2 ) {
dd = 1.0/sqrt(dd);
no[0] *= dd;
no[1] *= dd;
no[2] *= dd;
}
/* Tangent interpolation : possibly flip (back) t1 */
ps = t0[0]*t1[0] + t0[1]*t1[1] + t0[2]*t1[2];
if ( ps < 0.0 ) {
t1[0] *= -1.0;
t1[1] *= -1.0;
t1[2] *= -1.0;
}
to[0] = (1.0-s)*t0[0] + s*t1[0];
to[1] = (1.0-s)*t0[1] + s*t1[1];
to[2] = (1.0-s)*t0[2] + s*t1[2];
/* Projection of the tangent in the tangent plane defined by no */
ps = to[0]*no[0] + to[1]*no[1] + to[2]*no[2];
to[0] = to[0] -ps*no[0];
to[1] = to[1] -ps*no[1];
to[2] = to[2] -ps*no[2];
dd = to[0]*to[0] + to[1]*to[1] + to[2]*to[2];
if ( dd > _MMG5_EPSD2) {
dd = 1.0 / sqrt(dd);
to[0] *= dd;
to[1] *= dd;
to[2] *= dd;
}
return(1);
}
/** Compute point located at parameter value step from point ip0, as well as interpolate
of normals, tangent for a RIDGE edge */
inline int _MMG5_BezierRidge(MMG5_pMesh mesh,int ip0,int ip1,double s,double *o,double *no1,double *no2,double *to){
MMG5_pPoint p0,p1;
double ux,uy,uz,n01[3],n02[3],n11[3],n12[3],t0[3],t1[3];
double ps,ps2,b0[3],b1[3],bn[3],ll,il,ntemp[3],dd,alpha;
p0 = &mesh->point[ip0]; /* Ref point, from which step is counted */
p1 = &mesh->point[ip1];
if ( !p0->xp || !p1->xp ) return(0);
else if ( !(MG_GEO & p0->tag) || !(MG_GEO & p1->tag) ) return(0);
ux = p1->c[0] - p0->c[0];
uy = p1->c[1] - p0->c[1];
uz = p1->c[2] - p0->c[2];
ll = ux*ux + uy*uy + uz*uz;
if ( ll < _MMG5_EPSD2 ) return(0);
il = 1.0 / sqrt(ll);
if ( MG_SIN(p0->tag) ) {
t0[0] = ux * il;
t0[1] = uy * il;
t0[2] = uz * il;
}
else {
memcpy(t0,&(mesh->xpoint[p0->xp].t[0]),3*sizeof(double));
ps = t0[0]*ux + t0[1]*uy + t0[2]*uz;
if ( ps < 0.0 ) {
t0[0] *= -1.0;
t0[1] *= -1.0;
t0[2] *= -1.0;
}
}
if ( MG_SIN(p1->tag) ) {
t1[0] = -ux * il;
t1[1] = -uy * il;
t1[2] = -uz * il;
}
else {
memcpy(t1,&(mesh->xpoint[p1->xp].t[0]),3*sizeof(double));
ps = - ( t1[0]*ux + t1[1]*uy + t1[2]*uz );
if ( ps < 0.0 ) {
t1[0] *= -1.0;
t1[1] *= -1.0;
t1[2] *= -1.0;
}
}
alpha = _MMG5_BezierGeod(p0->c,p1->c,t0,t1);
b0[0] = p0->c[0] + alpha * t0[0];
b0[1] = p0->c[1] + alpha * t0[1];
b0[2] = p0->c[2] + alpha * t0[2];
b1[0] = p1->c[0] + alpha * t1[0];
b1[1] = p1->c[1] + alpha * t1[1];
b1[2] = p1->c[2] + alpha * t1[2];
o[0] = (1.0-s)*(1.0-s)*(1.0-s)*p0->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*p1->c[0];
o[1] = (1.0-s)*(1.0-s)*(1.0-s)*p0->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*p1->c[1];
o[2] = (1.0-s)*(1.0-s)*(1.0-s)*p0->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*p1->c[2];
if ( MG_SIN(p0->tag) && MG_SIN(p1->tag) ) {
memcpy(to,t0,3*sizeof(double));
return(1);
}
else if ( MG_SIN(p0->tag) ) {
memcpy(n11,&(mesh->xpoint[p1->xp].n1[0]),3*sizeof(double));
memcpy(n12,&(mesh->xpoint[p1->xp].n2[0]),3*sizeof(double));
