CoCalc -- refine_polyeder.c

GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
gap4r8 / pkg / carat / carat-2.1b1 / functions / Polyeder / refine_polyeder.c
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#include"typedef.h"
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#include"matrix.h"
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#include"longtools.h"
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#include"polyeder.h"
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/**************************************************************************\
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@---------------------------------------------------------------------------
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@---------------------------------------------------------------------------
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@ FILE: refine_polyeder.c
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@---------------------------------------------------------------------------
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@---------------------------------------------------------------------------
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@
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\**************************************************************************/
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static int g_option;
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static void re_sort(F,old_no, count, test, l)
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polyeder_TYP *F;
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int old_no, *test, l;
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int *count;
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{
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  int i;
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  int d=0;
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  for(i=0;i<old_no;i++)
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  {
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    if(count[i]< 0)
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      free_vertex(&(F->vert[i]));
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  }
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  for(i=0;d<F->vert_no;i++)
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  {
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    while(d<F->vert_no && F->vert[d] == NULL)
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      d++;
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    if(d != i)
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    {
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      F->vert[i] = F->vert[d];
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      F->vert[d] = NULL;
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    }
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    d++;
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  }
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  while(F->vert[i-1] == NULL)
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    i--;
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  F->vert_no = i;
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  d=0;
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  for(i=0;i<F->wall_no;i++)
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  {
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    if(test[i] == -1)
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      free_wall(&(F->wall[i]));
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  }
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  for(i=0;d<F->wall_no;i++)
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  {
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    while(d<F->wall_no && F->wall[d] == NULL)
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      d++;
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    if(d!= i)
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    {
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      F->wall[i] = F->wall[d];
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      F->wall[d] = NULL;
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    }
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    d++;
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  }
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  F->wall_no = i;
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}
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static void renumerate(v,test)
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vertex_TYP *v;
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int *test;
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{
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  int i,a;
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  for(i=0;i<v->wall_no;i++)
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  {
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     a = v->wall[i];
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     v->wall[i] = test[a];
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  }
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}
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static void add_wall_to_vertex(i, v)
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int i;
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vertex_TYP *v;
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{
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  if(v->wall_SIZE == 0)
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  {
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    v->wall = (int *)malloc(extsize1 *sizeof(int));
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    v->wall_SIZE = extsize1;
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  }
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  if(v->wall_no == v->wall_SIZE)
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  {
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    v->wall_SIZE += extsize1;
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    v->wall = (int *)realloc(v->wall,v->wall_SIZE *sizeof(int));
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  }
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  v->wall[v->wall_no] = i;
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  v->wall_no++;
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}
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static void delete_walls_from_vertex(v, test)
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vertex_TYP *v;
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int *test;
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{
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 int i,d;
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 d=0;
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 for(i=0; d<v->wall_no;i++)
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 {
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   while(d< v->wall_no && test[v->wall[d]] == -1)
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     d++;
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   v->wall[i] = v->wall[d];
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   d++;
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 }
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 v->wall_no = i;
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}
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static void add_wall_to_polyeder(F, w)
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polyeder_TYP *F;
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wall_TYP *w;
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{
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  if(F->wall_SIZE == 0)
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  {
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    F->wall = (wall_TYP **)malloc(extsize1 *sizeof(wall_TYP *));
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    F->wall_SIZE = extsize1;
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  }
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  if(F->wall_no == F->wall_SIZE)
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  {
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    F->wall_SIZE += extsize1;
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    F->wall = (wall_TYP **)realloc(F->wall,F->wall_SIZE *sizeof(wall_TYP *));
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  }
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  F->wall[F->wall_no] = copy_wall(w);
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  F->wall_no++;
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}
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static void add_vertex_to_polyeder(F, w)
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polyeder_TYP *F;
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vertex_TYP *w;
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{
