//Remove the supertriangle
private static void RemoveSuperTriangle(Triangle2 superTriangle, HalfEdgeData2 triangulationData)
{
//The super triangle doesnt exists anymore because we have split it into many new triangles
//But we can use its vertices to figure out which new triangles (or faces belonging to the triangle)
//we should delete
HashSet <HalfEdgeFace2> triangleFacesToDelete = new HashSet <HalfEdgeFace2>();
//Loop through all vertices belongin to the triangulation
foreach (HalfEdgeVertex2 v in triangulationData.vertices)
{
//If the face attached to this vertex already exists in the list of faces we want to delete
//Then dont add it again
if (triangleFacesToDelete.Contains(v.edge.face))
{
continue;
}
MyVector2 v1 = v.position;
//Is this vertex in the triangulation a vertex in the super triangle?
if (v1.Equals(superTriangle.p1) || v1.Equals(superTriangle.p2) || v1.Equals(superTriangle.p3))
{
triangleFacesToDelete.Add(v.edge.face);
}
}
//Debug.Log("Triangles to delete: " + trianglesToDelete.Count);
//Delete the new triangles with vertices attached to the super triangle
foreach (HalfEdgeFace2 f in triangleFacesToDelete)
{
HalfEdgeHelpMethods.DeleteTriangleFace(f, triangulationData, shouldSetOppositeToNull: true);
}
}
//Flip edges until we get a delaunay triangulation
private static void FlipEdges(HalfEdgeData2 triangleData)
{
//The edges we want to flip
HashSet <HalfEdge2> edges = triangleData.edges;
//To avoid getting stuck in infinite loop
int safety = 0;
//Count how many edges we have flipped, which may be interesting to display
int flippedEdges = 0;
while (true)
{
safety += 1;
if (safety > 100000)
{
Debug.Log("Stuck in endless loop when flipping edges to get a Delaunay triangulation");
break;
}
bool hasFlippedEdge = false;
//Search through all edges to see if we can flip an edge
foreach (HalfEdge2 thisEdge in edges)
{
//Is this edge sharing an edge with another triangle, otherwise its a border, and then we cant flip the edge
if (thisEdge.oppositeEdge == null)
{
continue;
}
//The positions of the vertices belonging to the two triangles that we might flip
//a-c should be the edge that we might flip
MyVector2 a = thisEdge.v.position;
MyVector2 b = thisEdge.nextEdge.v.position;
MyVector2 c = thisEdge.nextEdge.nextEdge.v.position;
MyVector2 d = thisEdge.oppositeEdge.nextEdge.v.position;
//Test if we should flip this edge
if (DelaunayMethods.ShouldFlipEdge(a, b, c, d))
{
flippedEdges += 1;
hasFlippedEdge = true;
HalfEdgeHelpMethods.FlipTriangleEdge(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 in " + flippedEdges + " flips");
break;
}
}
}
//Insert a new point in the triangulation we already have, so we need at least one triangle
public static void InsertNewPointInTriangulation(MyVector2 p, HalfEdgeData2 triangulationData, ref int missedPoints, ref int flippedEdges)
{
//Step 5. Insert the new point in the triangulation
//Find the existing triangle the point is in
HalfEdgeFace2 f = PointTriangulationIntersection.TriangulationWalk(p, null, triangulationData);
//We couldnt find a triangle maybe because the point is not in the triangulation?
if (f == null)
{
missedPoints += 1;
}
//Delete this triangle and form 3 new triangles by connecting p to each of the vertices in the old triangle
HalfEdgeHelpMethods.SplitTriangleFaceAtPoint(f, p, triangulationData);
//Step 6. Initialize stack. Place all triangles which are adjacent to the edges opposite p on a LIFO stack
//The report says we should place triangles, but it's easier to place edges with our data structure
Stack <HalfEdge2> trianglesToInvestigate = new Stack <HalfEdge2>();
AddTrianglesOppositePToStack(p, trianglesToInvestigate, triangulationData);
//Step 7. Restore delaunay triangulation
//While the stack is not empty
int safety = 0;
while (trianglesToInvestigate.Count > 0)
{
safety += 1;
if (safety > 1000000)
{
Debug.Log("Stuck in infinite loop when restoring delaunay in incremental sloan algorithm");
break;
}
//Step 7.1. Remove a triangle from the stack
HalfEdge2 edgeToTest = trianglesToInvestigate.Pop();
//Step 7.2. Do we need to flip this edge?
