mmg3d3.c

Go to the documentation of this file.

/* =============================================================================
**  This file is part of the mmg software package for the tetrahedral
**  mesh modification.
**  Copyright (c) Bx INP/CNRS/Inria/UBordeaux/UPMC, 2004-
**
**  mmg is free software: you can redistribute it and/or modify it
**  under the terms of the GNU Lesser General Public License as published
**  by the Free Software Foundation, either version 3 of the License, or
**  (at your option) any later version.
**
**  mmg is distributed in the hope that it will be useful, but WITHOUT
**  ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
**  FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
**  License for more details.
**
**  You should have received a copy of the GNU Lesser General Public
**  License and of the GNU General Public License along with mmg (in
**  files COPYING.LESSER and COPYING). If not, see
**  <http://www.gnu.org/licenses/>. Please read their terms carefully and
**  use this copy of the mmg distribution only if you accept them.
** =============================================================================
*/
 
#include "libmmg3d.h"
#include "libmmg3d_private.h"
#include "inlined_functions_3d_private.h"
#include "mmg3dexterns_private.h"
 
#define MMG5_DEGTOL  1.e-1
 
extern int8_t  ddb;
 
double MMG5_estavglen(MMG5_pMesh mesh) {
  MMG5_pTetra pt;
  MMG5_pPoint p1,p2;
  MMG5_int    k,na;
  double      len,lent,dna;
  int8_t      i,i1,i2;
 
  na = 0;
  lent = 0.0;
 
  for (k=1; k<=mesh->ne; k++) {
    pt = &mesh->tetra[k];
    for (i=0; i<6; i++) {
      i1 = MMG5_iare[i][0];
      i2 = MMG5_iare[i][1];
 
      p1 = &mesh->point[pt->v[i1]];
      p2 = &mesh->point[pt->v[i2]];
 
      len = (p2->c[0] - p1->c[0])*(p2->c[0] - p1->c[0])
        + (p2->c[1] - p1->c[1])*(p2->c[1] - p1->c[1])
        + (p2->c[2] - p1->c[2])*(p2->c[2] - p1->c[2]);
 
      lent += sqrt(len);
      na++;
    }
  }
 
  dna = (double)na;
  dna = 1.0 / dna;
  lent *= dna;
 
  return lent;
}
 
static
inline int MMG5_intdispvol(double *v1, double *v2, double *vp, double t) {
  int8_t i;
 
  for(i=0; i<3; i++)
    vp[i] = (1.0-t)*v1[i] + t*v2[i];
 
  return 1;
}
 
static MMG5_int MMG5_spllag(MMG5_pMesh mesh,MMG5_pSol disp,MMG5_pSol met,int itdeg, int* warn) {
  MMG5_pTetra    pt;
  MMG5_pxTetra   pxt;
  MMG5_pPoint    p0,p1;
  double         len,lmax,o[3],hma2;
  double         *m1,*m2,*mp;
  int            ilist,ier;
  MMG5_int       src,ns,k,ip,ip1,ip2,iadr;
  int64_t        list[MMG3D_LMAX+2];
  int8_t         imax,i,i1,i2;
  static int8_t  mmgWarn0 = 0;
 
  *warn=0;
  ns = 0;
  hma2 = mesh->info.hmax*mesh->info.hmax;
 
  for (k=1; k<=mesh->ne; k++) {
    pt  = &mesh->tetra[k];
    pxt = pt->xt ? &mesh->xtetra[pt->xt] : NULL;
 
    if ( !MG_EOK(pt) || (pt->tag & MG_REQ) )   continue;
    if ( pt->mark != itdeg ) continue;
 
    /* find longest, internal edge */
    imax = -1;
    lmax = 0.0;
    for (i=0; i<6; i++) {
      i1  = MMG5_iare[i][0];
      i2  = MMG5_iare[i][1];
      ip1 = pt->v[i1];
      ip2 = pt->v[i2];
      p0 = &mesh->point[ip1];
      p1 = &mesh->point[ip2];
 
      /* Skip the non-internal edges */
 
      // Fast check but incomplete: regular boundary edges may have no tags (bdy
      // tags are not added at new edges created during the split of boudary
      // faces for example).
      if ( pxt && (pxt->tag[i] & MG_BDY) )  continue;
 