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  if(F->vert_SIZE == 0)
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  {
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    F->vert = (vertex_TYP **)malloc(extsize1 *sizeof(vertex_TYP *));
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    F->vert_SIZE = extsize1;
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  }
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  if(F->vert_no == F->vert_SIZE)
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  {
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    F->vert_SIZE += extsize1;
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    F->vert = (vertex_TYP **)realloc(F->vert,F->vert_SIZE *sizeof(vertex_TYP *));
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  }
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  F->vert[F->vert_no] = w;
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  F->vert_no++;
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}
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static vertex_TYP *gis_neighbour(i,j,F)
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int i,j;
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polyeder_TYP *F;
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{
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  int k,l,m;
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  int a, u, tester1;
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  int anz;
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  vertex_TYP *erg;
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  matrix_TYP *A;
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  k=F->vert[j]->wall_no;
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  if(k>F->vert[i]->wall_no)
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    k=F->vert[i]->wall_no;
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  erg = init_vertex(F->vert[0]->dim, k+1);
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  anz=0;
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  u=0;
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  for(k=0;k<F->vert[i]->wall_no;k++)
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  {
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    a = F->vert[i]->wall[k];
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    for(l=u; l<F->vert[j]->wall_no && F->vert[j]->wall[l]< a; l++);
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    u=l;
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    if(u<F->vert[j]->wall_no && F->vert[j]->wall[u] == a)
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       { erg->wall[anz] = a; anz++;}
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  }
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  erg->wall_no = anz;
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  if(anz < F->vert[0]->dim-2)
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   { free_vertex(&erg); erg=NULL; return(NULL);}
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  A = init_mat(anz,F->vert[0]->dim, "l");
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  for(k=0;k<anz;k++)
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    for(l=0; l<F->vert[0]->dim;l++)
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      A->array.SZ[k][l] = F->wall[erg->wall[k]]->gl[l];
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  a = long_row_gauss(A);
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  free_mat(A);
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  if(a < F->vert[0]->dim-2)
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   { free_vertex(&erg); erg=NULL; return(NULL);}
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  return(erg);
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}
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static vertex_TYP *is_neighbour(i,j,F, vertex_no)
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int i,j;
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polyeder_TYP *F;
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int vertex_no;
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{
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  int k,l,m;
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  int a, u, tester1;
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  int anz;
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  vertex_TYP *erg;
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  k=F->vert[j]->wall_no;
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  if(k>F->vert[i]->wall_no)
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    k=F->vert[i]->wall_no;
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  erg = init_vertex(F->vert[0]->dim, k+1);
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  anz=0;
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  u=0;
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  for(k=0;k<F->vert[i]->wall_no;k++)
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  {
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    a = F->vert[i]->wall[k];
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    for(l=u; l<F->vert[j]->wall_no && F->vert[j]->wall[l]< a; l++);
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    u=l;
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    if(u<F->vert[j]->wall_no && F->vert[j]->wall[u] == a)
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       { erg->wall[anz] = a; anz++;}
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  }
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  erg->wall_no = anz;
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  if(anz < F->vert[0]->dim-2)
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   { free_vertex(&erg); erg=NULL; return(NULL);}
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  for(k=0; k<vertex_no ;k++)
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  {
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   if(k != i && k != j)
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   {
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     tester1 = TRUE;
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        u=0;
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     for(l=0; l<anz && tester1 == TRUE; l++)
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     {
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        a = erg->wall[l];
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        m=u;
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        while(m<F->vert[k]->wall_no && F->vert[k]->wall[m] <a)
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           m++;
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        if(m == F->vert[k]->wall_no || F->vert[k]->wall[m] != a)
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           tester1 = FALSE;
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        u=m;
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     }
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     if(tester1 == TRUE)
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       { free_vertex(&erg); erg=NULL; return(NULL);}
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   }
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  }
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  return(erg);
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}
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/**************************************************************************\
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@---------------------------------------------------------------------------
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@ int refine_polyeder(F, h)
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@ polyeder_TYP *F;
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@ wall_TYP *h;
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@ 
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@  calculates the intersection of the linear Polyeder 'F' with the halfspace
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@  defined by the inequality
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@              H :=  h->gl * X^{tr} >= 0
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@  and stores it in F.
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@  If the intersection of F and H is already F, 'refine_polyeder returns 0,
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@  otherwise 1.
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@  All vertices of the intersecting polyeder are calculated.
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@  If the intersection has not full dimension, i.e the new Polyeder is
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@  non-degenerate, F->is_denerate is set to 0.
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@
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@  CAUTION: The result is correct only if the new Polyeder is non-degenerate.