memcpy(n01,&(mesh->xpoint[p1->xp].n1[0]),3*sizeof(double));
memcpy(n02,&(mesh->xpoint[p1->xp].n2[0]),3*sizeof(double));
}
else if ( MG_SIN(p1->tag) ) {
memcpy(n01,&(mesh->xpoint[p0->xp].n1[0]),3*sizeof(double));
memcpy(n02,&(mesh->xpoint[p0->xp].n2[0]),3*sizeof(double));
memcpy(n11,&(mesh->xpoint[p0->xp].n1[0]),3*sizeof(double));
memcpy(n12,&(mesh->xpoint[p0->xp].n2[0]),3*sizeof(double));
}
else {
memcpy(n01,&(mesh->xpoint[p0->xp].n1[0]),3*sizeof(double));
memcpy(n02,&(mesh->xpoint[p0->xp].n2[0]),3*sizeof(double));
memcpy(n11,&(mesh->xpoint[p1->xp].n1[0]),3*sizeof(double));
memcpy(n12,&(mesh->xpoint[p1->xp].n2[0]),3*sizeof(double));
/* Switch normals of p1 for pairing */
ps = n01[0] * n11[0] + n01[1] * n11[1] + n01[2] * n11[2];
ps2 = n01[0] * n12[0] + n01[1] * n12[1] + n01[2] * n12[2];
if ( ps2 > ps ) {
memcpy(ntemp,n11,3*sizeof(double));
memcpy(n11,n12,3*sizeof(double));
memcpy(n12,ntemp,3*sizeof(double));
}
}
/* Normal n1 interpolation */
ps = ux*(n01[0] + n11[0]) + uy*(n01[1] + n11[1]) + uz*(n01[2] + n11[2]);
ps = 2.0*ps / ll;
bn[0] = n01[0] + n11[0] -ps*ux;
bn[1] = n01[1] + n11[1] -ps*uy;
bn[2] = n01[2] + n11[2] -ps*uz;
dd = bn[0]*bn[0] + bn[1]*bn[1] + bn[2]*bn[2];
if ( dd > _MMG5_EPSD2 ) {
dd = 1.0 / sqrt(dd);
bn[0] *= dd;
bn[1] *= dd;
bn[2] *= dd;
}
no1[0] = (1.0-s)*(1.0-s)*n01[0] + 2.0*s*(1.0-s)*bn[0] + s*s*n11[0];
no1[1] = (1.0-s)*(1.0-s)*n01[1] + 2.0*s*(1.0-s)*bn[1] + s*s*n11[1];
no1[2] = (1.0-s)*(1.0-s)*n01[2] + 2.0*s*(1.0-s)*bn[2] + s*s*n11[2];
dd = no1[0]*no1[0] + no1[1]*no1[1] + no1[2]*no1[2];
if ( dd > _MMG5_EPSD2 ) {
dd = 1.0 / sqrt(dd);
no1[0] *= dd;
no1[1] *= dd;
no1[2] *= dd;
}
/* Normal n2 interpolation */
ps = ux*(n02[0] + n12[0]) + uy*(n02[1] + n12[1]) + uz*(n02[2] + n12[2]);
ps = 2.0*ps/ll;
bn[0] = n02[0] + n12[0] -ps*ux;
bn[1] = n02[1] + n12[1] -ps*uy;
bn[2] = n02[2] + n12[2] -ps*uz;
dd = bn[0]*bn[0] + bn[1]*bn[1] + bn[2]*bn[2];
if ( dd > _MMG5_EPSD2 ) {
dd = 1.0 / sqrt(dd);
bn[0] *= dd;
bn[1] *= dd;
bn[2] *= dd;
}
no2[0] = (1.0-s)*(1.0-s)*n02[0] + 2.0*s*(1.0-s)*bn[0] + s*s*n12[0];
no2[1] = (1.0-s)*(1.0-s)*n02[1] + 2.0*s*(1.0-s)*bn[1] + s*s*n12[1];
no2[2] = (1.0-s)*(1.0-s)*n02[2] + 2.0*s*(1.0-s)*bn[2] + s*s*n12[2];
dd = no2[0]*no2[0] + no2[1]*no2[1] + no2[2]*no2[2];
if ( dd > _MMG5_EPSD2 ) {
dd = 1.0 / sqrt(dd);
no2[0] *= dd;
no2[1] *= dd;
no2[2] *= dd;
}
to[0] = no1[1]*no2[2] - no1[2]*no2[1];
to[1] = no1[2]*no2[0] - no1[0]*no2[2];
to[2] = no1[0]*no2[1] - no1[1]*no2[0];
dd = to[0]*to[0] + to[1]*to[1] + to[2]*to[2];
if ( dd > _MMG5_EPSD2 ) {
dd = 1.0/sqrt(dd);
to[0] *= dd;
to[1] *= dd;
to[2] *= dd;
}
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);
}
/**
* \param mesh pointer toward the mesh structure.
