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211function removeDoublyDefinedEdges(edgeBuffer){
edgeBuffer.sort((e1,e2)=>{
if(e1[0]<e2[0]){
return -1;
}else if(e1[0]>e2[0]){
return 1;
}
if(e1[1]<e2[1]){
return -1
}else if(e1[1]>e2[1]){
return 1;
}
return 0;
})
const newEdgeBuffer = [];
for(let j=0;j<edgeBuffer.length;j++){
const curr = edgeBuffer[j]
if(j>0
&& edgeBuffer[j-1][0]===curr[0]
&& edgeBuffer[j-1][1]===curr[1]){
if(newEdgeBuffer.length>0
&& newEdgeBuffer[newEdgeBuffer.length-1][0]===curr[0]
&& newEdgeBuffer[newEdgeBuffer.length-1][1]===curr[1]){
newEdgeBuffer.pop();
}
}else{
newEdgeBuffer.push(curr)
}
}
return newEdgeBuffer;
}
const _Delaunay = ()=>{
function Delaunay(verts){
function triangleCircumcenter(vertIds){
const x1=verts[vertIds[0]][0],
x2=verts[vertIds[1]][0],
x3=verts[vertIds[2]][0],
y1=verts[vertIds[0]][1],
y2=verts[vertIds[1]][1],
y3=verts[vertIds[2]][1];
const center = vec3.fromValues(
((y2-y1) * (y3*y3 - y1*y1 + x3*x3 - x1*x1) - (y3-y1)* (y2*y2 - y1*y1 + x2*x2 - x1*x1))/ (2 * (x3-x1) * (y2-y1) - 2 * ((x2-x1) * (y3-y1))),
((x2-x1) * (x3*x3 - x1*x1 + y3*y3 - y1*y1) - (x3-x1)* (x2*x2 - x1*x1 + y2*y2 - y1*y1))/ (2 * (y3-y1) * (x2-x1) - 2 * ((y2-y1) * (x3-x1)))
,z);
return center;
}
function triangleCentroid(vertIds){
const x1=verts[vertIds[0]][0],
x2=verts[vertIds[1]][0],
x3=verts[vertIds[2]][0],
y1=verts[vertIds[0]][1],
y2=verts[vertIds[1]][1],
y3=verts[vertIds[2]][1];
return vec3.fromValues((x1+x2+x3)/3,(y1+y2+y3)/3,z)
}
const triangles = [];
/* each triangle: {
vertIds:[],
center:vec3,
radius:Number,
}
*/
// determine the super triangle, add to the end of vertices list
if(verts.length===0){
return triangles;
}
var xLBound = verts[0][0], xUBound=verts[0][0], yLBound=verts[0][1], yUBound=verts[0][1];
const z = verts[0][2];
for(let i=1;i<verts.length;i++){
xLBound = Math.min(verts[i][0],xLBound);
xUBound = Math.max(verts[i][0],xUBound);
yLBound = Math.min(verts[i][1],yLBound);
yUBound = Math.max(verts[i][1],yUBound);
}
verts.push(vec3.fromValues(
(xLBound+xUBound)/2,yUBound+(yUBound-yLBound)/2,z
))
verts.push(vec3.fromValues(
xLBound-(xUBound-xLBound),yLBound,z
))
verts.push(vec3.fromValues(
xUBound+(xUBound-xLBound),yLBound,z
))
const superTVertIds = [verts.length-1,verts.length-2,verts.length-3];
const superTCenter = triangleCircumcenter(superTVertIds);
triangles.push({
vertIds:superTVertIds,
center:superTCenter,
centroid: triangleCentroid(superTVertIds),
radius:vec3.distance(superTCenter,verts[verts.length-1]),
})
for(let i=0;i<verts.length;i++){
var edgeBuffer = [];
for(let j=0;j<triangles.length;j++){
const triangle = triangles[j];
if(triangle.radius>=vec3.distance(verts[i],triangle.center)){
// if the point lies in the triangle circumcircle then
// - add the three triangle edges to the edge buffer
// - remove the triangle from the triangle list
var v1Id = triangle.vertIds[0],
v2Id = triangle.vertIds[1],
v3Id = triangle.vertIds[2];
if(i!==v1Id && i!==v2Id){
edgeBuffer.push([Math.min(v1Id,v2Id),Math.max(v1Id,v2Id)]);
}
if(i!==v2Id && i!==v3Id){
edgeBuffer.push([Math.min(v2Id,v3Id),Math.max(v2Id,v3Id)]);
}
if(i!==v1Id && i!==v3Id){
edgeBuffer.push([Math.min(v3Id,v1Id),Math.max(v3Id,v1Id)]);
}
triangles.splice(j,1);
j--;
}
}
// delete all doubly specified edges from the edge buffer
edgeBuffer = removeDoublyDefinedEdges(edgeBuffer)
// add to the triangle list all triangles formed between the point and the edges of the enclosing polygon
for(let j=0;j<edgeBuffer.length;j++){
const vertIds = [i,edgeBuffer[j][0],edgeBuffer[j][1]];
const center = triangleCircumcenter(vertIds);
const radius = vec3.distance(center,verts[i]);
if(isNaN(radius)){
// 3 verts are in a line
continue;
}
const newTriangle = {
vertIds,
center,
centroid: triangleCentroid(vertIds),
radius,
}
triangles.push(newTriangle);
}
}
// remove any triangles 1. from the triangle list that use the supertriangle vertices, 2. centroid of which is outside of the polygon (using winding number algorithm)
for(let i=0;i<triangles.length;i++){
const triangle = triangles[i]
if(triangle.vertIds.indexOf(verts.length-1)>-1
||triangle.vertIds.indexOf(verts.length-2)>-1
||triangle.vertIds.indexOf(verts.length-3)>-1
||isInsidePolygon(triangle.centroid,verts.slice(0,verts.length-3))===false){
triangles.splice(i,1);
i--;
}
}
// remove the supertriangle vertices from the vertex list
verts.splice(verts.length-3,3);
return triangles;
}
function isInsidePolygon(p, edgeVerts){
function isLeft(p1,p2,p){
return (p2[0]-p1[0])*(p[1]-p1[1])-(p2[1]-p1[1])*(p[0]-p1[0])
}
var windingNumber = 0;
for(let i=0;i<edgeVerts.length;i++){
// edge edgeVerts[i] to edgeVerts[i+1]
var p1 = edgeVerts[i], p2;
if(i===edgeVerts.length-1){
p2 = edgeVerts[0]
}else{
p2 = edgeVerts[i+1];
}
if(p1[1]<=p[1]){
if(p2[1]>p[1]){ // An upward crossing
if(isLeft(p1,p2,p)>0){
windingNumber++;
}
}
}else{
if(p2[1]<=p[1]){
if(isLeft(p1,p2,p)<0){
windingNumber--;
}
}
}
}
return windingNumber!==0;
}
return Delaunay
}