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// Robust version of Gilles Dumoulin's C++ port of Paul Bourke's
// triangulation code available from
// http://astronomy.swin.edu.au/~pbourke/papers/triangulate
// Used with permission of Paul Bourke.
// Segmentation fault and numerical robustness improvements by John C. Bowman
#include <cassert>
#include "Delaunay.h"
#include "predicates.h"
inline double max(double a, double b)
{
return (a > b) ? a : b;
}
int XYZCompare(const void *v1, const void *v2)
{
double x1=((XYZ*)v1)->p[0];
double x2=((XYZ*)v2)->p[0];
if(x1 < x2)
return(-1);
else if(x1 > x2)
return(1);
else
return(0);
}
inline double hypot2(double *x)
{
return x[0]*x[0]+x[1]*x[1];
}
///////////////////////////////////////////////////////////////////////////////
// Triangulate():
// Triangulation subroutine
// Takes as input NV vertices in array pxyz
// Returned is a list of ntri triangular faces in the array v
// These triangles are arranged in a consistent clockwise order.
// The triangle array v should be allocated to 4 * nv
// The vertex array pxyz must be big enough to hold 3 additional points.
// By default, the array pxyz is automatically presorted and postsorted.
///////////////////////////////////////////////////////////////////////////////
Int Triangulate(Int nv, XYZ pxyz[], ITRIANGLE v[], Int &ntri,
bool presort, bool postsort)
{
Int emax = 200;
if(presort) qsort(pxyz,nv,sizeof(XYZ),XYZCompare);
else postsort=false;
/* Allocate memory for the completeness list, flag for each triangle */
Int trimax = 4 * nv;
Int *complete = new Int[trimax];
/* Allocate memory for the edge list */
IEDGE *edges = new IEDGE[emax];
/*
Find the maximum and minimum vertex bounds.
This is to allow calculation of the bounding triangle
*/
double xmin = pxyz[0].p[0];
double ymin = pxyz[0].p[1];
double xmax = xmin;
double ymax = ymin;
for(Int i = 1; i < nv; i++) {
XYZ *pxyzi=pxyz+i;
double x=pxyzi->p[0];
double y=pxyzi->p[1];
if (x < xmin) xmin = x;
if (x > xmax) xmax = x;
if (y < ymin) ymin = y;
if (y > ymax) ymax = y;
}
double dx = xmax - xmin;
double dy = ymax - ymin;
/*
Set up the supertriangle.
This is a triangle which encompasses all the sample points.
The supertriangle coordinates are added to the end of the
vertex list. The supertriangle is the first triangle in
the triangle list.
*/
static const double margin=0.01;
double xmargin=margin*dx;
double ymargin=margin*dy;
pxyz[nv+0].p[0] = xmin-xmargin;
pxyz[nv+0].p[1] = ymin-ymargin;
pxyz[nv+1].p[0] = xmin-xmargin;
pxyz[nv+1].p[1] = ymax+ymargin+dx;
pxyz[nv+2].p[0] = xmax+xmargin+dy;
pxyz[nv+2].p[1] = ymin-ymargin;
v->p1 = nv;
v->p2 = nv+1;
v->p3 = nv+2;
complete[0] = false;
ntri = 1;
/*
Include each point one at a time into the existing mesh
*/
for(Int i = 0; i < nv; i++) {
Int nedge = 0;
double *d=pxyz[i].p;
/*
Set up the edge buffer.
If the point d lies inside the circumcircle then the
three edges of that triangle are added to the edge buffer
and that triangle is removed.
*/
for(Int j = 0; j < ntri; j++) {
if(complete[j])
continue;
ITRIANGLE *vj=v+j;
double *a=pxyz[vj->p1].p;
double *b=pxyz[vj->p2].p;
double *c=pxyz[vj->p3].p;
if(incircle(a,b,c,d) <= 0.0) { // Point d is inside or on circumcircle
/* Check that we haven't exceeded the edge list size */
if(nedge + 3 >= emax) {
emax += 100;
IEDGE *p_EdgeTemp = new IEDGE[emax];
for (Int i = 0; i < nedge; i++) {
p_EdgeTemp[i] = edges[i];
}
delete[] edges;
edges = p_EdgeTemp;
}
ITRIANGLE *vj=v+j;
Int p1=vj->p1;
Int p2=vj->p2;
Int p3=vj->p3;
edges[nedge].p1 = p1;
edges[nedge].p2 = p2;
edges[++nedge].p1 = p2;
edges[nedge].p2 = p3;
edges[++nedge].p1 = p3;
edges[nedge].p2 = p1;
++nedge;
ntri--;
v[j] = v[ntri];
complete[j] = complete[ntri];
j--;
} else {
double A=hypot2(a);
double B=hypot2(b);
double C=hypot2(c);
double a0=orient2d(a,b,c);
// Is d[0] > xc+r for circumcircle abc of radius r about (xc,yc)?
if(d[0]*a0 < 0.5*orient2d(A,a[1],B,b[1],C,c[1]))
complete[j]=
incircle(a[0]*a0,a[1]*a0,b[0]*a0,b[1]*a0,c[0]*a0,c[1]*a0,
d[0]*a0,0.5*orient2d(a[0],A,b[0],B,c[0],C)) > 0.0;
}
}
/*
Tag multiple edges
Note: if all triangles are specified anticlockwise then all
interior edges are opposite pointing in direction.
*/
for(Int j = 0; j < nedge - 1; j++) {
for(Int k = j + 1; k < nedge; k++) {
if((edges[j].p1 == edges[k].p2) && (edges[j].p2 == edges[k].p1)) {
edges[j].p1 = -1;
edges[j].p2 = -1;
edges[k].p1 = -1;
edges[k].p2 = -1;
}
}
}
/*
Form new triangles for the current point
Skipping over any tagged edges.
All edges are arranged in clockwise order.
*/
for(Int j = 0; j < nedge; j++) {
if(edges[j].p1 < 0 || edges[j].p2 < 0)
continue;
v[ntri].p1 = edges[j].p1;
v[ntri].p2 = edges[j].p2;
v[ntri].p3 = i;
complete[ntri] = false;
ntri++;
assert(ntri < trimax);
}
}
/*
Remove triangles with supertriangle vertices
These are triangles which have a vertex number greater than nv
*/
for(Int i = 0; i < ntri; i++) {
ITRIANGLE *vi=v+i;
if(vi->p1 >= nv || vi->p2 >= nv || vi->p3 >= nv) {
ntri--;
*vi = v[ntri];
i--;
}
}
delete[] edges;
delete[] complete;
if(postsort) {
for(Int i = 0; i < ntri; i++) {
ITRIANGLE *vi=v+i;
vi->p1=pxyz[vi->p1].i;
vi->p2=pxyz[vi->p2].i;
vi->p3=pxyz[vi->p3].i;
}
}
return 0;
}
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