* \param met pointer toward the metric structure.
* \param *warn \a warn is set to 1 if we don't have enough memory to complete mesh.
* \return -1 if failed.
* \return number of new points.
*
* Split edges of length bigger than _MMG5_LOPTL.
*
*/
static int _MMG5_adpspl(MMG5_pMesh mesh,MMG5_pSol met, int* warn) {
MMG5_pTetra pt;
MMG5_pxTetra pxt;
MMG5_Tria ptt;
MMG5_pPoint p0,p1,ppt;
MMG5_pxPoint pxp;
double dd,len,lmax,o[3],to[3],ro[3],no1[3],no2[3],v[3];
int k,ip,ip1,ip2,list[_MMG5_LMAX+2],ilist,ns,ref,ier;
char imax,tag,j,i,i1,i2,ifa0,ifa1;
*warn=0;
ns = 0;
for (k=1; k<=mesh->ne; k++) {
pt = &mesh->tetra[k];
if ( !MG_EOK(pt) || (pt->tag & MG_REQ) ) continue;
pxt = pt->xt ? &mesh->xtetra[pt->xt] : 0;
/* find longest edge */
imax = -1; lmax = 0.0;
for (i=0; i<6; i++) {
if ( pt->xt && (pxt->tag[i] & MG_REQ) ) continue;
ip1 = _MMG5_iare[i][0];
ip2 = _MMG5_iare[i][1];
len = _MMG5_lenedg(mesh,met,pt->v[ip1],pt->v[ip2]);
if ( len > lmax ) {
lmax = len;
imax = i;
}
}
if ( imax==-1 )
fprintf(stdout,"%s:%d: Warning: all edges of tetra %d are required or of length null.\n",
__FILE__,__LINE__,k);
if ( lmax < _MMG5_LOPTL ) continue;
/* proceed edges according to lengths */
ifa0 = _MMG5_ifar[imax][0];
ifa1 = _MMG5_ifar[imax][1];
i = (pt->xt && (pxt->ftag[ifa1] & MG_BDY)) ? ifa1 : ifa0;
j = _MMG5_iarfinv[i][imax];
i1 = _MMG5_idir[i][_MMG5_inxt2[j]];
i2 = _MMG5_idir[i][_MMG5_iprv2[j]];
ip1 = pt->v[i1];
ip2 = pt->v[i2];
p0 = &mesh->point[ip1];
p1 = &mesh->point[ip2];
/* Case of a boundary face */
if ( pt->xt && (pxt->ftag[i] & MG_BDY) ) {
if ( !(MG_GET(pxt->ori,i)) ) continue;
ref = pxt->edg[_MMG5_iarf[i][j]];
tag = pxt->tag[_MMG5_iarf[i][j]];
if ( tag & MG_REQ ) continue;
tag |= MG_BDY;
ilist = _MMG5_coquil(mesh,k,imax,list);
if ( !ilist ) continue;
else if ( ilist < 0 )
return(-1);
if ( tag & MG_NOM ){
if( !_MMG5_BezierNom(mesh,ip1,ip2,0.5,o,no1,to) )
continue;
else if ( MG_SIN(p0->tag) && MG_SIN(p1->tag) ) {
_MMG5_tet2tri(mesh,k,i,&ptt);
_MMG5_nortri(mesh,&ptt,no1);
if ( !MG_GET(pxt->ori,i) ) {
no1[0] *= -1.0;
no1[1] *= -1.0;
no1[2] *= -1.0;
}
}
}
else if ( tag & MG_GEO ) {
if ( !_MMG5_BezierRidge(mesh,ip1,ip2,0.5,o,no1,no2,to) )
continue;
if ( MG_SIN(p0->tag) && MG_SIN(p1->tag) ) {
