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sqrt3_subdiv.c
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#include"utils.h"
/*#include<stdlib.h>
#include<math.h>
#include<stdio.h>
#include<cblas.h>*/
#include"matrix_ops.h"
#define PI 3.141592653589793
void sqrt3_subdiv(int *tlist,double *vlist,int nfac,int nvert,int **tlistn2,double **vlistn2,int *nfacn2,int *nvertn2,double **D2)
{
/*Subdivide polyhedron given by facet list tlist and vertex list vlist using the Sqrt3 subdivision.
* MEMORY IS ALLOCATED HERE */
/*Number of vertices in subdivided triangle:
* We know that nvert=2+1/2*nfac*/
int nfacn=3*nfac;
int nvertn=2+nfacn/2;
int * tlistn=calloc(3*nfacn,sizeof(int));
double * vlistn=calloc(3*nvertn,sizeof(double));
double *D=calloc(nvertn*nvert,sizeof(double));
//print_matrixI(tlistn,nfacn,3);
/*Generate adjacency matrix: Facets with common edge (i1,i2) are A(i1,i2) and A(i2,i1);*/
/*Note that facet numbering in A starts from 1*/
int *A=calloc(nvert*nvert,sizeof(int));
int *vMo=calloc(nvert*nvert,sizeof(int));
int i0,i1,i2;
double v0x,v0y,v0z;
double v1x,v1y,v1z;
double v2x,v2y,v2z;
double cx,cy,cz;
int *centindex=calloc(nfac,sizeof(int));
for(int j=0;j<nfac;j++)
{
i0=get_elI(tlist,nfac,3,j,0)-1;
i1=get_elI(tlist,nfac,3,j,1)-1;
i2=get_elI(tlist,nfac,3,j,2)-1;
set_elI(vMo,nvert,nvert,1,i0,i1);
set_elI(vMo,nvert,nvert,1,i0,i2);
set_elI(vMo,nvert,nvert,1,i1,i0);
set_elI(vMo,nvert,nvert,1,i1,i2);
set_elI(vMo,nvert,nvert,1,i2,i0);
set_elI(vMo,nvert,nvert,1,i2,i1);
set_elI(A,nvert,nvert,j+1,i0,i1);
set_elI(A,nvert,nvert,j+1,i1,i2);
set_elI(A,nvert,nvert,j+1,i2,i0);
}
/* Update old vertices*/
int nbv=0;
double bn1=0,bn2x,bn2y,bn2z;
int *V;
int vindex=0;
int count=0;
for(int j=0;j<nvert;j++)
{
nbv=ind2vec(vMo,nvert,&V,j);
bn1=1.0/(9.0*nbv)*(4.0-2.0*cos(2.0*PI/nbv));
bn2x=(1.0-nbv*bn1)*get_el(vlist,nvert,3,j,0)+bn1*sum_matelC(vlist,nvert,3,V,nbv,0);
bn2y=(1.0-nbv*bn1)*get_el(vlist,nvert,3,j,1)+bn1*sum_matelC(vlist,nvert,3,V,nbv,1);
bn2z=(1.0-nbv*bn1)*get_el(vlist,nvert,3,j,2)+bn1*sum_matelC(vlist,nvert,3,V,nbv,2);
set_el(vlistn,nvertn,3,bn2x,j,0);
set_el(vlistn,nvertn,3,bn2y,j,1);
set_el(vlistn,nvertn,3,bn2z,j,2);
set_el(D,nvertn,nvert,1.0-nbv*bn1,j,j);
for(int k=0;k<nbv;k++)
set_el(D,nvertn,nvert,bn1,j,V[k]);
free(V);
}
/* Add new vertices and triangles, minus one triangle*/
for(int j=0;j<nfac;j++)
{
i0=get_elI(tlist,nfac,3,j,0)-1;
i1=get_elI(tlist,nfac,3,j,1)-1;
i2=get_elI(tlist,nfac,3,j,2)-1;
v0x=get_el(vlist,nvert,3,i0,0);
v0y=get_el(vlist,nvert,3,i0,1);
v0z=get_el(vlist,nvert,3,i0,2);
v1x=get_el(vlist,nvert,3,i1,0);
