//Alternative 1. Triangulate with some algorithm - then flip edges until we have a delaunay triangulation
public static List <Triangle> TriangulateByFlippingEdges(List <Vector3> sites)
{
//Step 1. Triangulate the points with some algorithm
//Vector3 to vertex
List <Vertex> vertices = new List <Vertex>();
for (int i = 0; i < sites.Count; i++)
{
vertices.Add(new Vertex(sites[i]));
}
//Triangulate the convex hull of the sites
List <Triangle> triangles = IncrementalTriangulationAlgorithm.TriangulatePoints(vertices);
//List triangles = TriangulatePoints.TriangleSplitting(vertices);
//Step 2. Change the structure from triangle to half-edge to make it faster to flip edges
List <HalfEdge> halfEdges = Delaunay.TransformFromTriangleToHalfEdge(triangles);
//Step 3. Flip edges until we have a delaunay triangulation
int safety = 0;
int flippedEdges = 0;
while (true)
{
safety += 1;
if (safety > 100000)
{
Debug.WriteLine("Stuck in endless loop");
break;
}
bool hasFlippedEdge = false;
//Search through all edges to see if we can flip an edge
for (int i = 0; i < halfEdges.Count; i++)
{
HalfEdge thisEdge = halfEdges[i];
//Is this edge sharing an edge, otherwise its a border, and then we cant flip the edge
if (thisEdge.oppositeEdge == null)
{
continue;
}
//The vertices belonging to the two triangles, c-a are the edge vertices, b belongs to this triangle
Vertex a = thisEdge.v;
Vertex b = thisEdge.nextEdge.v;
Vertex c = thisEdge.prevEdge.v;
Vertex d = thisEdge.oppositeEdge.nextEdge.v;
Vector2 aPos = a.GetPos2D_XZ();
Vector2 bPos = b.GetPos2D_XZ();
Vector2 cPos = c.GetPos2D_XZ();
Vector2 dPos = d.GetPos2D_XZ();
//Use the circle test to test if we need to flip this edge
if (Delaunay.IsPointInsideOutsideOrOnCircle(aPos, bPos, cPos, dPos) < 0f)
{
//Are these the two triangles that share this edge forming a convex quadrilateral?
//Otherwise the edge cant be flipped
if (Delaunay.IsQuadrilateralConvex(aPos, bPos, cPos, dPos))
{
//If the new triangle after a flip is not better, then dont flip
//This will also stop the algoritm from ending up in an endless loop
if (Delaunay.IsPointInsideOutsideOrOnCircle(bPos, cPos, dPos, aPos) < 0f)
{
continue;
}
//Flip the edge
flippedEdges += 1;
hasFlippedEdge = true;
FlipEdge(thisEdge);
}
}
}
//We have searched through all edges and havent found an edge to flip, so we have a Delaunay triangulation!
if (!hasFlippedEdge)
{
//Debug.Log("Found a delaunay triangulation");
break;
}
}
//Debug.Log("Flipped edges: " + flippedEdges);
//Dont have to convert from half edge to triangle because the algorithm will modify the objects, which belongs to the
//original triangles, so the triangles have the data we need
return(triangles);
}