_MMG5_tet2tri(mesh,k,i,&ptt);
_MMG5_nortri(mesh,&ptt,no1);
no2[0] = to[1]*no1[2] - to[2]*no1[1];
no2[1] = to[2]*no1[0] - to[0]*no1[2];
no2[2] = to[0]*no1[1] - to[1]*no1[0];
dd = no2[0]*no2[0] + no2[1]*no2[1] + no2[2]*no2[2];
if ( dd > _MMG5_EPSD2 ) {
dd = 1.0 / sqrt(dd);
no2[0] *= dd;
no2[1] *= dd;
no2[2] *= dd;
}
}
}
else if ( tag & MG_REF ) {
if ( !_MMG5_BezierRef(mesh,ip1,ip2,0.5,o,no1,to) )
continue;
}
else {
if ( !_MMG5_norface(mesh,k,i,v) ) continue;
if ( !_MMG5_BezierReg(mesh,ip1,ip2,0.5,v,o,no1) )
continue;
}
ier = _MMG5_simbulgept(mesh,list,ilist,o);
if ( !ier ) {
ier = _MMG5_dichoto1b(mesh,list,ilist,o,ro);
memcpy(o,ro,3*sizeof(double));
}
ip = _MMG5_newPt(mesh,o,tag);
if ( !ip ) {
/* reallocation of point table */
_MMG5_POINT_REALLOC(mesh,met,ip,mesh->gap,
*warn=1;
break
,o,tag);
}
//CECILE
if ( met->m )
met->m[ip] = 0.5 * (met->m[ip1]+met->m[ip2]);
//CECILE
ier = _MMG5_split1b(mesh,met,list,ilist,ip,1);
/* if we realloc memory in _MMG5_split1b pt and pxt pointers are not valid */
pt = &mesh->tetra[k];
pxt = pt->xt ? &mesh->xtetra[pt->xt] : 0;
if ( ier < 0 ) {
fprintf(stdout," ## Error: unable to split.\n");
return(-1);
}
else if ( !ier ) {
_MMG5_delPt(mesh,ip);
continue;
}
ns++;
ppt = &mesh->point[ip];
if ( MG_EDG(tag) || (tag & MG_NOM) )
ppt->ref = ref;
else
ppt->ref = pxt->ref[i];
if ( met->m )
met->m[ip] = 0.5 * (met->m[ip1]+met->m[ip2]);
pxp = &mesh->xpoint[ppt->xp];
if ( tag & MG_NOM ){
memcpy(pxp->n1,no1,3*sizeof(double));
memcpy(pxp->t,to,3*sizeof(double));
}
else if ( tag & MG_GEO ) {
memcpy(pxp->n1,no1,3*sizeof(double));
memcpy(pxp->n2,no2,3*sizeof(double));
memcpy(pxp->t,to,3*sizeof(double));
}
else if ( tag & MG_REF ) {
memcpy(pxp->n1,no1,3*sizeof(double));
memcpy(pxp->t,to,3*sizeof(double));
}
else
memcpy(pxp->n1,no1,3*sizeof(double));
}
/* Case of an internal face */
else {
if ( (p0->tag & MG_BDY) && (p1->tag & MG_BDY) ) continue;
/**
* \param pb pointer toward the Bezier structure.
* \param uv coordinates of the point in the parametric space.
* \param o computed coordinates of the point in the real space.
* \param no computed normal.
* \param to computed tangent.
* \return 1.
*
* Compute \a o, \a no and \a to at \f$(u,v)\f$ in Bezier patch.
