mlists.c

来自「FreeFem++可以生成高质量的有限元网格。可以用于流体力学」· C语言 代码 · 共 1,310 行 · 第 1/3 页

#include "medit.h"
#include "extern.h"
#include "sproto.h"


static int ct[4][3] = { {0,1,2}, {0,3,1}, {1,3,2}, {0,2,3} };
static int ch[6][4] = { {0,1,2,3}, {4,5,6,7}, {0,1,5,4}, 
            {1,2,6,5}, {2,3,7,6}, {0,3,7,4} };


/* recursively subdivide a triangle */
void cutTriangle(pScene sc,triangle t) {
  triangle      t1,t2;
  double        kc,x,dd,rgb[4],maxe;
  int           i,ia,ib,ic,iedge;
  static double hsv[3] = { 0.0f, 1.0f, 0.80f };

  /* analyze triangle edges */
  if ( t.va < sc->iso.val[0] )  
    t.va = sc->iso.val[0];
  else if ( t.va > sc->iso.val[MAXISO-1] )
    t.va = sc->iso.val[MAXISO-1];
  if ( t.vb < sc->iso.val[0] )  
    t.vb = sc->iso.val[0];
  else if ( t.vb > sc->iso.val[MAXISO-1] )
    t.vb = sc->iso.val[MAXISO-1];
  if ( t.vc < sc->iso.val[0] )  
    t.vc = sc->iso.val[0];
  else if ( t.vc > sc->iso.val[MAXISO-1] )
    t.vc = sc->iso.val[MAXISO-1];

  for (ia=0; ia<MAXISO-1; ia++)
    if ( t.va < sc->iso.val[ia] )  break;

  for (ib=0; ib<MAXISO-1; ib++)
    if ( t.vb < sc->iso.val[ib] )  break;

  for (ic=0; ic<MAXISO-1; ic++)
    if ( t.vc < sc->iso.val[ic] )  break;

  /* search longest edge */
  maxe  = fabs(t.va-t.vb);
  iedge = 1;
  if ( maxe < fabs(t.vb-t.vc) ) {
    maxe  = fabs(t.vb-t.vc);
    iedge = 2;
  }
  if ( maxe < fabs(t.va-t.vc) ) {
    maxe = fabs(t.va-t.vc);
    iedge = 3;
  }

  /* split longest edge */
  if ( maxe > 0.0 ) {
    switch( iedge ) {
    case 1:  /* edge a-b */
      x  = ia < ib ? sc->iso.val[ia] : sc->iso.val[ib];
      dd = (x-t.va) / (t.vb-t.va);
      if ( dd > 0.001 && dd < 0.999 ) {
        memcpy(&t1,&t,sizeof(struct triangle));
        memcpy(&t2,&t,sizeof(struct triangle));
        for (i=0; i<3; i++) {
          t1.b[i]  = t2.a[i]  = t.a[i]  + dd*(t.b[i] -t.a[i]);
          t1.nb[i] = t2.na[i] = t.na[i] + dd*(t.nb[i]-t.na[i]);
        }
        t1.vb = t2.va = x;
        cutTriangle(sc,t1);
        cutTriangle(sc,t2);
        return;
      }
      break;

    case 2:  /* edge b-c */
      x  = ib < ic ? sc->iso.val[ib] : sc->iso.val[ic];
      dd = (x-t.vb) / (t.vc-t.vb);
      if ( dd > 0.001f && dd < 0.999f ) {
        memcpy(&t1,&t,sizeof(struct triangle));
        memcpy(&t2,&t,sizeof(struct triangle));
        for (i=0; i<3; i++) {
          t1.c[i]  = t2.b[i]  = t.b[i]  + dd*(t.c[i] -t.b[i]);
          t1.nc[i] = t2.nb[i] = t.nb[i] + dd*(t.nc[i]-t.nb[i]);
        }
        t1.vc = t2.vb = x;
        cutTriangle(sc,t1);
        cutTriangle(sc,t2);
        return;
      }
      break;
    case 3:  /* edge c-a */
      x  = ia < ic ? sc->iso.val[ia] : sc->iso.val[ic];
      dd = (x-t.va) / (t.vc-t.va);
      if ( dd > 0.001f && dd < 0.999f ) {
        memcpy(&t1,&t,sizeof(struct triangle));
        memcpy(&t2,&t,sizeof(struct triangle));
        for (i=0; i<3; i++) {
          t1.c[i]  = t2.a[i]  = t.a[i]  + dd*(t.c[i] -t.a[i]);
          t1.nc[i] = t2.na[i] = t.na[i] + dd*(t.nc[i]-t.na[i]);
        }
        t1.vc = t2.va = x;
        cutTriangle(sc,t1);
        cutTriangle(sc,t2);
        return;
      }
      break;
    }
  }