      // Slower test but allowing to be sure to detect boundary edges
      uint16_t  tag = 0;
      MMG5_int ref = 0;
      if ( !MMG3D_get_shellEdgeTag(mesh,k,i,&tag,&ref) ) {
        fprintf(stderr,"\n  ## Warning: %s: 0. unable to get edge info"
                " (tetra %" MMG5_PRId").\n",__func__,MMG3D_indElt(mesh,k));
        continue;
      }
 
      if ( tag & MG_BDY ) {
        continue;
      }
 
      /* Here we are sure to work on a non-boundary edge */
      len = (p1->c[0]-p0->c[0])*(p1->c[0]-p0->c[0])
        + (p1->c[1]-p0->c[1])*(p1->c[1]-p0->c[1])
        + (p1->c[2]-p0->c[2])*(p1->c[2]-p0->c[2]);
 
      if ( len > lmax ) {
        lmax = len;
        imax = i;
      }
    }
 
    if ( imax==-1 ) {
      if ( !mmgWarn0 ){
        mmgWarn0 = 1;
        fprintf(stderr,"\n  ## Warning: %s: No possible edge split in tetra %" MMG5_PRId
                ".\n",__func__,MMG3D_indElt(mesh,k));
      }
      continue;
    }
 
    if ( lmax < hma2 )  continue;
 
    /* proceed edges according to lengths */
    i1  = MMG5_iare[imax][0];
    i2  = MMG5_iare[imax][1];
    ip1 = pt->v[i1];
    ip2 = pt->v[i2];
    p0 = &mesh->point[ip1];
    p1 = &mesh->point[ip2];
 
    /* Deal only with internal faces */
    int8_t isbdy;
    ilist = MMG5_coquil(mesh,k,imax,list,&isbdy);
 
    if ( !ilist ) continue;
    else if ( ilist<0 ) return -1;
    else if ( isbdy ) {
      /* Skip bdy edges */
      continue;
    }
 
#ifndef NDEBUG
    if ( pxt ) {
      assert( !(pxt->tag[imax] & MG_BDY) ); }
#endif
 
    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]);
 
#ifdef USE_POINTMAP
    src = p0->src;
#else
    src = 1;
#endif
    ip = MMG3D_newPt(mesh,o,MG_NOTAG,src);
 
    if ( !ip )  {
      /* reallocation of point table */
      MMG5_int oldnpmax = mesh->npmax;
      MMG3D_POINT_REALLOC(mesh,met,ip,mesh->gap,*warn=1;break,o,MG_NOTAG,src);
      if( disp->m ) {
        MMG5_ADD_MEM(mesh,(disp->size*(mesh->npmax-disp->npmax))*sizeof(double),
                     "larger displacement",
                     MMG5_SAFE_RECALLOC(mesh->point,mesh->npmax+1,oldnpmax+1,MMG5_Point,,);
                     mesh->memCur -= (mesh->npmax - oldnpmax)*sizeof(MMG5_Point);
                     mesh->npmax = oldnpmax;
                     mesh->np = mesh->npmax-1;
                     mesh->npnil = 0;
                     break);
        MMG5_SAFE_REALLOC(disp->m,disp->size*(disp->npmax+1),
                          disp->size*(mesh->npmax+1),
                          double,"larger displacement",
                          MMG5_SAFE_RECALLOC(mesh->point,mesh->npmax+1,oldnpmax+1,MMG5_Point,,);
                          mesh->memCur -= (mesh->npmax - oldnpmax)*sizeof(MMG5_Point);
                          mesh->npmax = oldnpmax;
                          mesh->np = mesh->npmax-1;
                          mesh->npnil = 0;
                          break);
      }
      disp->npmax = mesh->npmax;
    }
 
    /* Interpolation of metric, if any */
    if ( met->m ) {
      if ( !MMG5_intmet(mesh,met,k,imax,ip,0.5) ) {
        MMG3D_delPt(mesh,ip);
        return -1;
      }
    }
 