*
*/
int _MMG5_bezierInt(_MMG5_pBezier pb,double uv[2],double o[3],double no[3],double to[3]) {
double dd,u,v,w,ps,ux,uy,uz;
char i;
memset(to,0,3*sizeof(double));
u = uv[0];
v = uv[1];
w = 1 - u - v;
/* coordinates + normals */
for (i=0; i<3; i++) {
o[i] = pb->b[0][i]*w*w*w + pb->b[1][i]*u*u*u + pb->b[2][i]*v*v*v \
+ 3.0 * (pb->b[3][i]*u*u*v + pb->b[4][i]*u*v*v + pb->b[5][i]*w*v*v \
+ pb->b[6][i]*w*w*v + pb->b[7][i]*w*w*u + pb->b[8][i]*w*u*u)\
+ 6.0 * pb->b[9][i]*u*v*w;
/* quadratic interpolation of normals */
no[i] = pb->n[0][i]*w*w + pb->n[1][i]*u*u + pb->n[2][i]*v*v \
+ 2.0 * (pb->n[3][i]*u*v + pb->n[4][i]*v*w + pb->n[5][i]*u*w);
/* linear interpolation, not used here
no[i] = pb->n[0][i]*w + pb->n[1][i]*u + pb->n[2][i]*v; */
}
/* tangent */
if ( w < _MMG5_EPSD2 ) {
ux = pb->b[2][0] - pb->b[1][0];
uy = pb->b[2][1] - pb->b[1][1];
uz = pb->b[2][2] - pb->b[1][2];
dd = ux*ux + uy*uy + uz*uz;
if ( dd > _MMG5_EPSD2 ) {
dd = 1.0 / sqrt(dd);
ux *= dd;
uy *= dd;
uz *= dd;
}
/* corners */
if ( MG_SIN(pb->p[1]->tag) ) {
pb->t[1][0] = ux;
pb->t[1][1] = uy;
pb->t[1][2] = uz;
}
if ( MG_SIN(pb->p[2]->tag) ) {
pb->t[2][0] = ux;
pb->t[2][1] = uy;
pb->t[2][2] = uz;
}
ps = pb->t[1][0]* pb->t[2][0] + pb->t[1][1]* pb->t[2][1] + pb->t[1][2]* pb->t[2][2];
if ( ps > 0.0 ) {
to[0] = pb->t[1][0]*u + pb->t[2][0]*v;
to[1] = pb->t[1][1]*u + pb->t[2][1]*v;
to[2] = pb->t[1][2]*u + pb->t[2][2]*v;
}
else {
to[0] = -pb->t[1][0]*u + pb->t[2][0]*v;
to[1] = -pb->t[1][1]*u + pb->t[2][1]*v;
to[2] = -pb->t[1][2]*u + pb->t[2][2]*v;
}
}
if ( u < _MMG5_EPSD2 ) {
ux = pb->b[2][0] - pb->b[0][0];
uy = pb->b[2][1] - pb->b[0][1];
uz = pb->b[2][2] - pb->b[0][2];
dd = ux*ux + uy*uy + uz*uz;
if ( dd > _MMG5_EPSD2 ) {
dd = 1.0 / sqrt(dd);
ux *= dd;
uy *= dd;
uz *= dd;
}
/* corners */
if ( MG_SIN(pb->p[0]->tag) ) {
pb->t[0][0] = ux;
pb->t[0][1] = uy;
pb->t[0][2] = uz;
}
if ( MG_SIN(pb->p[2]->tag) ) {
pb->t[2][0] = ux;
pb->t[2][1] = uy;
pb->t[2][2] = uz;
}
ps = pb->t[0][0]* pb->t[2][0] + pb->t[0][1]* pb->t[2][1] + pb->t[0][2]* pb->t[2][2];
if ( ps > 0.0 ) {
to[0] = pb->t[0][0]*w + pb->t[2][0]*v;
to[1] = pb->t[0][1]*w + pb->t[2][1]*v;
to[2] = pb->t[0][2]*w + pb->t[2][2]*v;
}
else {
to[0] = -pb->t[0][0]*w + pb->t[2][0]*v;
to[1] = -pb->t[0][1]*w + pb->t[2][1]*v;
to[2] = -pb->t[0][2]*w + pb->t[2][2]*v;
}
}
if ( v < _MMG5_EPSD2 ) {
ux = pb->b[1][0] - pb->b[0][0];