  /* draw triangle */
  if ( t.va < sc->iso.val[0] ) 
    t.va = sc->iso.val[0];  
  else if ( t.va > sc->iso.val[MAXISO-1] )
    t.va = sc->iso.val[MAXISO-1];
  kc = (t.va-sc->iso.val[ia-1]) / (sc->iso.val[ia] - sc->iso.val[ia-1]);
  hsv[0] = sc->iso.col[ia-1]*(1.0-kc)+sc->iso.col[ia]*kc;
  hsvrgb(hsv,rgb);

  glColor4dv(rgb);
  glNormal3fv(t.na);
  glVertex3fv(t.a);

  if ( t.vb < sc->iso.val[0] ) 
    t.vb = sc->iso.val[0];
  else if ( t.vb > sc->iso.val[MAXISO-1] )
    t.vb = sc->iso.val[MAXISO-1];
  kc = (t.vb-sc->iso.val[ib-1]) / (sc->iso.val[ib] - sc->iso.val[ib-1]);
  hsv[0] = sc->iso.col[ib-1]*(1.0-kc)+sc->iso.col[ib]*kc;
  hsvrgb(hsv,rgb);

  glColor4dv(rgb);
  glNormal3fv(t.nb);
  glVertex3fv(t.b);

  if ( t.vc < sc->iso.val[0] ) 
    t.vc = sc->iso.val[0];
  else if ( t.vc > sc->iso.val[MAXISO-1] )
    t.vc = sc->iso.val[MAXISO-1];
  kc = (t.vc-sc->iso.val[ic-1]) / (sc->iso.val[ic] - sc->iso.val[ic-1]);
  hsv[0] = sc->iso.col[ic-1]*(1.0-kc)+sc->iso.col[ic]*kc;
  hsvrgb(hsv,rgb);

  glColor4dv(rgb);
  glNormal3fv(t.nc);
  glVertex3fv(t.c);
}


/* metric map: use linear interpolation on values
   rather than color interpolation ! */
GLuint listTriaMap(pScene sc,pMesh mesh) {
  pMaterial  pm;
  pTriangle  pt;
  pPoint     p0,p1,p2;
  pSolution  ps0,ps1,ps2;
  GLint      dlist;
  double     ax,ay,az,bx,by,bz,dd;
  float      cx,cy,cz,n[3];
  int        k,m,is0,is1,is2;
  triangle   t;

  /* default */
  if ( !mesh->nt )  return(0);
  if ( egal(sc->iso.val[0],sc->iso.val[MAXISO-1]) )  return(0);
  if ( ddebug ) printf("create display list map / TRIA\n");

  /* build display list */
  dlist = glGenLists(1);
  glNewList(dlist,GL_COMPILE);
  if ( glGetError() )  return(0);

  /* build list */
  for (m=0; m<sc->par.nbmat; m++) {
    pm = &sc->material[m];
    k  = pm->depmat[LTria];
    if ( !k || pm->flag )  continue;

    if ( sc->type & S_FLAT ) {
      glBegin(GL_TRIANGLES);
      while ( k != 0 ) {
        pt = &mesh->tria[k];
        if ( !pt->v[0] ) {
          k = pt->nxt;
          continue;
        }
        p0 = &mesh->point[pt->v[0]];
        p1 = &mesh->point[pt->v[1]];
        p2 = &mesh->point[pt->v[2]];
  
        /* compute normal */
        ax = p1->c[0] - p0->c[0];
        ay = p1->c[1] - p0->c[1];
        az = p1->c[2] - p0->c[2];
        bx = p2->c[0] - p0->c[0];
        by = p2->c[1] - p0->c[1];
        bz = p2->c[2] - p0->c[2];
        n[0] = ay*bz - az*by;
        n[1] = az*bx - ax*bz;
        n[2] = ax*by - ay*bx;
        dd = n[0]*n[0] + n[1]*n[1] + n[2]*n[2];
        if ( dd > 0.0f ) {
          dd = 1.0f / sqrt(dd);
          n[0] *= dd;
          n[1] *= dd;
          n[2] *= dd;
        }
        memcpy(t.na,n,3*sizeof(float));
        memcpy(t.nb,n,3*sizeof(float));
        memcpy(t.nc,n,3*sizeof(float));