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@
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@---------------------------------------------------------------------------
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@
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\**************************************************************************/
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int refine_polyeder(F, h)
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polyeder_TYP *F;
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wall_TYP *h;
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{
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 int i,j,k;
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 int l;
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 int old_no;
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 int *count;
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 int waste;
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 int tester, *test;
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 int anz;
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 int p,n, z;
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 vertex_TYP *v;
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 int *wall_test, *necessary;
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 p=0;n=0;
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 old_no = F->vert_no;
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 count = (int *)malloc(F->vert_no *sizeof(int *));
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 for(i=0;i<F->vert_no;i++)
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  count[i] = 0;
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 for(i=0;i<old_no;i++)
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 {
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     count[i] = wall_times_vertex(h,F->vert[i]);
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    if(count[i] > 0)
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      p++;
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    if(count[i] < 0)
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      n++;
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    if(count[i] == 0)
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      z++;
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 }
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 if(n == 0)
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 {
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   free(count);
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   return(0);
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 }
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 if(p == 0)
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 {
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   F->is_degenerate = TRUE;
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 }
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 g_option = FALSE;
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 if(is_option('g') == TRUE)
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    g_option = TRUE;
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 wall_test = (int *)malloc(F->wall_no *sizeof(int));
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 for(i=0;i<F->wall_no;i++)
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     wall_test[i] = 2;
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 for(i=0;i<old_no;i++)
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 {
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   if(count[i]>0)
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   {
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      for(j=0;j<F->vert[i]->wall_no;j++)
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      {
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        if(wall_test[F->vert[i]->wall[j]] == 2)
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          wall_test[F->vert[i]->wall[j]] = 1;
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        if(wall_test[F->vert[i]->wall[j]] == -1)
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          wall_test[F->vert[i]->wall[j]] = 0;
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      }
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   }
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   if(count[i] < 0)
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   {
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      for(j=0;j<F->vert[i]->wall_no;j++)
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      {
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        if(wall_test[F->vert[i]->wall[j]] == 2)
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          wall_test[F->vert[i]->wall[j]] = -1;
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        if(wall_test[F->vert[i]->wall[j]] == 1)
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          wall_test[F->vert[i]->wall[j]] = 0;
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      }
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   }
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 }
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 necessary = (int *)malloc(F->vert_no *sizeof(int));
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 for(i=0;i<old_no;i++)
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   necessary[i] = FALSE;
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 for(i=0;i<old_no;i++)
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 {
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  if(count[i] != 0)
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  {
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   k=0;
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   for(j=0;j<F->vert[i]->wall_no && necessary[i] == FALSE;j++)
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   {
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     if( wall_test[F->vert[i]->wall[j]] == 0)
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       k++;
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     if(k>= F->vert[i]->dim-2)
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     {
359
       if(count[i] > 0)
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         necessary[i] = 1;
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       if(count[i] < 0)
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         necessary[i] = -1;
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       if(count[i] == 0)
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         necessary[i] = 0;
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     }
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   }
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  }
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 }
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370
 if(F->vert[0]->dim == 2)
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 {
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   for(i=0;i<old_no;i++)
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   {
374
     if(count[i] > 0)
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       necessary[i] = 1;
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     if(count[i] < 0)
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       necessary[i] = -1;
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     if(count[i] == 0)
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       necessary[i] = 0;
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   }
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 }
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383

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 for(i=0;i<old_no;i++)
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 {
386
  if(necessary[i] == -1)
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  {  
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    for(j=0;j<old_no;j++)
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    {
390
     if(necessary[j] == 1)
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     {
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        if(g_option == TRUE)
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          v = gis_neighbour(i, j, F);
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        else
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          v = is_neighbour(i, j, F, old_no);
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        if(v != NULL)
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        {
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          for(k=0; k<v->dim; k++)
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            v->v[k] = count[j] * F->vert[i]->v[k] - count[i] *F->vert[j]->v[k];
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          normal_vertex(v);
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          add_vertex_to_polyeder(F, v);
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        }
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     }
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    }
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  }
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 }
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  add_wall_to_polyeder(F, h);
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  test = (int *)malloc((F->wall_no) *sizeof(int));
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  l=0;
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  for(i=0; i<F->wall_no-1;i++)
411
  {
412
    tester = 0;
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    for(j=0;j<old_no && tester == 0; j++)
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    {
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     if(count[j] > 0)
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       if(is_vertex_of_wallno(F->vert[j], i) == TRUE)
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          tester = 1;
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    }
419
    if(tester == 0)
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     test[i] = -1;
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    else
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     {test[i] = l; l++;}
423
  }
424
  test[F->wall_no-1] = l;
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  l++;
426
  if(test[0] == -1)
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    F->is_closed = TRUE;
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  for(i=0;i<old_no; i++)
430
  {
431
    if(count[i] == 0)
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      add_wall_to_vertex(F->wall_no-1, F->vert[i]);
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  }
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  for(i=0;i<old_no;i++)
436
  {
437
     if(count[i]==0)
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       delete_walls_from_vertex(F->vert[i],test);
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     if(count[i]>=0)
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       renumerate(F->vert[i],test);
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  }
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  for(i=old_no; i<F->vert_no;i++)
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  {
444
     F->vert[i]->wall[F->vert[i]->wall_no] = F->wall_no-1;
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     F->vert[i]->wall_no++;
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     renumerate(F->vert[i],test);
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  }
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449
  re_sort(F, old_no, count, test,l);
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   free(count);
452
   free(test);
453
   free(necessary);
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   free(wall_test);
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  return(1);
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}
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