    /* Interpolation of displacement */
    if ( disp->m ) {
      iadr = disp->size*ip1;
      m1 = &disp->m[iadr];
      iadr = disp->size*ip2;
      m2 = &disp->m[iadr];
      iadr = disp->size*ip;
      mp = &disp->m[iadr];
 
      if ( !MMG5_intdispvol(m1,m2,mp,0.5) ) {
        MMG3D_delPt(mesh,ip);
        return -1;
      }
    }
 
    /* Il y a un check sur la taille des arêtes ici aussi ! */
    ier = MMG5_split1b(mesh,met,list,ilist,ip,1,1,0);
    if ( ier < 0 ) {
      fprintf(stderr,"\n  ## Error: %s: unable to split.\n",__func__);
      return -1;
    }
    else if ( !ier ) {
      MMG3D_delPt(mesh,ip);
    }
    else {
      ns++;
    }
  }
 
  return ns;
}
 
MMG5_int MMG5_swptetlag(MMG5_pMesh mesh,MMG5_pSol met,double crit,MMG3D_pPROctree PROctree,int itdeg) {
  MMG5_pTetra  pt;
  MMG5_pxTetra pxt;
  int          ilist,it,maxit,ier;
  MMG5_int     k,nconf,ns,nns;
  int64_t      list[MMG3D_LMAX+2];
  int8_t       i;
 
  maxit = 2;
  it = nns = 0;
 
  do {
    ns = 0;
    for (k=1; k<=mesh->ne; k++) {
      pt = &mesh->tetra[k];
      if ( !MG_EOK(pt) || (pt->tag & MG_REQ) )  continue;
      if ( pt->mark != itdeg ) continue;
 
      for (i=0; i<6; i++) {
        /* Prevent swap of a ref or tagged edge */
        if ( pt->xt ) {
          pxt = &mesh->xtetra[pt->xt];
          if ( pxt->edg[i] || pxt->tag[i] ) continue;
        }
 
        nconf = MMG5_chkswpgen(mesh,met,k,i,&ilist,list,crit,2);
 
        if ( nconf<0 ) return -1;
        else if ( nconf ) {
          ier = MMG5_swpgen(mesh,met,nconf,ilist,list,PROctree,2);
          if ( ier > 0 )  ns++;
          else if ( ier < 0 ) return -1;
          break;
        }
      }
    }
    nns += ns;
  }
  while ( ++it < maxit && ns > 0 );
  return nns;
}
 
MMG5_int MMG5_movtetlag(MMG5_pMesh mesh,MMG5_pSol met, int itdeg) {
  MMG5_pTetra   pt;
  MMG5_pPoint   ppt;
  int           ier,ilistv,it;
  MMG5_int      k,nm,nnm,base;
  int64_t       listv[MMG3D_LMAX+2];
  uint8_t       i;
  int           maxit;
 
  base = 1;
  for (k=1; k<=mesh->np; k++)
    mesh->point[k].flag = base;
 
  maxit = 2;
  it = nnm = 0;
 
  do {
    base++;
    nm = 0;
    for (k=1; k<=mesh->ne; k++) {
      pt = &mesh->tetra[k];
      if ( !MG_EOK(pt) || pt->ref < 0 || (pt->tag & MG_REQ) )   continue;
      if ( pt->mark != itdeg ) continue;
 
      /* point i */
      for (i=0; i<4; i++) {
        ppt = &mesh->point[pt->v[i]];
        if ( ppt->flag == base )  continue;
        else if ( ppt->tag & MG_BDY ) continue;
 
        ilistv = MMG5_boulevolp(mesh,k,i,listv);
        if ( !ilistv )  continue;
 
        ier = MMG5_movintpt_iso(mesh,met, NULL, listv,ilistv,0);
 
        if ( ier ) {
          nm++;
          ppt->flag = base;
 
          /* Somehow interpolate displacement ? */
        }
      }
    }
    nnm += nm;
  }
  while( ++it < maxit && nm > 0 );
 
  return nnm;
}
 
static MMG5_int MMG5_coltetlag(MMG5_pMesh mesh,MMG5_pSol met,int itdeg) {
  MMG5_pTetra pt;
  MMG5_pPoint p0,p1;
  double      ll,ux,uy,uz,hmi2;
  int         ilist;
  int64_t     list[MMG3D_LMAX+2];
  MMG5_int    k,nc,nnm,base;
  int         ier;
  int8_t      i,j,ip,iq,isnm;
  int16_t     tag0, tag1;
 
  nc = nnm = 0;
  hmi2 = mesh->info.hmin*mesh->info.hmin;
 
