//Method 2. Triangulation walk
//This assumes there are no holes in the mesh
//And that we have a super-triangle around the triangulation
private static void FindIntersectingEdges_TriangleWalk(HalfEdgeData2 triangleData, MyVector2 c_p1, MyVector2 c_p2, List <HalfEdge2> intersectingEdges)
{
//Step 1. Begin at a triangle connected to the constraint edges's vertex c_p1
HalfEdgeFace2 f = null;
foreach (HalfEdgeFace2 testFace in triangleData.faces)
{
//The edges the triangle consists of
HalfEdge2 e1 = testFace.edge;
HalfEdge2 e2 = e1.nextEdge;
HalfEdge2 e3 = e2.nextEdge;
//Does one of these edges include the first vertex in the constraint edge
if (e1.v.position.Equals(c_p1) || e2.v.position.Equals(c_p1) || e3.v.position.Equals(c_p1))
{
f = testFace;
break;
}
}
//Step2. Walk around p1 until we find a triangle with an edge that intersects with the edge p1-p2
//Step3. March from one triangle to the next in the general direction of p2
}
//Find all triangles opposite of vertex p
//But we will find all edges opposite to p, and from these edges we can find the triangles
private static void AddTrianglesOppositePToStack(MyVector2 p, Stack <HalfEdge2> trianglesOppositeP, HalfEdgeData2 triangulationData)
{
//Find a vertex at position p and then rotate around it, triangle-by-triangle, to find all opposite edges
HalfEdgeVertex2 rotateAroundThis = null;
foreach (HalfEdgeVertex2 v in triangulationData.vertices)
{
if (v.position.Equals(p))
{
rotateAroundThis = v;
}
}
//Which triangle is this vertex a part of, so we know when we have rotated all the way around
HalfEdgeFace2 tStart = rotateAroundThis.edge.face;
HalfEdgeFace2 tCurrent = null;
int safety = 0;
while (tCurrent != tStart)
{
safety += 1;
if (safety > 10000)
{
Debug.Log("Stuck in endless loop when finding opposite edges in Delaunay Sloan");
break;
}
//The edge opposite to p
HalfEdge2 edgeOppositeRotateVertex = rotateAroundThis.edge.nextEdge.oppositeEdge;
//Try to add the edge to the list iof triangles we are interested in
//Null might happen if we are at the border
//A stack might include duplicates so we have to check for that as well
if (edgeOppositeRotateVertex != null && !trianglesOppositeP.Contains(edgeOppositeRotateVertex))
{
trianglesOppositeP.Push(edgeOppositeRotateVertex);
}
//Rotate left - this assumes we can always rotate left so no holes are allowed
//and neither can we investigate one of the vertices thats a part of the supertriangle
//which we dont need to worry about because p is never a part of the supertriangle
rotateAroundThis = rotateAroundThis.edge.oppositeEdge.v;
//In which triangle are we now?
tCurrent = rotateAroundThis.edge.face;
}
}
//
// Find which triangles are within a constraint
//
public static HashSet <HalfEdgeFace2> FindTrianglesWithinConstraint(HalfEdgeData2 triangleData, List <MyVector2> constraints)
{
HashSet <HalfEdgeFace2> trianglesToDelete = new HashSet <HalfEdgeFace2>();
//Store the triangles we flood fill in this queue
Queue <HalfEdgeFace2> trianglesToCheck = new Queue <HalfEdgeFace2>();
//Step 1. Find all half-edges in the current triangulation which are constraint
//Maybe faster to find all constraintEdges for ALL constraints because we are doing this per hole and hull
//We have to find ALL because some triangles are not connected and will thus be missed if we find just a single start-triangle
//Is also needed when flood-filling so we dont jump over a constraint
HashSet <HalfEdge2> constraintEdges = FindAllConstraintEdges(constraints, triangleData);
//Each edge is associated with a face which should be deleted
foreach (HalfEdge2 e in constraintEdges)
{
if (!trianglesToCheck.Contains(e.face))
{
trianglesToCheck.Enqueue(e.face);
}
}
//Step 2. Find the rest of the triangles within the constraint by using a flood-fill algorithm
int safety = 0;
List <HalfEdge2> edgesToCheck = new List <HalfEdge2>();
while (true)
{
safety += 1;
if (safety > 100000)
{
Debug.Log("Stuck in infinite loop when looking for triangles within constraint");
break;
}
//Stop if we are out of neighbors
if (trianglesToCheck.Count == 0)
{
break;
}
//Pick the first triangle in the list and investigate its neighbors
HalfEdgeFace2 t = trianglesToCheck.Dequeue();
//Add it for deletion
trianglesToDelete.Add(t);
//Investigate the triangles on the opposite sides of these edges
edgesToCheck.Clear();
edgesToCheck.Add(t.edge);
edgesToCheck.Add(t.edge.nextEdge);
edgesToCheck.Add(t.edge.nextEdge.nextEdge);
//A triangle is a neighbor within the constraint if:
//- The neighbor is not an outer border meaning no neighbor exists
//- If we have not already visited the neighbor
//- If the edge between the neighbor and this triangle is not a constraint
foreach (HalfEdge2 e in edgesToCheck)
{
//No neighbor exists
if (e.oppositeEdge == null)
{
continue;
}
HalfEdgeFace2 neighbor = e.oppositeEdge.face;
//We have already visited this neighbor
if (trianglesToDelete.Contains(neighbor) || trianglesToCheck.Contains(neighbor))
{
continue;
}
//This edge is a constraint and we can't jump across constraints
if (constraintEdges.Contains(e))
{
continue;
}
trianglesToCheck.Enqueue(neighbor);
}
}
return(trianglesToDelete);
}
IEnumerator InsertPoints(HashSet <MyVector2> points, HalfEdgeData2 triangulationData, Triangle2 superTriangle)
{
//VISUALZ
ShowTriangles(triangulationData);
//VISUALZ - dont show the colored mesh until its finished because its flickering
controller.shouldDisplayColoredMesh = false;
yield return(new WaitForSeconds(controller.pauseTime));
//Step 4. Loop over each point we want to insert and do Steps 5-7
//These are for display purposes only
int missedPoints = 0;
int flippedEdges = 0;
foreach (MyVector2 p in points)
{
//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);
//VISUALZ
//Display the point as a black circle
ShowCircle(p);
yield return(new WaitForSeconds(controller.pauseTime));
ShowTriangles(triangulationData);
yield return(new WaitForSeconds(controller.pauseTime));
//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;
//VISUALZ
controller.flipText.text = "Flipped edges: " + flippedEdges;
ShowTriangles(triangulationData);
yield return(new WaitForSeconds(controller.pauseTime));
}
}
}
//Dont show the last point we added
controller.ResetBlackMeshes();
//Step 8. Delete the vertices belonging to the supertriangle
StartCoroutine(RemoveSuperTriangle(superTriangle, triangulationData));
yield return(null);
}