        if ( sc->shrink < 1.0 ) {
          cx = (p0->c[0] + p1->c[0] + p2->c[0]) / 3.0;
          cy = (p0->c[1] + p1->c[1] + p2->c[1]) / 3.0;
          cz = (p0->c[2] + p1->c[2] + p2->c[2]) / 3.0;
          t.a[0] = sc->shrink*(p0->c[0]-cx)+cx;
          t.a[1] = sc->shrink*(p0->c[1]-cy)+cy;
          t.a[2] = sc->shrink*(p0->c[2]-cz)+cz;
          t.b[0] = sc->shrink*(p1->c[0]-cx)+cx;
          t.b[1] = sc->shrink*(p1->c[1]-cy)+cy;
          t.b[2] = sc->shrink*(p1->c[2]-cz)+cz;
          t.c[0] = sc->shrink*(p2->c[0]-cx)+cx;
          t.c[1] = sc->shrink*(p2->c[1]-cy)+cy;
          t.c[2] = sc->shrink*(p2->c[2]-cz)+cz;
        }
        else {
          t.a[0] = p0->c[0];
          t.a[1] = p0->c[1];
          t.a[2] = p0->c[2];
          t.b[0] = p1->c[0];
          t.b[1] = p1->c[1];
          t.b[2] = p1->c[2];
          t.c[0] = p2->c[0];
          t.c[1] = p2->c[1];
          t.c[2] = p2->c[2];
        }
        if ( mesh->typage == 2 ) {
          ps0  = &mesh->sol[pt->v[0]];
          ps1  = &mesh->sol[pt->v[1]];
          ps2  = &mesh->sol[pt->v[2]];
          t.va = ps0->bb;
          t.vb = ps1->bb;
          t.vc = ps2->bb;
        }
        else {
          ps0 = &mesh->sol[k];
          t.va = t.vb = t.vc = ps0->bb;
        }
        cutTriangle(sc,t);
        k = pt->nxt;
      }
      glEnd();
    }
    else {
      glBegin(GL_TRIANGLES);
      while ( k != 0 ) {
        pt = &mesh->tria[k];
        if ( !pt->v[0] ) {
          k = pt->nxt;
          continue;
        }
        p0 = &mesh->point[pt->v[0]];
        p1 = &mesh->point[pt->v[1]];
        p2 = &mesh->point[pt->v[2]];

        /* compute normal */
        ax = p1->c[0] - p0->c[0];
        ay = p1->c[1] - p0->c[1];
        az = p1->c[2] - p0->c[2];
        bx = p2->c[0] - p0->c[0];
        by = p2->c[1] - p0->c[1];
        bz = p2->c[2] - p0->c[2];
        n[0] = ay*bz - az*by;
        n[1] = az*bx - ax*bz;
        n[2] = ax*by - ay*bx;
        dd = n[0]*n[0] + n[1]*n[1] + n[2]*n[2];
        if ( dd > 0.0f ) {
      dd = 1.0f / sqrt(dd);
      n[0] *= dd;
      n[1] *= dd;
      n[2] *= dd;
        }

        is0 = is1 = is2 = 0;
        if ( mesh->extra->iv ) {
          if ( pt->v[0] <= mesh->nvn )
            is0 = mesh->extra->nv[pt->v[0]];
          if ( pt->v[1] <= mesh->nvn )
            is1 = mesh->extra->nv[pt->v[1]];
          if ( pt->v[2] <= mesh->nvn )
            is2 = mesh->extra->nv[pt->v[2]];
        }
        if ( !is0 && pt->v[0] <= mesh->extra->it )
          is0 = mesh->extra->nt[3*(k-1)+1];
        if ( !is1 && pt->v[1] <= mesh->extra->it )  
          is1 = mesh->extra->nt[3*(k-1)+2];
        if ( !is2 && pt->v[2] <= mesh->extra->it )
          is2 = mesh->extra->nt[3*(k-1)+3];

