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power.cpp
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#include <stdio.h>
#include <stdlib.h>
#include <stdarg.h>
#include <assert.h>
#include <float.h>
#include <math.h>
/*
* Power Crust software, by Nina Amenta, Sunghee Choi and Ravi Krishna Kolluri.
* Copyright (c) 2000 by the University of Texas
* Permission to use, copy, modify, and distribute this software for any
* purpose without fee under the GNU Public License is hereby granted,
* provided that this entire notice is included in all copies of any software
* which is or includes a copy or modification of this software and in all copies
* of the supporting documentation for such software.
* THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
* WARRANTY. IN PARTICULAR, NEITHER THE AUTHORS NOR AT&T MAKE ANY
* REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
* OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
*/
#include "hull.h"
extern double theta;
extern FILE *PC, *PNF, *INFPOLE,*AXIS,*AXISFACE; /* *RT, *PS, *PR; */
int numvtxs=0, numfaces=0;
extern int num_vtxs,num_faces;
extern double theta;
extern struct polelabel *adjlist;
extern struct queuenode *queue;
extern long site_numm(site p);
extern void triorthocenter(double a[], double b[], double c[],
double orthocenter[], double* cnum);
extern void tetorthocenter(double a[], double b[], double c[], double d[],
double orthocenter[], double* cnum);
/* some new variables */
extern int num_poles,num_axedgs,num_axfaces;
int v1[6]={0,0,0,1,1,2};
int v2[6]={1,2,3,2,3,3};
int v3[6]={2,3,1,3,0,0};
int v4[6]={3,1,2,0,2,1};
void *compute_2d_power_vv(simplex *s, void *p) {
/* computes Voronoi vertices */
static out_func *out_func_here;
point v[MAXDIM];
int j,k,inf=0, index;
double cc[2], cond, ta[3][3];
if (p) {out_func_here = (out_func*)p; if (!s) return NULL;}
index = 0;
for (j=0;j<3;j++) {
v[j] = s->neigh[j].vert;
/* v[j] stores coordinates of j'th vertex of simplex s; j=0..3 */
if (v[j]==infinity) { /* means simplex s is on the convex hull */
inf=1;
continue; /* skip the rest of the for loop; process next vertex */
}
/*i=(site_num)(v[j]); i is the index of the vertex v[j] */
for (k=0;k<3;k++) {
ta[index][k] = v[j][k]/mult_up;
/* restore original coords */
/* if inf=1, ta[0],ta[1] are non-infinite vertices of s*/
/* inf=0, ta[0],ta[1],ta[2] are 3 vertices of s */
}
index++;
}
printf("\n");
if (!inf) { /* if not faces on convex hull, compute circumcenter*/
for (k=0;k<3;k++)
/* printf("%f %f %f\n",ta[k][0],ta[k][1],ta[k][2]);*/
triorthocenter(ta[0], ta[1], ta[2], cc, &cond);
/* cc is the displacement of orthocenter from ta[0] */
/* cond is the denominator ( orient2d ) value */
if (cond!=0) { /* ignore them if cond = 0 */
s->vv = (Coord*) malloc(sizeof(Coord)*2);
for (k=0;k<2;k++) {
s->vv[k] = ta[0][k]+cc[k];
}
s->status = VV;
}
else { /* if cond=0, s is SLIVER */
fprintf(DFILE,"sliver!\n");
s->vv = NULL;
s->status = SLV;
}
}
else { /* if on conv hull, ignore */