  /* init of point flags, otherwise it can be uninitialized */
  for (k=1; k<=mesh->np; k++)
    mesh->point[k].flag = 0;
 
  for (k=1; k<=mesh->ne; k++) {
    base = ++mesh->base;
    pt = &mesh->tetra[k];
    if ( !MG_EOK(pt) || (pt->tag & MG_REQ) )   continue;
    if ( pt->mark != itdeg ) continue;
 
    for (i=0; i<4; i++) {
      ier = 0;
      for (j=0; j<3; j++) {
        ip = MMG5_idir[i][MMG5_inxt2[j]];
        iq = MMG5_idir[i][MMG5_iprv2[j]];
        assert( 0<=ip && ip<4 && "unexpected local index for vertex");
        assert( 0<=iq && iq<4 && "unexpected local index for vertex");
 
        p0 = &mesh->point[pt->v[ip]];
        p1 = &mesh->point[pt->v[iq]];
        tag0 = p0->tag & ~MG_OLDPARBDY;
        tag1 = p1->tag & ~MG_OLDPARBDY;
        if ( p0->flag == base )  continue;
        else if ( p0->tag & MG_BDY ) continue;
        else if ( (p0->tag & MG_REQ) || (tag0 > tag1) )  continue;
 
        /* check length */
        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 > hmi2 )  continue;
 
        isnm = 0;
        ilist = MMG5_boulevolp(mesh,k,ip,list);
        ilist = MMG5_chkcol_int(mesh,met,k,i,j,list,ilist,2);
 
        if ( ilist > 0 ) {
          ier = MMG5_colver(mesh,met,list,ilist,iq,2);
          if ( ier < 0 ) return -1;
          else if ( ier ) {
            MMG3D_delPt(mesh,ier);
            break;
          }
        }
        else if ( ilist < 0 ) return -1;
      }
      if ( ier ) {
        p1->flag = base;
        if ( isnm )  nnm++;
        nc++;
        break;
      }
    }
  }
 
  return nc;
}
 
MMG5_int MMG5_chkmovmesh(MMG5_pMesh mesh,MMG5_pSol disp,short t,MMG5_int *tetIdx) {
  MMG5_pTetra  pt;
  MMG5_pPoint  ppt;
  double       *v,c[4][3],tau;
  MMG5_int     k,np;
  MMG5_int     idx;
  int8_t       i,j;
 
  /* Pseudo time-step = fraction of disp to perform */
  tau = (double)t / MMG3D_SHORTMAX;
  idx = 0;
 
  for (k=1; k<=mesh->ne; k++) {
    pt = &mesh->tetra[k];
    if ( !MG_EOK(pt) ) continue;
 
    for (i=0; i<4; i++) {
      np = pt->v[i];
      ppt = &mesh->point[np];
      v = &disp->m[3*np];
      for (j=0; j<3; j++)
        c[i][j] = ppt->c[j]+tau*v[j];
    }
 
    //     Other criteria : eg. a rate of degradation, etc... ?
    if( MMG5_caltet_iso_4pt(c[0],c[1],c[2],c[3]) < MMG5_EPSOK) {
 
      if ( tetIdx ) {
        tetIdx[idx++] = k;
      }
      else {
        return 1;
      }
    }
  }
  return idx;
}
 
int MMG5_dispmesh(MMG5_pMesh mesh,MMG5_pSol disp,short t,int itdeg) {
  MMG5_pTetra   pt;
  MMG5_pPoint   ppt;
  double        *v,tau,ctau,c[4][3],ocal,ncal;
  MMG5_int      k,np;
  int8_t        i,j;
 
  tau = (double)t /MMG3D_SHORTMAX;
  ctau = 1.0 - tau;
 