//If p is outside or on the circumcircle for this triangle, we have a delaunay triangle and can return to next loop
MyVector2 a = edgeToTest.v.position;
MyVector2 b = edgeToTest.prevEdge.v.position;
MyVector2 c = edgeToTest.nextEdge.v.position;
//abc are here counter-clockwise
if (DelaunayMethods.ShouldFlipEdgeStable(a, b, c, p))
{
HalfEdgeHelpMethods.FlipTriangleEdge(edgeToTest);
//Step 7.3. Place any triangles which are now opposite p on the stack
AddTrianglesOppositePToStack(p, trianglesToInvestigate, triangulationData);
flippedEdges += 1;
}
}
}
//
// Remove all triangles that are inside the constraint
//
//This assumes the vertices in the constraint are ordered clockwise
private static void RemoveSuperfluousTriangles(HalfEdgeData2 triangleData, List <MyVector2> constraints)
{
//This assumes we have at least 3 vertices in the constraint because we cant delete triangles inside a line
if (constraints.Count < 3)
{
return;
}
HashSet <HalfEdgeFace2> trianglesToBeDeleted = FindTrianglesWithinConstraint(triangleData, constraints);
//Delete the triangles
foreach (HalfEdgeFace2 t in trianglesToBeDeleted)
{
HalfEdgeHelpMethods.DeleteTriangleFace(t, triangleData, true);
}
}
//
// Try to restore the delaunay triangulation by flipping newly created edges
//
//This process is similar to when we created the original delaunay triangulation
//This step can maybe be skipped if you just want a triangulation and Ive noticed its often not flipping any triangles
private static void RestoreDelaunayTriangulation(MyVector2 c_p1, MyVector2 c_p2, List <HalfEdge2> newEdges)
{
int safety = 0;
int flippedEdges = 0;
//Repeat 4.1 - 4.3 until no further swaps take place
while (true)
{
safety += 1;
if (safety > 100000)
{
Debug.Log("Stuck in endless loop when delaunay after fixing constrained edges");
break;
}
bool hasFlippedEdge = false;
//Step 4.1. Loop over each edge in the list of newly created edges
for (int j = 0; j < newEdges.Count; j++)
{
HalfEdge2 e = newEdges[j];
//Step 4.2. Let the newly created edge be defined by the vertices
MyVector2 v_k = e.v.position;
MyVector2 v_l = e.prevEdge.v.position;
//If this edge is equal to the constrained edge, then skip to step 4.1
//because we are not allowed to flip the constrained edge
if ((v_k.Equals(c_p1) && v_l.Equals(c_p2)) || (v_l.Equals(c_p1) && v_k.Equals(c_p2)))
{
continue;
}
//Step 4.3. If the two triangles that share edge v_k and v_l don't satisfy the delaunay criterion,
//so that a vertex of one of the triangles is inside the circumcircle of the other triangle, flip the edge
//The third vertex of the triangle belonging to this edge
MyVector2 v_third_pos = e.nextEdge.v.position;
//The vertice belonging to the triangle on the opposite side of the edge and this vertex is not a part of the edge
MyVector2 v_opposite_pos = e.oppositeEdge.nextEdge.v.position;
//Test if we should flip this edge
if (DelaunayMethods.ShouldFlipEdge(v_l, v_k, v_third_pos, v_opposite_pos))
{
//Flip the edge
hasFlippedEdge = true;
HalfEdgeHelpMethods.FlipTriangleEdge(e);
flippedEdges += 1;
}
}
//We have searched through all edges and havent found an edge to flip, so we cant improve anymore
if (!hasFlippedEdge)
{
Debug.Log("Found a constrained delaunay triangulation in " + flippedEdges + " flips");
break;
}
}
}
//
// Remove the edges that intersects with a constraint by flipping triangles
//
//The idea here is that all possible triangulations for a set of points can be found
//by systematically swapping the diagonal in each convex quadrilateral formed by a pair of triangles
//So we will test all possible arrangements and will always find a triangulation which includes the constrained edge
private static List <HalfEdge2> RemoveIntersectingEdges(MyVector2 v_i, MyVector2 v_j, Queue <HalfEdge2> intersectingEdges)
{
List <HalfEdge2> newEdges = new List <HalfEdge2>();
int safety = 0;
//While some edges still cross the constrained edge, do steps 3.1 and 3.2
while (intersectingEdges.Count > 0)
{
safety += 1;
if (safety > 100000)
{
Debug.Log("Stuck in infinite loop when fixing constrained edges");
break;
}
//Step 3.1. Remove an edge from the list of edges that intersects the constrained edge
HalfEdge2 e = intersectingEdges.Dequeue();
//The vertices belonging to the two triangles
MyVector2 v_k = e.v.position;
MyVector2 v_l = e.prevEdge.v.position;
MyVector2 v_3rd = e.nextEdge.v.position;
//The vertex belonging to the opposite triangle and isn't shared by the current edge
MyVector2 v_opposite_pos = e.oppositeEdge.nextEdge.v.position;
//Step 3.2. If the two triangles don't form a convex quadtrilateral
//place the edge back on the list of intersecting edges (because this edge cant be flipped)
//and go to step 3.1
if (!_Geometry.IsQuadrilateralConvex(v_k, v_l, v_3rd, v_opposite_pos))
{
intersectingEdges.Enqueue(e);
continue;
}
else
{
//Flip the edge like we did when we created the delaunay triangulation
HalfEdgeHelpMethods.FlipTriangleEdge(e);
//The new diagonal is defined by the vertices
MyVector2 v_m = e.v.position;
MyVector2 v_n = e.prevEdge.v.position;
//If this new diagonal intersects with the constrained edge, add it to the list of intersecting edges
if (IsEdgeCrossingEdge(v_i, v_j, v_m, v_n))
{
intersectingEdges.Enqueue(e);
}
//Place it in the list of newly created edges
else
{
newEdges.Add(e);
}
}
}
return(newEdges);
}