s->vv = NULL;
s->status = CNV;
}
return NULL;
}
/*
void *reg_triang(simplex *s, void *p) {
static out_func *out_func_here;
point v[MAXDIM];
int j,k,vnum;
double cc[3], cond, ta[4][4];
if (p) {out_func_here = (out_func*)p; if (!s) return NULL;}
for (j=0;j<cdim;j++) {
v[j] = s->neigh[j].vert;
if (v[j]==infinity) {
return NULL;
}
}
for (j=0;j<cdim;j++) {
vnum=0;
for (k=0;k<cdim;k++) {
if (k==j) continue;
v[vnum++] = (s->neigh[k].vert);
}
fprintf(RT,"3 %d %d %d\n",(site_num)(v[0]),(site_num)(v[1]),(site_num)(v[2]));
}
return NULL;
}
*/
void *compute_3d_power_vv(simplex *s, void *p) {
static out_func *out_func_here;
point v[MAXDIM];
int j,k,inf=0, index, visited_edge;
double cc[3], cond, ta[4][4], d, r1, r2, e;
struct edgesimp *newplist, *pindex;
if (p) {
out_func_here = (out_func*)p;
if (!s) return NULL;
}
index = 0;
for (j=0;j<cdim;j++) {
v[j] = s->neigh[j].vert;
/* v[j] stores coordinates of j'th vertex of simplex s; j=0..3 */
if (v[j]==infinity) { /* means simplex s is on the convex hull */
inf=1;
continue; /* skip the rest of the for loop; process next vertex */
}
/*i=(site_num)(v[j]); i is the index of the vertex v[j] */
for (k=0;k<4;k++) {
ta[index][k] = v[j][k]/mult_up; /* restore original coords */
/* if inf=1, ta[0],ta[1],ta[2] are non-infinite vertices of s*/
/* inf=0, ta[0],ta[1],ta[2],ta[3] are 4 vertices of s */
}
index++;
}
/* if not faces on convex hull, process */
if (!inf) {
/* build structure for each edge, including angle of intersection */
for (k=0;k<6;k++) {
if (s->edgestatus[k]==FIRST_EDGE) { /* not visited edge */
pindex = adjlist[site_numm(v[v1[k]])].eptr;
visited_edge = 0;
while (pindex!= NULL) {
if (pindex->pid == site_numm(v[v2[k]])) { /* already in the list */
visited_edge = 1;
break;
}
pindex = pindex->next;
}
if (!visited_edge) {
d = sqdist(ta[v1[k]],ta[v2[k]]);
r1 = SQ(ta[v1[k]][0])+SQ(ta[v1[k]][1])+SQ(ta[v1[k]][2])-ta[v1[k]][3];
r2 = SQ(ta[v2[k]][0])+SQ(ta[v2[k]][1])+SQ(ta[v2[k]][2])-ta[v2[k]][3];
e = 2 * sqrt(r1) * sqrt(r2);
newplist = (struct edgesimp *) malloc(sizeof(struct edgesimp));
newplist->simp = s;
newplist->kth = k;
newplist->angle = (r1+r2-d)/e;
newplist->pid = site_numm(v[v1[k]]);
newplist->next = adjlist[site_numm(v[v2[k]])].eptr;
adjlist[site_numm(v[v2[k]])].eptr = newplist;
newplist = (struct edgesimp *) malloc(sizeof(struct edgesimp));
newplist->simp = s;
newplist->kth = k;
newplist->angle = (r1+r2-d)/e;
newplist->pid = site_numm(v[v2[k]]);
newplist->next = adjlist[site_numm(v[v1[k]])].eptr;
adjlist[site_numm(v[v1[k]])].eptr = newplist;
s->edgestatus[k] = VISITED;
}
}
}
tetorthocenter(ta[0], ta[1], ta[2], ta[3], cc, &cond);
/* cc is the displacement of orthocenter from ta[0] */
/* cond is the denominator ( orient2d ) value */
if (cond!=0) { /* ignore them if cond = 0 */
s->vv = (Coord*) malloc(sizeof(Coord)*3);
for (k=0;k<3;k++) {
s->vv[k] = ta[0][k]+cc[k];
}
s->status = VV;
}
else { /* if cond=0, s is SLIVER */
fprintf(DFILE,"sliver!\n");
s->vv = NULL;
