//
// Enforce delaunay on triangle t. Assume that p1 & p2 are the
// endpoints to the edge that is being checked for delaunay
//
void enforceDelaunay(TRIANGLE *t, R_POINT *p1, R_POINT *p2, R_POINT *p3,
double e, TIN_TILE *tt){
assert(t);
// Since we have tiles we cannot garauntee global delaunay. We must
// not enforce delaunay on boundary edges, that is edges that are on
// the same boundary together.
if(!(edgeOnBoundary(p1,p2,tt))){
// Find the triangle on the other side of edge p1p2
TRIANGLE *tn = whichTri(t,p1,p2,tt);
// If tn is NULL then we are done, otherwise we need to check delaunay
if(tn != NULL){
// Find point across from edge p1p2 in tn
R_POINT *d = findThirdPoint(tn->p1,tn->p2,tn->p3,p1,p2);
if(CircumCircle(d->x,d->y,p1->x,p1->y,p2->x,p2->y,p3->x,p3->y)){
edgeSwap(t,tn,p1,p3,p2,d,e,tt);
}
}
}
}
/*
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 malloced to 3 * nv
The vertex array pxyz must be big enough to hold 3 more points
The vertex array must be sorted in increasing x values say
qsort(p,nv,sizeof(XYZ),XYZCompare);
:
int XYZCompare(void *v1,void *v2)
{
XYZ *p1,*p2;
p1 = v1;
p2 = v2;
if (p1->x < p2->x)
return(-1);
else if (p1->x > p2->x)
return(1);
else
return(0);
}
*/
int Triangulate(int nv,XYZ *pxyz,ITRIANGLE *v,int *ntri, vector<IEDGE> & edges)
{
bool *complete = NULL;
//IEDGE *edges = NULL;
int nedge = 0;
int trimax,emax = 200;
int status = 0;
int inside;
int i,j,k;
double xp,yp,x1,y1,x2,y2,x3,y3,xc,yc,r;
double xmin,xmax,ymin,ymax,xmid,ymid;
double dx,dy,dmax;
/* Allocate memory for the completeness list, flag for each triangle */
trimax = 4 * nv;
if ((complete = (bool*)malloc(trimax*sizeof(bool))) == NULL) {
status = 1;
goto skip;
}
edges.resize(emax);
/* Allocate memory for the edge list */
/*if ((edges = (IEDGE*)malloc(emax*(long)sizeof(IEDGE))) == NULL) {
status = 2;
goto skip;
}*/
/*
Find the maximum and minimum vertex bounds.
This is to allow calculation of the bounding triangle
*/
xmin = pxyz[0].x;
ymin = pxyz[0].y;
xmax = xmin;
ymax = ymin;
for (i=1;i<nv;i++) {
if (pxyz[i].x < xmin) xmin = pxyz[i].x;
if (pxyz[i].x > xmax) xmax = pxyz[i].x;
if (pxyz[i].y < ymin) ymin = pxyz[i].y;
if (pxyz[i].y > ymax) ymax = pxyz[i].y;
}
dx = xmax - xmin;
dy = ymax - ymin;
dmax = (dx > dy) ? dx : dy;
xmid = (xmax + xmin) / 2.0;
ymid = (ymax + ymin) / 2.0;
/*
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.
*/
pxyz[nv+0].x = xmid - 20 * dmax;
pxyz[nv+0].y = ymid - dmax;
pxyz[nv+0].z = 0.0;
pxyz[nv+1].x = xmid;
pxyz[nv+1].y = ymid + 20 * dmax;
pxyz[nv+1].z = 0.0;
pxyz[nv+2].x = xmid + 20 * dmax;
pxyz[nv+2].y = ymid - dmax;
pxyz[nv+2].z = 0.0;
v[0].p1 = nv;
v[0].p2 = nv+1;
v[0].p3 = nv+2;
complete[0] = false;
*ntri = 1;
/*
Include each point one at a time into the existing mesh
*/
for (i=0;i<nv;i++) {
xp = pxyz[i].x;
yp = pxyz[i].y;
nedge = 0;
/*
Set up the edge buffer.
If the point (xp,yp) lies inside the circumcircle then the
three edges of that triangle are added to the edge buffer
and that triangle is removed.