v1y=get_el(vlist,nvert,3,i1,1);
v1z=get_el(vlist,nvert,3,i1,2);
v2x=get_el(vlist,nvert,3,i2,0);
v2y=get_el(vlist,nvert,3,i2,1);
v2z=get_el(vlist,nvert,3,i2,2);
cx=(v0x+v1x+v2x)/3.0;
cy=(v0y+v1y+v2y)/3.0;
cz=(v0z+v1z+v2z)/3.0;
vindex=count+nvert;
count++;
set_el(vlistn,nvertn,3,cx,vindex,0);
set_el(vlistn,nvertn,3,cy,vindex,1);
set_el(vlistn,nvertn,3,cz,vindex,2);
set_elI(centindex,1,nfac,vindex,0,j);
set_el(D,nvertn,nvert,1.0/3.0, vindex,i0);
set_el(D,nvertn,nvert,1.0/3.0, vindex,i1);
set_el(D,nvertn,nvert,1.0/3.0, vindex,i2);
}
/*Now we flip the edge between facets*/
int tcount=0;
int nf1,nf2,nf3;
for(int j=0;j<nfac;j++)
{
i0=get_elI(tlist,nfac,3,j,0)-1;
i1=get_elI(tlist,nfac,3,j,1)-1;
i2=get_elI(tlist,nfac,3,j,2)-1;
/*Take the neighbor facets*/
nf1=get_elI(A,nvert,nvert,i1,i0);
nf2=get_elI(A,nvert,nvert,i2,i1);
nf3=get_elI(A,nvert,nvert,i0,i2);
if(nf1>0)
{
/*tlistn(tcount,:)=[centindex(j) i1 centindex(nf1)];*/
// printf("nf1: %d %d %d %d\n",nf1,centindex[j]+1,i0+1,centindex[nf1-1]+1);
set_elI(tlistn,nfacn,3,centindex[j]+1,tcount,0); /*centindex+1 or not? CHECK THIS!*/
set_elI(tlistn,nfacn,3,i0+1,tcount,1);
set_elI(tlistn,nfacn,3,centindex[nf1-1]+1,tcount,2);
tcount++;
set_elI(tlistn,nfacn,3,centindex[nf1-1]+1,tcount,0);
set_elI(tlistn,nfacn,3,i1+1,tcount,1);
set_elI(tlistn,nfacn,3,centindex[j]+1,tcount,2);
tcount++;
set_elI(A,nvert,nvert,0,i1,i0);
set_elI(A,nvert,nvert,0,i0,i1);
}
if(nf2>0)
{
set_elI(tlistn,nfacn,3,centindex[j]+1,tcount,0); /*centindex+1 or not? CHECK THIS!*/
set_elI(tlistn,nfacn,3,i1+1,tcount,1);
set_elI(tlistn,nfacn,3,centindex[nf2-1]+1,tcount,2);
tcount++;
set_elI(tlistn,nfacn,3,centindex[nf2-1]+1,tcount,0); /*centindex+1 or not? CHECK THIS!*/
set_elI(tlistn,nfacn,3,i2+1,tcount,1);
set_elI(tlistn,nfacn,3,centindex[j]+1,tcount,2);
tcount++;
set_elI(A,nvert,nvert,0,i2,i1);
set_elI(A,nvert,nvert,0,i1,i2);
}
if(nf3>0)
{
set_elI(tlistn,nfacn,3,centindex[j]+1,tcount,0); /*centindex+1 or not? CHECK THIS!*/
set_elI(tlistn,nfacn,3,i2+1,tcount,1);
set_elI(tlistn,nfacn,3,centindex[nf3-1]+1,tcount,2);
tcount++;
set_elI(tlistn,nfacn,3,centindex[nf3-1]+1,tcount,0); /*centindex+1 or not? CHECK THIS!*/
set_elI(tlistn,nfacn,3,i0+1,tcount,1);
set_elI(tlistn,nfacn,3,centindex[j]+1,tcount,2);
tcount++;
set_elI(A,nvert,nvert,0,i2,i0);
set_elI(A,nvert,nvert,0,i0,i2);
}
}
*vlistn2=vlistn;
*tlistn2=tlistn;
*nfacn2=nfacn;
*nvertn2=nvertn;
*D2=D;
free(A);
free(vMo);
free(centindex);
}
void map_sqrt_subdiv_limit(int *tlist,double *vlist,int nfac,int nvert,double **D2)
{
/*
* Map vertices to limit vertices.