s->status = SLV;
}
}
else { /* if on conv hull, ignore */
s->vv = NULL;
s->status = CNV;
}
return NULL;
}
void *compute_3d_power_edges(simplex *s, void *p) {
static out_func *out_func_here;
point v[MAXDIM];
int j, k, inf=0, numedges, ns, l, nedge0, nedge1, nremv, nnextv, l1, l2, nk;
site edge0, edge1, nextv, remv, prevv;
double ta[4][4], r1, r2, d, e;
simplex *prevs, *nexts;
if (p) {out_func_here = (out_func*)p; if (!s) return NULL;}
if ((s->status == CNV)||(s->status == SLV)) return NULL; /* skip inf faces */
for (j=0;j<cdim;j++) {
v[j] = s->neigh[j].vert;
for (k=0;k<4;k++) {
ta[j][k] = v[j][k]/mult_up; /* restore original coords */
}
}
if (!inf) {
for (k=0;k<6;k++) { /* for each edge */
if (s->edgestatus[k]==FIRST_EDGE) { /* not visited edge */
/* check the dihedral angle */
d = sqdist(ta[v1[k]],ta[v2[k]]);
r1 = SQ(ta[v1[k]][0])+SQ(ta[v1[k]][1])+
SQ(ta[v1[k]][2])-ta[v1[k]][3];
r2 = SQ(ta[v2[k]][0])+SQ(ta[v2[k]][1])+
SQ(ta[v2[k]][2])-ta[v2[k]][3];
e = 2 * sqrt(r1) * sqrt(r2);
if ((d >= (r1+r2+e)) || ((d-r1-r2)/e > theta )) {
/* fprintf(DFILE,"%f\n",(d-r1-r2)/e);*/
/* edge0, edge1 are the vertices of the edge */
edge0 = s->neigh[v1[k]].vert;
edge1 = s->neigh[v2[k]].vert;
nextv = s->neigh[v3[k]].vert;
/* nextv is the opposite vtx of the next simplex */
remv = s->neigh[v4[k]].vert;
/* remv is a vtx of the next simplex with edge0, edge1 */
prevv = remv;
/* prevv is the vtx shared by prevs and nexts besides edge0, edge1 */
/* construct its dual power face */
s->edgestatus[k]=POW;
/* visit the next simplex */
/* print orthocenter of s->neigh[v3[k]].simp ...*/
prevs = s;
nexts = s->neigh[v3[k]].simp;
ns = v3[k];
numedges=0;
while (nexts != s) {
if (nexts->status == CNV) {
fprintf(DFILE,"inf reg face\n");
break;
}
else {
fprintf(PC,"%f %f %f\n",prevs->vv[0],prevs->vv[1],prevs->vv[2]);
numedges++;numvtxs++;
/* find edgenumber k of nexts for this edge */
for (l=0;l<4;l++) {
if (nexts->neigh[l].vert==edge0) {
/* l == v1[k] */
nedge0 = l;continue;
}
else if (nexts->neigh[l].vert==edge1) {
/* l == v2[k] */
nedge1 = l;continue;
}
else if (nexts->neigh[l].vert==prevv) {
nremv = l;continue;
}
else if (nexts->neigh[l].vert==nextv) {
nnextv = l;
continue;
}
else {
nnextv = l;
}
}
if (nedge0 > nedge1) { l1 = nedge1; l2 = nedge0; }
else { l2 = nedge1; l1 = nedge0; }
if (l1==0) {
if (l2==1) nk = 0;
else if (l2==2) nk = 1;
else nk = 2;
}
else if (l1==1) {
if (l2==2) nk = 3;
else nk = 4;
}
else nk = 5;
/* found nk for the edge */
nexts->edgestatus[nk]=POW; /* record that it's visited */
/* visit next simplex (opposite vertex ns )*/
prevs = nexts;
prevv = nexts->neigh[nnextv].vert;
nexts = nexts->neigh[nremv].simp;
}
}
fprintf(PC,"%f %f %f\n", prevs->vv[0], prevs->vv[1], prevs->vv[2]);
numedges++;numvtxs++;
fprintf(PNF,"%d ",numedges);
for (l=numedges;l>0;l--) {
fprintf(PNF, "%d ",numvtxs-l);
}
fprintf(PNF,"\n");numfaces++;
}
else {
s->edgestatus[k]=NOT_POW;
}
} /* skip if the edge is visited before */
}
}
/* ignore inf faces */
return NULL;
}