*/
for (j=0;j<(*ntri);j++) {
if (complete[j])
continue;
x1 = pxyz[v[j].p1].x;
y1 = pxyz[v[j].p1].y;
x2 = pxyz[v[j].p2].x;
y2 = pxyz[v[j].p2].y;
x3 = pxyz[v[j].p3].x;
y3 = pxyz[v[j].p3].y;
inside = CircumCircle(xp,yp,x1,y1,x2,y2,x3,y3,&xc,&yc,&r);
if (xc < xp && ((xp-xc)*(xp-xc)) > r)
complete[j] = true;
if (inside) {
/* Check that we haven't exceeded the edge list size */
if (nedge+3 >= emax) {
emax += 100;
/*if ((edges = (IEDGE*)realloc(edges,emax*(long)sizeof(IEDGE))) == NULL) {
status = 3;
goto skip;
}*/
edges.resize(emax);
}
edges[nedge+0].p1 = v[j].p1;
edges[nedge+0].p2 = v[j].p2;
edges[nedge+1].p1 = v[j].p2;
edges[nedge+1].p2 = v[j].p3;
edges[nedge+2].p1 = v[j].p3;
edges[nedge+2].p2 = v[j].p1;
nedge += 3;
v[j] = v[(*ntri)-1];
complete[j] = complete[(*ntri)-1];
(*ntri)--;
j--;
}
}
/*
Tag multiple edges
Note: if all triangles are specified anticlockwise then all
interior edges are opposite pointing in direction.
*/
for (j=0;j<nedge-1;j++) {
for (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;
}
/* Shouldn't need the following, see note above */
if ((edges[j].p1 == edges[k].p1) && (edges[j].p2 == edges[k].p2)) {
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 (j=0;j<nedge;j++) {
if (edges[j].p1 < 0 || edges[j].p2 < 0)
continue;
if ((*ntri) >= trimax) {
status = 4;
goto skip;
}
v[*ntri].p1 = edges[j].p1;
v[*ntri].p2 = edges[j].p2;
v[*ntri].p3 = i;
complete[*ntri] = false;
(*ntri)++;
}
}
/*
Remove triangles with supertriangle vertices
These are triangles which have a vertex number greater than nv
*/
for (i=0;i<(*ntri);i++) {
if (v[i].p1 >= nv || v[i].p2 >= nv || v[i].p3 >= nv) {
v[i] = v[(*ntri)-1];
(*ntri)--;
i--;
}
}
skip:
//free(edges);
free(complete);
return(status);
}
void Triangulate(std::vector<float2>& pxyz, std::vector<int3>& triangles) {
int nv = (int)pxyz.size();
std::vector<int2> edges;
bool inside;
int i, j, k;
float xp, yp, x1, y1, x2, y2, x3, y3, xc, yc, r;
float xmin, xmax, ymin, ymax, xmid, ymid;
float dx, dy, dmax;
std::vector<bool> complete;
/*
Find the maximum and minimum vertex bounds.
This is to allow calculation of the bounding triangle
*/
xmin = pxyz[0].x;
ymin = pxyz[0].y;
xmax = xmin;
ymax = ymin;
for (i = 1; i < nv; i++) {
if (pxyz[i].x < xmin) xmin = pxyz[i].x;
if (pxyz[i].x > xmax) xmax = pxyz[i].x;
if (pxyz[i].y < ymin) ymin = pxyz[i].y;
if (pxyz[i].y > ymax) ymax = pxyz[i].y;
}
dx = xmax - xmin;
dy = ymax - ymin;
dmax = (dx > dy) ? dx : dy;
xmid = (xmax + xmin) *0.5f;
ymid = (ymax + ymin) *0.5f;
float scale = 20.0f;
triangles.clear();
pxyz.push_back(float2(xmid - scale * dmax, ymid - dmax));
pxyz.push_back(float2(xmid, ymid + scale * dmax));
pxyz.push_back(float2(xmid + scale * dmax, ymid - dmax));
triangles.push_back(int3( nv, nv + 1, nv + 2 ));
complete.push_back(false);
for (i = 0; i < (int)pxyz.size(); i++) {
xp = pxyz[i].x;
yp = pxyz[i].y;
edges.clear();
for (j = 0; j < (int)triangles.size(); j++) {
if (complete[j])
continue;
x1 = pxyz[triangles[j].x].x;
y1 = pxyz[triangles[j].x].y;
x2 = pxyz[triangles[j].y].x;
y2 = pxyz[triangles[j].y].y;
x3 = pxyz[triangles[j].z].x;
y3 = pxyz[triangles[j].z].y;
inside = CircumCircle(xp, yp, x1, y1, x2, y2, x3, y3, xc, yc, r);
if (xc + r < xp)complete[j] = true;
if (inside) {
edges.push_back(int2( triangles[j].x, triangles[j].y ));
edges.push_back(int2(triangles[j].y, triangles[j].z ));
edges.push_back(int2(triangles[j].z, triangles[j].x ));
triangles.erase(triangles.begin() + j);
complete.erase(complete.begin() + j);
j--;
}
}
/*
Tag multiple edges
Note: if all triangles are specified anticlockwise then all
interior edges are opposite pointing in direction.
*/
for (j = 0; j < (int)edges.size() - 1; j++) {
for (k = j + 1; k < (int)edges.size(); k++) {
if ((edges[j].x == edges[k].y) && (edges[j].y == edges[k].x)) {
edges[j] = int2(-1, -1 );
edges[k] = int2(-1, -1 );
}
/* Shouldn't need the following, see note above */
if ((edges[j].x == edges[k].x) && (edges[j].y == edges[k].y)) {
edges[j] = int2(-1, -1 );
edges[k] = int2(-1, -1 );
}
}
}
/*
Form new triangles for the current point
Skipping over any tagged edges.