        if ( sc->shrink < 1.0 ) {
          cx = (p0->c[0] + p1->c[0] + p2->c[0]) / 3.;
          cy = (p0->c[1] + p1->c[1] + p2->c[1]) / 3.;
          cz = (p0->c[2] + p1->c[2] + p2->c[2]) / 3.;
          t.a[0] = sc->shrink*(p0->c[0]-cx)+cx;
          t.a[1] = sc->shrink*(p0->c[1]-cy)+cy;
          t.a[2] = sc->shrink*(p0->c[2]-cz)+cz;
          t.b[0] = sc->shrink*(p1->c[0]-cx)+cx;
          t.b[1] = sc->shrink*(p1->c[1]-cy)+cy;
          t.b[2] = sc->shrink*(p1->c[2]-cz)+cz;
          t.c[0] = sc->shrink*(p2->c[0]-cx)+cx;
          t.c[1] = sc->shrink*(p2->c[1]-cy)+cy;
          t.c[2] = sc->shrink*(p2->c[2]-cz)+cz;
        }
        else {
          t.a[0] = p0->c[0];
          t.a[1] = p0->c[1];
          t.a[2] = p0->c[2];
          t.b[0] = p1->c[0];
          t.b[1] = p1->c[1];
          t.b[2] = p1->c[2];
          t.c[0] = p2->c[0];
          t.c[1] = p2->c[1];
          t.c[2] = p2->c[2];
        }
        if ( !is0 )
          memcpy(t.na,n,3*sizeof(float));
        else {
          t.na[0] = mesh->extra->n[3*(is0-1)+1];
          t.na[1] = mesh->extra->n[3*(is0-1)+2];
          t.na[2] = mesh->extra->n[3*(is0-1)+3];
        }
        if ( !is1 )
          memcpy(t.nb,n,3*sizeof(float));
        else {
          t.nb[0] = mesh->extra->n[3*(is1-1)+1];
          t.nb[1] = mesh->extra->n[3*(is1-1)+2];
          t.nb[2] = mesh->extra->n[3*(is1-1)+3];
        }
        if ( !is2 )
          memcpy(t.nc,n,3*sizeof(float));
        else {
          t.nc[0] = mesh->extra->n[3*(is2-1)+1];
          t.nc[1] = mesh->extra->n[3*(is2-1)+2];
          t.nc[2] = mesh->extra->n[3*(is2-1)+3];
        }
        if ( mesh->typage == 2 ) {
      ps0  = &mesh->sol[pt->v[0]];
      ps1  = &mesh->sol[pt->v[1]];
      ps2  = &mesh->sol[pt->v[2]];
      t.va = ps0->bb;
      t.vb = ps1->bb;
      t.vc = ps2->bb;
        }
        else {
      ps0 = &mesh->sol[k];
      t.va = t.vb = t.vc = ps0->bb;
        }
        cutTriangle(sc,t);
        k = pt->nxt;
      }
      glEnd();
    }
  }

  glEndList();
  return(dlist);
}


/* build list of quadrilaterals */
GLuint listQuadMap(pScene sc,pMesh mesh) {
  pMaterial  pm;
  pQuad      pq;
  pPoint     p0,p1,p2,p3;
  pSolution  ps0,ps1,ps2,ps3;
  GLint      dlist = 0;
  double     ax,ay,az,bx,by,bz,dd;
  float      cx,cy,cz,n[3];
  int        k,m,is0,is1,is2,is3;
  triangle   t1,t2;

  /* default */
  if ( !mesh->nq ) return(0);
  if ( egal(sc->iso.val[0],sc->iso.val[MAXISO-1]) )  return(0);
  if ( ddebug ) printf("create display list map / QUADS\n");

  /* build display list */
  dlist = glGenLists(1);
  glNewList(dlist,GL_COMPILE);
  if ( glGetError() )  return(0);

  /* build list */
  for (m=0; m<sc->par.nbmat; m++) {
    pm = &sc->material[m];
    k  = pm->depmat[LQuad];
    if ( !k || pm->flag )  continue;

    glBegin(GL_TRIANGLES);
    while ( k != 0 ) {
      pq = &mesh->quad[k];
      if ( pq->v[0] == 0 ) {
        k = pq->nxt;
        continue;
      }
      p0 = &mesh->point[pq->v[0]];
      p1 = &mesh->point[pq->v[1]];
      p2 = &mesh->point[pq->v[2]];
      p3 = &mesh->point[pq->v[3]];
      
      /* compute normal */
      ax = p1->c[0] - p0->c[0];
      ay = p1->c[1] - p0->c[1];
      az = p1->c[2] - p0->c[2];
      bx = p2->c[0] - p0->c[0];
      by = p2->c[1] - p0->c[1];
      bz = p2->c[2] - p0->c[2];
      n[0] = ay*bz - az*by;
      n[1] = az*bx - ax*bz;
      n[2] = ax*by - ay*bx;
      dd = n[0]*n[0] + n[1]*n[1] + n[2]*n[2];
      if ( dd > 0.0f ) {
        dd = 1.0f / sqrt(dd);
        n[0] *= dd;
        n[1] *= dd;
        n[2] *= dd;
      }

      if ( sc->shrink < 1.0 ) {
        cx = 0.25 * (p0->c[0] + p1->c[0] + p2->c[0] + p3->c[0]);
        cy = 0.25 * (p0->c[1] + p1->c[1] + p2->c[1] + p3->c[1]);
        cz = 0.25 * (p0->c[2] + p1->c[2] + p2->c[2] + p3->c[2]);
        t1.a[0] = t2.a[0] = sc->shrink*(p0->c[0]-cx)+cx;
        t1.a[1] = t2.a[1] = sc->shrink*(p0->c[1]-cy)+cy;
        t1.a[2] = t2.a[2] = sc->shrink*(p0->c[2]-cz)+cz;

        t1.b[0] = sc->shrink*(p1->c[0]-cx)+cx;
        t1.b[1] = sc->shrink*(p1->c[1]-cy)+cy;
        t1.b[2] = sc->shrink*(p1->c[2]-cz)+cz;

        t1.c[0] = t2.b[0] = sc->shrink*(p2->c[0]-cx)+cx;