* Here it is assumed that tlist,vlist results from sqrt(3) subdivision
* D2 will contain the derivative matrix wrt vertices
* NOTE: vlist is overwritten
*/
double *vlistn=calloc(3*nvert,sizeof(double));
//int *tlistn=calloc(3*nfac,sizeof(int));
double *D=calloc(nvert*nvert,sizeof(double));
int *vMo=calloc(nvert*nvert,sizeof(int));
int i1,i2,i3;
for(int j=0;j<nfac;j++)
{
i1=tlist[3*j+0]-1;
i2=tlist[3*j+1]-1;
i3=tlist[3*j+2]-1;
set_elI(vMo,nvert,nvert,1,i1,i2);
set_elI(vMo,nvert,nvert,1,i1,i3);
set_elI(vMo,nvert,nvert,1,i2,i1);
set_elI(vMo,nvert,nvert,1,i2,i3);
set_elI(vMo,nvert,nvert,1,i3,i1);
set_elI(vMo,nvert,nvert,1,i3,i2);
}
int *Neigh=calloc(nvert,sizeof(int));
int n=0;
double vxsum;
double vysum;
double vzsum;
double an;
double bn;
for(int j=0;j<nvert;j++)
{
n=0;
vxsum=0;
vysum=0;
vzsum=0;
for(int k=0;k<nvert;k++)
{
if(get_elI(vMo,nvert,nvert,j,k))
{
Neigh[n++]=k;
vxsum+=vlist[3*k];
vysum+=vlist[3*k+1];
vzsum+=vlist[3*k+2];
}
}
an=1.0/9.0*(4-2*cos(2*PI/n));
bn=3.0*an/(1.0+3*an);
vlistn[3*j+0]=(1-bn)*vlist[3*j+0]+bn*1.0/n*vxsum;
vlistn[3*j+1]=(1-bn)*vlist[3*j+1]+bn*1.0/n*vysum;
vlistn[3*j+2]=(1-bn)*vlist[3*j+2]+bn*1.0/n*vzsum;
set_el(D,nvert,nvert,1-bn,j,j);
for(int k=0;k<n;k++)
set_el(D,nvert,nvert,bn/n,j,Neigh[k]);
}
*D2=D;
memcpy(vlist,vlistn,sizeof(double)*3*nvert);
free(vlistn);
free(vMo);
free(Neigh);
}
void Sqrt3_Subdiv(int *tlist,double* vlist,int nfac,int nvert,int **tlistn,double **vlistn,int *nfacn,int *nvertn,double **D,int sdstep)
/*Do subdivision*/
{
int *tlistn2,*tlistn3;
double *vlistn2,*vlistn3,*D2,*D3,*DL,*DT;
int nvertn2,nfacn2;
if(sdstep==2)
{
sqrt3_subdiv(tlist,vlist,nfac,nvert,&tlistn2,&vlistn2,&nfacn2,&nvertn2,&D2);
sqrt3_subdiv(tlistn2,vlistn2,nfacn2,nvertn2,tlistn,vlistn,nfacn,nvertn,&D3);
map_sqrt_subdiv_limit(*tlistn,*vlistn,*nfacn,*nvertn,&DL);
free(vlistn2);
free(tlistn2);
DT=calloc(*nvertn*nvert,sizeof(double));
*D=calloc(*nvertn*nvert,sizeof(double));
matrix_prod(D3,*nvertn,nvertn2,D2,nvert,DT);
matrix_prod(DL,*nvertn,*nvertn,DT,nvert,*D);
free(D2);
free(D3);
free(DL);
free(DT);
}
else if(sdstep==1)
{
sqrt3_subdiv(tlist,vlist,nfac,nvert,tlistn,vlistn,nfacn,nvertn,&DT);
map_sqrt_subdiv_limit(*tlistn,*vlistn,*nfacn,*nvertn,&DL);
*D=calloc(*nvertn*nvert,sizeof(double));