All edges are arranged in clockwise order.
*/
for (j = 0; j < (int)edges.size(); j++) {
if (edges[j].x < 0 || edges[j].y < 0)
continue;
triangles.push_back(int3(edges[j].x, edges[j].y, i ));
complete.push_back(false);
}
}
}
int Triangulate(int nv, XYZ pxyz[], ITRIANGLE v[], int &ntri) {
int *complete = NULL;
IEDGE *edges = NULL;
IEDGE *p_EdgeTemp;
int nedge = 0;
int trimax, emax = 200;
int status = 0;
int inside;
int i, j, k;
double xp, yp, x1, y1, x2, y2, x3, y3, xc, yc, r;
double xmin, xmax, ymin, ymax, xmid, ymid;
double dx, dy, dmax;
/* Allocate memory for the completeness list, flag for each triangle */
trimax = 4 * nv;
complete = new int[trimax];
/* Allocate memory for the edge list */
edges = new IEDGE[emax];
/*
Find the maximum and minimum vertex bounds.
This is to allow calculation of the bounding triangle
*/
xmin = pxyz[0].x;
ymin = pxyz[0].y;
xmax = xmin;
ymax = ymin;
for(i = 1; i < nv; i++){
if (pxyz[i].x < xmin) xmin = pxyz[i].x;
if (pxyz[i].x > xmax) xmax = pxyz[i].x;
if (pxyz[i].y < ymin) ymin = pxyz[i].y;
if (pxyz[i].y > ymax) ymax = pxyz[i].y;
}
dx = xmax - xmin;
dy = ymax - ymin;
dmax = (dx > dy) ? dx : dy;
xmid = (xmax + xmin) / 2.0;
ymid = (ymax + ymin) / 2.0;
/*
Set up the supertriangle
his 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.
*/
pxyz[nv+0].x = xmid - 20 * dmax;
pxyz[nv+0].y = ymid - dmax;
pxyz[nv+1].x = xmid;
pxyz[nv+1].y = ymid + 20 * dmax;
pxyz[nv+2].x = xmid + 20 * dmax;
pxyz[nv+2].y = ymid - dmax;
v[0].p1 = nv;
v[0].p2 = nv+1;
v[0].p3 = nv+2;
complete[0] = false;
ntri = 1;
/*
Include each point one at a time into the existing mesh
*/
for(i = 0; i < nv; i++){
xp = pxyz[i].x;
yp = pxyz[i].y;
nedge = 0;
/*
Set up the edge buffer.
If the point (xp,yp) lies inside the circumcircle then the
three edges of that triangle are added to the edge buffer
and that triangle is removed.
*/
for(j = 0; j < ntri; j++){
if(complete[j]) continue;
x1 = pxyz[v[j].p1].x;
y1 = pxyz[v[j].p1].y;
x2 = pxyz[v[j].p2].x;
y2 = pxyz[v[j].p2].y;
x3 = pxyz[v[j].p3].x;
y3 = pxyz[v[j].p3].y;
inside = CircumCircle(xp, yp, x1, y1, x2, y2, x3, y3, xc, yc, r);
if (xc + r < xp)
// Suggested
// if (xc + r + EPSILON < xp)
complete[j] = true;
if(inside){
/* Check that we haven't exceeded the edge list size */
if(nedge + 3 >= emax){
emax += 100;
p_EdgeTemp = new IEDGE[emax];
for (int i = 0; i < nedge; i++) { // Fix by John Bowman
p_EdgeTemp[i] = edges[i];
}
delete []edges;
edges = p_EdgeTemp;
}
edges[nedge+0].p1 = v[j].p1;
edges[nedge+0].p2 = v[j].p2;
edges[nedge+1].p1 = v[j].p2;
edges[nedge+1].p2 = v[j].p3;
edges[nedge+2].p1 = v[j].p3;
edges[nedge+2].p2 = v[j].p1;
nedge += 3;
v[j] = v[ntri-1];
complete[j] = complete[ntri-1];
ntri--;
j--;
}
}
/*
Tag multiple edges
Note: if all triangles are specified anticlockwise then all
interior edges are opposite pointing in direction.
*/
for(j = 0; j < nedge - 1; j++){
for(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;
}
/* Shouldn't need the following, see note above */
if((edges[j].p1 == edges[k].p1) && (edges[j].p2 == edges[k].p2)){
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(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++;
}
}
/*
Remove triangles with supertriangle vertices
These are triangles which have a vertex number greater than nv
*/
for(i = 0; i < ntri; i++) {
if(v[i].p1 >= nv || v[i].p2 >= nv || v[i].p3 >= nv) {
v[i] = v[ntri-1];
ntri--;
i--;
}
}
delete[] edges;
delete[] complete;
return 0;
}