uy = pb->b[1][1] - pb->b[0][1];
uz = pb->b[1][2] - pb->b[0][2];
dd = ux*ux + uy*uy + uz*uz;
if ( dd > _MMG5_EPSD2 ) {
dd = 1.0 / sqrt(dd);
ux *= dd;
uy *= dd;
uz *= dd;
}
/* corners */
if ( MG_SIN(pb->p[0]->tag) ) {
pb->t[0][0] = ux;
pb->t[0][1] = uy;
pb->t[0][2] = uz;
}
if ( MG_SIN(pb->p[1]->tag) ) {
pb->t[1][0] = ux;
pb->t[1][1] = uy;
pb->t[1][2] = uz;
}
ps = pb->t[0][0]* pb->t[1][0] + pb->t[0][1]* pb->t[1][1] + pb->t[0][2]* pb->t[1][2];
if ( ps > 0.0 ) {
to[0] = pb->t[0][0]*w + pb->t[1][0]*u;
to[1] = pb->t[0][1]*w + pb->t[1][1]*u;
to[2] = pb->t[0][2]*w + pb->t[1][2]*u;
}
else {
to[0] = -pb->t[0][0]*w + pb->t[1][0]*u;
to[1] = -pb->t[0][1]*w + pb->t[1][1]*u;
to[2] = -pb->t[0][2]*w + pb->t[1][2]*u;
}
}
dd = no[0]*no[0] + no[1]*no[1] + no[2]*no[2];
if ( dd > _MMG5_EPSD2 ) {
dd = 1.0 / sqrt(dd);
no[0] *= dd;
no[1] *= dd;
no[2] *= dd;
}
dd = to[0]*to[0] + to[1]*to[1] + to[2]*to[2];
if ( dd > _MMG5_EPSD2 ) {
dd = 1.0 / sqrt(dd);
to[0] *= dd;
to[1] *= dd;
to[2] *= dd;
}
return(1);
}
/** check for singularities */
static int _MMG5_singul(MMG5_pMesh mesh) {
MMG5_pTria pt;
MMG5_pPoint ppt,p1,p2;
double ux,uy,uz,vx,vy,vz,dd;
int list[_MMG5_LMAX+2],k,nc,ng,nr,ns,nre;
char i;
nre = nc = 0;
for (k=1; k<=mesh->nt; k++) {
pt = &mesh->tria[k];
if ( !MG_EOK(pt) ) continue;
for (i=0; i<3; i++) {
ppt = &mesh->point[pt->v[i]];
if ( !MG_VOK(ppt) || MG_SIN(ppt->tag) || ppt->tag & MG_NOM ) continue;
else if ( MG_EDG(ppt->tag) ) {
ns = _MMG5_bouler(mesh,k,i,list,&ng,&nr);
if ( !ns ) continue;
if ( (ng+nr) > 2 ) {
ppt->tag |= MG_CRN + MG_REQ;
nre++;
nc++;
}
else if ( (ng == 1) && (nr == 1) ) {
ppt->tag |= MG_REQ;
nre++;
}
else if ( ng == 1 && !nr ){
ppt->tag |= MG_CRN + MG_REQ;
nre++;
nc++;
}
else if ( nr == 1 && !ng ){
ppt->tag |= MG_CRN + MG_REQ;
nre++;
nc++;
}
/* check ridge angle */
else {
p1 = &mesh->point[list[1]];
p2 = &mesh->point[list[2]];
ux = p1->c[0] - ppt->c[0];
uy = p1->c[1] - ppt->c[1];
uz = p1->c[2] - ppt->c[2];
vx = p2->c[0] - ppt->c[0];
vy = p2->c[1] - ppt->c[1];
vz = p2->c[2] - ppt->c[2];
dd = (ux*ux + uy*uy + uz*uz) * (vx*vx + vy*vy + vz*vz);
if ( fabs(dd) > _MMG5_EPSD ) {
dd = (ux*vx + uy*vy + uz*vz) / sqrt(dd);
if ( dd > -mesh->info.dhd ) {
ppt->tag |= MG_CRN;
nc++;
}
}
}
}
}
}
if ( abs(mesh->info.imprim) > 3 && nre > 0 )
fprintf(stdout," %d corners, %d singular points detected\n",nc,nre);
return(1);
}