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find_edge.c
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find_edge.c
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#include<string.h>
#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#include"utils.h"
int linesegment_intersect(double *a,double *b,double *x,double *y,double *p,double *dpx,double *dpy,double* dpox,double* dpoy)
{
/*
* Check whether line determined by points a,b
*intersects the line segment determined by x,y
*If intersection, inters=true and the intersection is x+t(y-x)
*p=(px,py)
*dpx=[dpx/dx0,dpx/dx1,dpx/dy0,dpx/dy1] IF x=(x0,y0), y=(x1,y1). NOTE THAT
*HERE x=(x0,x1) y=(y0,y1). SO dpx is derivative wrt 1.point x-coord,
*1.point y-coord, 2.point x-coord 2.point y-coord
*dtdx=[dt/dx0 dt/dy0], dtdy=[dt/dx1,dt/dy1];Checks whether line determined by point a,b
*/
double eps=1E-10;
int inters=0;
double t=0;
double b0=b[0];
double b1=b[1];
double a0=a[0];
double a1=a[1];
double x0=x[0];
double x1=x[1];
double y0=y[0];
double y1=y[1];
double dtdx[2],dtdy[2];
double denom=(b0-a0)*(x1-y1)-(b1-a1)*(x0-y0);
double s;
if(fabs(denom)<eps)
return 0;
t=((a0-x0)*(b1-a1)-(a1-x1)*(b0-a0))/denom;
if(t<0 || t>1)
return 0;
s=-((x0-a0)*(y1-x1)-(x1-a1)*(y0-x0))/denom;
if(s<0 || s>1)
return 0;
p[0]=x[0]+t*(y[0]-x[0]);
p[1]=x[1]+t*(y[1]-x[1]);
dtdx[0]=(a1-b1)*(a1*(b0-y0)+b1*y0-b0*y1+a0*(-b1+y1))/pow(denom,2);
dtdx[1]=(a1 - b1)*(-b1*x0 + a1*(-b0 + x0) + a0*(b1 - x1) + b0*x1)/pow(denom,2);
dtdy[0]=(a0 - b0)*(-b1*y0 + a1*(-b0 + y0) + a0*(b1 - y1) + b0*y1)/pow(denom,2);
dtdy[1]=-(a0 - b0)*(-b1*x0 + a1*(-b0 + x0) + a0*(b1 - x1) + b0*x1)/pow(denom,2);
dpx[0]=1+dtdx[0]*(y0-x0)-t;
dpx[1]=dtdy[0]*(y0-x0);
dpx[2]=dtdx[1]*(y0-x0)+t;
dpx[3]=dtdy[1]*(y0-x0);
dpy[0]=dtdx[0]*(y1-x1);
dpy[1]=1+dtdy[0]*(y1-x1)-t;
dpy[2]=dtdx[1]*(y1-x1);
dpy[3]=dtdy[1]*(y1-x1)+t;
////
double ddenom=pow(a1*(x0 - y0) + b1*(-x0 + y0) - (a0 - b0)*(x1 - y1),2);
dpox[0]=(pow(b1,2)*pow(x0 - y0,2) + pow(a0 - b0,2)*pow(x1 - y1,2) +b1*(x0 - y0)*(-2*b0*x1 + x1*y0 + a0*(x1 - y1) + 2*b0*y1 - x0*y1) - a1*(x0 - y0)*(-2*b0*x1 + b1*(x0 - y0) + x1*y0 + a0*(x1 - y1) + 2*b0*y1 - x0*y1))/ddenom; //dp[0]/doffx
dpox[1]=-((a1 - b1)*(x1 - y1)*(a1*(x0 - y0) + x1*y0 - x0*y1 + a0*(-x1 + y1)))/ddenom; //dp[1]/doffx
dpoy[0]=-((a0 - b0)*(x0 - y0)*(-(x1*y0) + a1*(-x0 + y0) + a0*(x1 - y1) + x0*y1))/ddenom; //dp[0]/doffy
dpoy[1]=(pow(a1,2)*pow(x0 - y0,2) + pow(b1,2)*pow(x0 - y0,2) - a1*(x0 - y0)*(2*b1*(x0 - y0) + (a0 - b0)*(x1 - y1)) + 2*(a0 - b0)*b1*(x0 - y0)*(x1 - y1) - (a0 - b0)*(x1 - y1)*(-(x1*y0) + b0*(x1 - y1) + x0*y1))/ddenom;
return 1;
}
void find_edge(int *tlist,double *vlist2,int nfac,int nvert,int *visible,double *offset,double *a,double *b,int *cledge,double *clpoint,int *inters,double *dclpx,double *dclpy,double *dclpdoffx,double *dclpdoffy)
{
/*
* *Find outer edge that line a->b intersects
*We assume the shape is already rotated and projected to plane
*determined by the z axis.