matrix_prod(DL,*nvertn,*nvertn,DT,nvert,*D);
free(DT);
free(DL);
}
else if(sdstep==0)
{
*tlistn=calloc(nfac*3,sizeof(int));
*vlistn=calloc(nvert*3,sizeof(double));
memcpy(*tlistn,tlist,sizeof(int)*3*nfac);
memcpy(*vlistn,vlist,sizeof(double)*3*nvert);
*nfacn=nfac;
*nvertn=nvert;
*D=calloc(*nvertn*nvert,sizeof(double));
map_sqrt_subdiv_limit(*tlistn,*vlistn,*nfacn,*nvertn,D);
}
else if(sdstep==-1)
{
*tlistn=calloc(nfac*3,sizeof(int));
*vlistn=calloc(nvert*3,sizeof(double));
*D=NULL;
memcpy(*tlistn,tlist,sizeof(int)*3*nfac);
memcpy(*vlistn,vlist,sizeof(double)*3*nvert);
*nfacn=nfac;
*nvertn=nvert;
}
else
{
fprintf(stderr,"sdstep value %d not currently supported\n",sdstep);
exit(-1);
}
}
/*
int main()
{
char filename[]="mshape.txt";
int *tlist,*tlistn,*tlistn2;
double *vlist,*vlistn,*vlistn2,*D2,*D;
int nvert,nfac,nvertn,nfacn,nvertn2,nfacn2;
read_shape(filename,&tlist,&vlist,&nfac,&nvert,0);
printf("nfac: %d nvert: %d\n",nfac,nvert);
// sqrt3_subdiv(tlist,vlist,nfac,nvert,&tlistn,&vlistn,&nfacn,&nvertn,&D);
// printf("nfac: %d nvert: %d\n",nfacn,nvertn);
// sqrt3_subdiv(tlistn,vlistn,nfacn,nvertn,&tlistn2,&vlistn2,&nfacn2,&nvertn2,&D2);
//printf("nfac: %d nvert: %d\n",nfacn2,nvertn2);
//print_matrixI(tlist,nfac,3);
//print_matrix(vlist,nvert,3);
//sqrt3_subdiv(tlist,nfac,vlist,nvert,&tlistn,&nfacn,&vlistn,&nvertn,&D);
Sqrt3_Subdiv(tlist,vlist,nfac,nvert,&tlistn,&vlistn,&nfacn,&nvertn,&D,1);
printf("nfacn: %d nvertn: %d\n",nfacn,nvertn);
//print_matrix(D,nvertn,nvert);
//print_matrixI(tlistn,10,3);
//print_matrixI(tlist,8,3);
write_shape_file("/tmp/sshape.txt",tlistn,vlistn,nfacn,nvertn);
write_matrix_file("/tmp/D.txt",D,nvertn,nvert);
free(tlistn);
free(vlistn);
free(tlist);
free(vlist);
*/
/*
int tlist[]={1,2, 3,
1, 3, 4,
1, 4, 5,
1, 5, 2,
6, 3, 2,
6, 4, 3,
6, 5, 4,
6, 2, 5};
double vlist[]={ 0, 0, 1.0000,
1.0000, 0, 0.0000,
0.0000, 1.0000, 0.0000,
-1.0000, 0.0000, 0.0000,
-0.0000, -1.0000, 0.0000,
0.0000, 0, -1.0000};
double *vlistn,*D;
int *tlistn,nvertn,nvert,nfac,nfacn;
nvert=6;
nfac=8;
sqrt3_subdiv(tlist,vlist,nfac,nvert,&tlistn,&vlistn,&nfacn,&nvertn,&D);
printf("nfacn: %d nvertn: %d\n",nfacn,nvertn);
write_shape_file("/tmp/sshape.txt",tlistn,vlistn,nfacn,nvertn);
write_matrix_file("/tmp/D.txt",D,nvertn,nvert);
}
*/