/* the function for computing the medial axis */
void *compute_axis (simplex *s, void *p) {
static out_func *out_func_here;
point v[MAXDIM];
point point1,point2;
int pindex,qindex;
int edgedata[6];
int indices[6]; /* store the indices */
int j, k, inf=0;
double ta[4][4];
if (p) {out_func_here = (out_func*)p; if (!s) return NULL;}
if ((s->status == CNV)||(s->status == SLV)) return NULL; /* skip inf faces */
for (j=0;j<cdim;j++) {
v[j] = s->neigh[j].vert;
for (k=0;k<4;k++) {
ta[j][k] = v[j][k]/mult_up; /* restore original coords */
}
}
if (!inf) {
for (k=0;k<6;k++) { /* for each edge */
edgedata[k]=0;
if ((s->edgestatus[k]!=POW) ) { /* not dual to a power face */
point1 = v[v1[k]];
point2 = v[v2[k]];
pindex=site_numm(point1);
qindex=site_numm(point2);
if(adjlist[pindex].label==IN && adjlist[qindex].label==IN)
{
if(s->edgestatus[k]!=ADDAXIS) {
num_axedgs++;
fprintf(AXIS,"2 %d %d \n ",pindex,qindex);
}
edgedata[k]=VALIDEDGE;
indices[v1[k]]=pindex ;
indices[v2[k]]=qindex ;
s->edgestatus[k]=ADDAXIS;
}
/* now start adding triangles if present */
}
}
if((edgedata[0]==VALIDEDGE)&& (edgedata[1]==VALIDEDGE)
&& (edgedata[3]==VALIDEDGE))
{
fprintf(AXIS,"3 %d %d %d \n",indices[v1[0]],
indices[v2[1]],indices[v1[3]]);
fprintf(AXISFACE,"3 %d %d %d \n",indices[v1[0]],
indices[v2[1]],indices[v1[3]]);
num_axedgs++;
num_axfaces++;
}
if((edgedata[1]==VALIDEDGE)&& (edgedata[2]==VALIDEDGE)
&& (edgedata[5]==VALIDEDGE))
{
fprintf(AXIS,"3 %d %d %d \n",indices[v1[1]],
indices[v2[2]],indices[v1[5]]);
fprintf(AXISFACE,"3 %d %d %d \n",indices[v1[1]],
indices[v2[2]],indices[v1[5]]);
num_axedgs++;
num_axfaces++;
}
if((edgedata[0]==VALIDEDGE)&& (edgedata[2]==VALIDEDGE)
&& (edgedata[4]==VALIDEDGE))
{
fprintf(AXIS,"3 %d %d %d \n",indices[v1[0]],
indices[v2[2]],indices[v1[4]]);
fprintf(AXISFACE,"3 %d %d %d \n",indices[v1[0]],
indices[v2[2]],indices[v1[4]]);
num_axedgs++;
num_axfaces++;
}
if((edgedata[3]==VALIDEDGE)&& (edgedata[4]==VALIDEDGE)
&& (edgedata[5]==VALIDEDGE))
{
fprintf(AXIS,"3 %d %d %d \n",indices[v1[3]],
indices[v2[4]],indices[v1[5]]);
fprintf(AXISFACE,"3 %d %d %d \n",indices[v1[3]],
indices[v2[4]],indices[v1[5]]);
num_axedgs++;
num_axfaces++;
}
}
return NULL;
}
/* To print out powercrust faces */
void construct_face(simplex *s, short k)
{
site edge0, edge1, nextv, remv, prevv,outsite,insite;
simplex *prevs, *nexts;
int j, numedges, l1, l2, nk, l, ns, nedge0, nedge1, nremv, nnextv, i;
char cface[200];
char indface[1024][32]; /* the indices of the face */
double plane[3][3];
double outpole[3],inpole[3];
cface[0] = '\0';
edge0 = s->neigh[v1[k]].vert;
edge1 = s->neigh[v2[k]].vert;
if(adjlist[site_numm(edge0)].label==OUT) {
outsite=edge0;
insite=edge1;
}
else {
outsite=edge1;
insite=edge0;
}
for(j=0;j<3;j++){
outpole[j]=outsite[j]/mult_up;
inpole[j]=insite[j]/mult_up;
}
nextv = s->neigh[v3[k]].vert;
/* nextv is the opposite vtx of the next simplex */
remv = s->neigh[v4[k]].vert;
/* remv is a vtx of the next simplex with edge0, edge1 */
prevv = remv;