*Adj is the nvertxnvert adjavency matrix, where Adj(i,j)!=0 if vertices i
*and j are connected by an edge
*OUTPUT
*cledge closest edge to a, corresponds to vertices cledge[0] and cledge[1]
* clt is t value corresponding to the intersection point,
*clpoint=vlist(cledge[0],:)+clt*(vlist(cledge[1],:)-vlist(cledge[0],:))
*/
double eps=1E-10;
int *A=calloc(nvert*nvert,sizeof(int));
int i1,i2,i3;
double u1,u2,w1,w2,n3;
double *v1,*v2,*v3;
double interp[2],ip[2];
double dpx[4],dpy[4];
double dist,cldist=1E9;
double doffx[2],doffy[2];
double *vlist=calloc(3*nvert,sizeof(double));
memcpy(vlist,vlist2,sizeof(double)*nvert*3);
// memcpy(A,Adj,sizeof(int)*nvert*nvert);
double bbx[2],bby[2];
double offx=offset[0];
double offy=offset[1];
//Add offsets to vlist
for(int j=0;j<nvert;j++)
{
vlist[3*j]+=offx;
vlist[3*j+1]+=offy;
}
bbx[0]=minv(vlist,nvert,0);
bbx[1]=maxv(vlist,nvert,0);
bby[0]=minv(vlist,nvert,1);
bby[1]=maxv(vlist,nvert,1);
int t=1;
double p[2];
double b11,b12,b21,b22;
double bv11,bv12,bv21,bv22;
a[0]=offx;
a[1]=offy;
p[0]=a[0]+t*(b[0]-a[0]);
p[1]=a[1]+t*(b[1]-a[1]);
while(p[0]<bbx[1] && p[0]>bbx[0] && p[1]<bby[1] && p[1]>bby[0])
{
t++;
p[0]=a[0]+t*(b[0]-a[0]);
p[1]=a[1]+t*(b[1]-a[1]);
}
// b11=fmin(0,p[0]);
// b12=fmin(0,p[1]);
// b21=fmax(0,p[0]);
// b22=fmax(0,p[1]);
// p is a point on line a-b outside the shape. We use p to find the closest
//and farthest intersection points of model and and chord a->b.
clpoint[0]=0;
clpoint[1]=0;
int sinters=0;
for(int j=0;j<nfac;j++)
{
i1=tlist[3*j]-1;
i2=tlist[3*j+1]-1;
i3=tlist[3*j+2]-1;
if(visible[j]==0)
continue;
v1=vlist+3*i1;
v2=vlist+3*i2;
v3=vlist+3*i3;
// bv11=fmin(v1[0],fmin(v2[0],v3[0]));
// bv12=fmin(v1[1],fmin(v2[1],v3[1]));
// bv21=fmax(v1[0],fmax(v2[0],v3[0]));
// bv22=fmax(v1[1],fmax(v2[1],v3[1]));
// if(b12>bv22 || b22<bv12)
// continue;
// if(b21<bv11 || bv21<b11)
// continue;
if(linesegment_intersect(a,p,v1,v2,ip,dpx,dpy,doffx,doffy))
{
sinters=1;
//ip is the intersection point of line a->b and the current edge
dist=sqrt(pow(ip[0]-p[0],2)+pow(ip[1]-p[1],2));
if(dist<cldist)
{
cldist=dist;
cledge[0]=i1;
cledge[1]=i2;
clpoint[0]=ip[0];
clpoint[1]=ip[1];
memcpy(dclpx,dpx,sizeof(double)*4);
memcpy(dclpy,dpy,sizeof(double)*4);
memcpy(dclpdoffx,doffx,2*sizeof(double));
memcpy(dclpdoffy,doffy,2*sizeof(double));
}
}
if(linesegment_intersect(a,p,v2,v3,ip,dpx,dpy,doffx,doffy))
{
sinters=1;
dist=sqrt(pow(ip[0]-p[0],2)+pow(ip[1]-p[1],2));
if(dist<cldist)
{
cldist=dist;
cledge[0]=i2;
cledge[1]=i3;
clpoint[0]=ip[0];
clpoint[1]=ip[1];
memcpy(dclpx,dpx,sizeof(double)*4);
memcpy(dclpy,dpy,sizeof(double)*4);
memcpy(dclpdoffx,doffx,2*sizeof(double));
memcpy(dclpdoffy,doffy,2*sizeof(double));
}
}
if(linesegment_intersect(a,p,v3,v1,ip,dpx,dpy,doffx,doffy))
{
sinters=1;
dist=sqrt(pow(ip[0]-p[0],2)+pow(ip[1]-p[1],2));
if(dist<cldist)
{
cldist=dist;
cledge[0]=i3;
cledge[1]=i1;
clpoint[0]=ip[0];
clpoint[1]=ip[1];
memcpy(dclpx,dpx,sizeof(double)*4);
memcpy(dclpy,dpy,sizeof(double)*4);
memcpy(dclpdoffx,doffx,2*sizeof(double));
memcpy(dclpdoffy,doffy,2*sizeof(double));
}
}
}
free(A);
free(vlist);
*inters=sinters;
}