  /* Identify elements which are very distorted in the process */
  for (k=1; k<=mesh->ne; k++) {
    pt  = &mesh->tetra[k];
    if ( !MG_EOK(pt) ) continue;
 
    for (i=0; i<4; i++) {
      np = pt->v[i];
      ppt = &mesh->point[np];
      for (j=0; j<3; j++)
        c[i][j] = ppt->c[j];
    }
 
    ocal = MMG5_caltet_iso_4pt(c[0],c[1],c[2],c[3]);
 
    for (i=0; i<4; i++) {
      np = pt->v[i];
      v = &disp->m[3*np];
      for (j=0; j<3; j++)
        c[i][j] += tau*v[j];
    }
 
    ncal = MMG5_caltet_iso_4pt(c[0],c[1],c[2],c[3]);
 
    if ( ncal < MMG5_DEGTOL*ocal )
      pt->mark = itdeg;
 
  }
 
  /* Perform physical displacement */
  for (k=1; k<=mesh->np; k++) {
    ppt = &mesh->point[k];
 
    if ( !MG_VOK(ppt) ) continue;
    v = &disp->m[3*k];
 
    for (i=0; i<3; i++) {
      ppt->c[i] = ppt->c[i] + tau*v[i];
      v[i] *= ctau;
    }
  }
 
  return 1;
}
 
 
int MMG5_mmg3d3(MMG5_pMesh mesh,MMG5_pSol disp,MMG5_pSol met,MMG5_int **invalidTets) {
  double   avlen,tau,hmintmp,hmaxtmp;
  int      itdc,itmn,maxitmn,maxitdc,iit,warn;
  MMG5_int nspl,ns,nm,nc,k;
  MMG5_int nns,nnm,nnc,nnspl,nnns,nnnm,nnnc,nnnspl;
  MMG5_int ninvalidTets;
  short    t,lastt;
  int8_t   ier;
 
  maxitmn = 10;
  maxitdc = 100;
  t  = 0;
  tau = 0.0;
  ninvalidTets = 0;
 
  nnnspl = nnnc = nnns = nnnm = lastt = 0;
 
  if ( abs(mesh->info.imprim) > 4 || mesh->info.ddebug )
    fprintf(stdout,"  ** LAGRANGIAN MOTION\n");
 
  /* Field mark stores information about whether a tetra has been greatly deformed during current step */
  for (k=1; k<=mesh->ne; k++)
    mesh->tetra[k].mark = 0;
 
  /* Estimates of the minimum and maximum edge lengths in the mesh */
  avlen = MMG5_estavglen(mesh);
 
  hmintmp = mesh->info.hmin;
  hmaxtmp = mesh->info.hmax;
 
  mesh->info.hmax = MMG3D_LLONG*avlen;
  mesh->info.hmin = MMG3D_LSHRT*avlen;
 
  for (itmn=0; itmn<maxitmn; itmn++) {
 
#ifdef USE_ELAS
    /* Extension of the displacement field */
    if ( !MMG5_velextLS(mesh,disp) ) {
      fprintf(stderr,"\n  ## Problem in func. MMG5_velextLS. Exit program.\n");
      return 0;
    }
#else
    fprintf(stderr,"\n  ## Error: %s: you need to compile with the USE_ELAS"
            " CMake's flag set to ON to use the rigidbody movement.\n",__func__);
    return 0;
#endif
 
    //MMG5_saveDisp(mesh,disp);
 
    /* Sequence of dichotomy loops to find the largest admissible displacements */
    for (itdc=0; itdc<maxitdc; itdc++) {
      nnspl = nnc = nns = nnm = 0;
 
      t = MMG5_dikmov(mesh,disp,&lastt,MMG3D_SHORTMAX,MMG5_chkmovmesh);
      if ( t == 0 ) {
        if ( abs(mesh->info.imprim) > 4 || mesh->info.ddebug )
          fprintf(stderr,"\n   *** Stop: impossible to proceed further\n");
        break;
      }
 
      ier = MMG5_dispmesh(mesh,disp,t,itdc);
      if ( !ier ) {
        fprintf(stderr,"\n  ** Impossible motion\n");
        return 0;
      }
 
      tau = tau + ((double)t /MMG3D_SHORTMAX)*(1.0-tau);
      if ( (abs(mesh->info.imprim) > 3 ) || mesh->info.ddebug )
        printf("   ---> Realized displacement: %f\n",tau);
 