/* prevv is the vtx shared by prevs and nexts besides edge0, edge1 */
/* construct its dual power face */
s->edgestatus[k]=POW;
/* visit the next simplex */
/* print orthocenter of s->neigh[v3[k]].simp ...*/
prevs = s;
nexts = s->neigh[v3[k]].simp;
ns = v3[k];
numedges=0;
while (nexts != s) {
if (nexts->status == CNV) {
fprintf(DFILE,"inf reg face\n");
break;
}
else {
if (prevs->status != POLE_OUTPUT) {
/* this vertex is not yet output */
prevs->status = POLE_OUTPUT;
prevs->poleindex = num_vtxs++;
fprintf(PC,"%f %f %f\n",prevs->vv[0],prevs->vv[1],prevs->vv[2]);
}
if(numedges<3){
plane[numedges][0]=prevs->vv[0];
plane[numedges][1]=prevs->vv[1];
plane[numedges][2]=prevs->vv[2];
}
sprintf(indface[numedges],"%ld ",prevs->poleindex);
/* strcat(cface,tempface);*/
numedges++;
/* find edgenumber k of nexts for this edge */
for (l=0;l<4;l++) {
if (nexts->neigh[l].vert==edge0) {
/* l == v1[k] */
nedge0 = l;continue;
}
else if (nexts->neigh[l].vert==edge1) {
/* l == v2[k] */
nedge1 = l;continue;
}
else if (nexts->neigh[l].vert==prevv) {
nremv = l;continue;
}
else if (nexts->neigh[l].vert==nextv) {
/* if (nexts->neigh[nremv].simp == s) { */
nnextv = l;
continue;
/*}
else fprintf(DFILE,"cannot happen l=%d!!\n",l); */
}
else {
nnextv = l;
}
}
if (nedge0 > nedge1) { l1 = nedge1; l2 = nedge0; }
else { l2 = nedge1; l1 = nedge0; }
if (l1==0) {
if (l2==1) nk = 0;
else if (l2==2) nk = 1;
else nk = 2;
}
else if (l1==1) {
if (l2==2) nk = 3;
else nk = 4;
}
else nk = 5;
/* found nk for the edge */
nexts->edgestatus[nk]=POW; /* record that it's visited */
/* visit next simplex (opposite vertex ns )*/
prevs = nexts;
prevv = nexts->neigh[nnextv].vert;
nexts = nexts->neigh[nremv].simp;
}
}
if (prevs->status != POLE_OUTPUT) {
prevs->status = POLE_OUTPUT;
prevs->poleindex = num_vtxs++;
fprintf(PC,"%f %f %f\n", prevs->vv[0], prevs->vv[1], prevs->vv[2]);
}
if(numedges<3) {
plane[numedges][0]=prevs->vv[0];
plane[numedges][1]=prevs->vv[1];
plane[numedges][2]=prevs->vv[2];
}
sprintf(indface[numedges],"%ld ",prevs->poleindex);
numedges++;
fprintf(PNF,"%d ",numedges);
if(!correct_orientation(plane[0],plane[1],plane[2],inpole,outpole))
for(i=numedges-1;i>=0;i--)
fprintf(PNF,"%s ",indface[i]);
else
for(i=0;i<numedges;i++)
fprintf(PNF,"%s ",indface[i]);
fprintf(PNF,"\n");
num_faces++;
}
int correct_orientation(double *p1,double *p2,double *p3,double *inp,double *outp) {
double normal[3];
double v1[3],v2[3];
double xcross,ycross,zcross;
int numplus=0,numminus=0;
normal[0]=outp[0]-inp[0];
normal[1]=outp[1]-inp[1];
normal[2]=outp[2]-inp[2];
v1[0]=p2[0]-p1[0];
v1[1]=p2[1]-p1[1];
v1[2]=p2[2]-p1[2];
v2[0]=p3[0]-p2[0];
v2[1]=p3[1]-p2[1];
v2[2]=p3[2]-p2[2];
xcross=v1[1]*v2[2]-v1[2]*v2[1];
ycross=v1[2]*v2[0]-v1[0]*v2[2];
zcross=v1[0]*v2[1]-v1[1]*v2[0];
if((xcross*normal[0]) > 0)
numplus++;
else
numminus++;
if((ycross*normal[1]) > 0)
numplus++;
else
numminus++;
if((zcross*normal[2]) > 0)
numplus++;
else
numminus++;
if(numplus > numminus)
return 1;
else
return 0;
}