      /* Local remeshing depending on the option */
      if ( mesh->info.lag > 0 ) {
        for ( iit=0; iit<5; iit++) {
 
          nspl = nc = ns = nm = 0;
 
          if ( mesh->info.lag > 1 ) {
            if ( !mesh->info.noinsert ) {
              /* Split of points */
              nspl = MMG5_spllag(mesh,disp,met,itdc,&warn);
              if ( nspl < 0 ) {
                fprintf(stderr,"\n  ## Problem in spllag. Exiting.\n");
                return 0;
              }
 
              /* Collapse of points */
              nc = MMG5_coltetlag(mesh,met,itdc);
              if ( nc < 0 ) {
                fprintf(stderr,"\n  ## Problem in coltetlag. Exiting.\n");
                return 0;
              }
            }
          }
 
          /* Swap of edges in tetra that have resulted distorted from the process */
          /* I do not know whether it is safe to put NULL in metric here (a
           * priori ok, since there is no vertex creation or suppression) */
          if ( !mesh->info.noswap ) {
            ns = MMG5_swptetlag(mesh,met,MMG3D_LSWAPIMPROVE,NULL,itdc);
            if ( ns < 0 ) {
              fprintf(stderr,"\n  ## Problem in swaptetlag. Exiting.\n");
              return 0;
            }
          }
 
          /* Relocate vertices of tetra which have been distorted in the displacement process */
          nm = MMG5_movtetlag(mesh,met,itdc);
          if ( nm < 0 ) {
            fprintf(stderr,"\n  ## Problem in movtetlag. Exiting.\n");
            return 0;
          }
 
          if ( (abs(mesh->info.imprim) > 4 || mesh->info.ddebug) && (nspl+nc+ns+nm > 0) )
            printf(" %" MMG5_PRId " edges splitted, %" MMG5_PRId " vertices collapsed, %" MMG5_PRId " elements"
                   " swapped, %" MMG5_PRId " vertices moved.\n",nspl,nc,ns,nm);
          nnspl+= nspl;
          nnm  += nm;
          nnc  += nc;
          nns  += ns;
        }
        /* Five iterations of local remeshing have been performed: print final stats */
        if ( abs(mesh->info.imprim) > 3 && abs(mesh->info.imprim) < 5 && (nnspl+nnm+nns+nnc > 0) )
          printf(" %" MMG5_PRId " edges splitted, %" MMG5_PRId " vertices collapsed, %" MMG5_PRId " elements"
                 " swapped, %" MMG5_PRId " vertices moved.\n",nnspl,nnc,nns,nnm);
      }
 
      nnnspl += nnspl;
      nnnm   += nnm;
      nnnc   += nnc;
      nnns   += nns;
 
      if ( t == MMG3D_SHORTMAX ) break;
    }
 
    /* End of dichotomy loop: maximal displacement of the extended velocity
     * field has been performed */
    if ( mesh->info.imprim > 1 && abs(mesh->info.imprim) < 4 ) {
      printf("   ---> Realized displacement: %f\n",tau);
    }
 
    if ( abs(mesh->info.imprim) > 2 && mesh->info.lag )
      printf(" %"MMG5_PRId" edges splitted, %"MMG5_PRId" vertices collapsed,"
             " %"MMG5_PRId" elements swapped, %"MMG5_PRId" vertices moved.\n",
             nnnspl,nnnc,nnns,nnnm);
 
    if ( t == MMG3D_SHORTMAX || (t==0 && itdc==0) ) break;
  }
 
  /* Reinsert standard values for hmin, hmax */
  mesh->info.hmin = hmintmp;
  mesh->info.hmax = hmaxtmp;
 
  if ( tau < MMG5_EPSD2 ) {
    MMG5_SAFE_CALLOC(*invalidTets,mesh->np,MMG5_int,
                     printf("## Warning: Not enough memory to keep track of"
                            " the invalid tetrahedron.\n");
                     MMG5_DEL_MEM(mesh,disp->m);
                     return 1);
    ninvalidTets = MMG5_chkmovmesh(mesh,disp,lastt,*invalidTets);
    assert ( ninvalidTets );
  }
 
  /* Clean memory */
  /* Doing this, memcur of mesh is decreased by size of displacement */
  MMG5_DEL_MEM(mesh,disp->m);
 
  if ( ninvalidTets ) {
    return -ninvalidTets;
  }
  else {
    return 1;
  }
}