//Remove the supertriangle
IEnumerator 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);
//VISUALZ
ShowTriangles(triangulationData);
yield return(new WaitForSeconds(controller.pauseTime));
}
//VISUALZ - show the colored mesh when its finished
controller.shouldDisplayColoredMesh = true;
yield return(null);
}
//Is an edge between p1 and p2 a constraint?
//private static bool IsEdgeAConstraint(MyVector2 p1, MyVector2 p2, List<MyVector2> constraints)
//{
// for (int i = 0; i < constraints.Count; i++)
// {
// MyVector2 c_p1 = constraints[i];
// MyVector2 c_p2 = constraints[MathUtility.ClampListIndex(i + 1, constraints.Count)];
// if (AreTwoEdgesTheSame(p1, p2, c_p1, c_p2))
// {
// return true;
// }
// }
// return false;
//}
//Is an edge crossing another edge?
private static bool IsEdgeCrossingEdge(MyVector2 e1_p1, MyVector2 e1_p2, MyVector2 e2_p1, MyVector2 e2_p2)
{
//We will here run into floating point precision issues so we have to be careful
//To solve that you can first check the end points
//and modify the line-line intersection algorithm to include a small epsilon
//First check if the edges are sharing a point, if so they are not crossing
if (e1_p1.Equals(e2_p1) || e1_p1.Equals(e2_p2) || e1_p2.Equals(e2_p1) || e1_p2.Equals(e2_p2))
{
return(false);
}
//Then check if the lines are intersecting
if (!_Intersections.LineLine(new Edge2(e1_p1, e1_p2), new Edge2(e2_p1, e2_p2), includeEndPoints: false))
{
return(false);
}
return(true);
}
//Find a triangle which has an edge going from p1 to p2
//private static HalfEdgeFace2 FindTriangleWithEdge(MyVector2 p1, MyVector2 p2, HalfEdgeData2 triangleData)
//{
// HashSet<HalfEdge2> edges = triangleData.edges;
// foreach (HalfEdge2 e in edges)
// {
// //An edge is going TO a vertex
// MyVector2 e_p1 = e.prevEdge.v.position;
// MyVector2 e_p2 = e.v.position;
// if (e_p1.Equals(p1) && e_p2.Equals(p2))
// {
// return e.face;
// }
// }
// return null;
//}
//Find all half-edges that are constraint
private static HashSet <HalfEdge2> FindAllConstraintEdges(List <MyVector2> constraints, HalfEdgeData2 triangleData)
{
HashSet <HalfEdge2> constrainEdges = new HashSet <HalfEdge2>();
//Create a new set with all constrains, and as we discover new constraints, we delete constrains, which will make searching faster
//A constraint can only exist once!
HashSet <Edge2> constraintsEdges = new HashSet <Edge2>();
for (int i = 0; i < constraints.Count; i++)
{
MyVector2 c_p1 = constraints[i];
MyVector2 c_p2 = constraints[MathUtility.ClampListIndex(i + 1, constraints.Count)];
constraintsEdges.Add(new Edge2(c_p1, c_p2));
}
//All edges we have to search
HashSet <HalfEdge2> edges = triangleData.edges;
foreach (HalfEdge2 e in edges)
{
//An edge is going TO a vertex
MyVector2 e_p1 = e.prevEdge.v.position;
MyVector2 e_p2 = e.v.position;
//Is this edge a constraint?
foreach (Edge2 c_edge in constraintsEdges)
{
if (e_p1.Equals(c_edge.p1) && e_p2.Equals(c_edge.p2))
{
constrainEdges.Add(e);
constraintsEdges.Remove(c_edge);
//Move on to the next edge
break;
}
}
//We have found all constraint, so don't need to search anymore
if (constraintsEdges.Count == 0)
{
break;
}
}
return(constrainEdges);
}
//
// 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 IEnumerator RestoreDelaunayTriangulation(MyVector2 c_p1, MyVector2 c_p2, List <HalfEdge2> newEdges, HalfEdgeData2 triangleData, Normalizer2 normalizer)
{
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;
//
// PAUSE AND VISUALIZE
//
visualizeController.DisplayMeshMain(triangleData, normalizer);
yield return(new WaitForSeconds(0.5f));
}
}
//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;
}
}
}
private IEnumerator RunAlgorithm(List <MyVector2> points)
{
//The list with points on the convex hull
List <MyVector2> pointsOnConvexHull = new List <MyVector2>();
//Step 0. Normalize the data to range [0, 1] or everything will break at larger sizes :(
//Make sure the data is already normalized!!!
//Step 1. Find the vertex with the smallest x coordinate
//If several points have the same x coordinate, find the one with the smallest y
MyVector2 startPos = points[0];
for (int i = 1; i < points.Count; i++)
{
MyVector2 testPos = points[i];
//Because of precision issues, we use a small value to test if they are the same
if (testPos.x < startPos.x || ((Mathf.Abs(testPos.x - startPos.x) < MathUtility.EPSILON && testPos.y < startPos.y)))
{
startPos = points[i];
}
}
//This vertex is always on the convex hull
pointsOnConvexHull.Add(startPos);
//VISUALIZE
ShowHull(pointsOnConvexHull, null);
yield return(new WaitForSeconds(controller.pauseTime));
//But we can't remove it from the list of all points because we need it to stop the algorithm
//points.Remove(startPos);
//Step 2. Loop to find the other points on the hull
MyVector2 previousPoint = pointsOnConvexHull[0];
int counter = 0;
while (true)
{
//We might have colinear points, so we need a list to save all points added this iteration
List <MyVector2> pointsToAddToTheHull = new List <MyVector2>();
//Pick next point randomly
MyVector2 nextPoint = points[Random.Range(0, points.Count)];
//If we are coming from the first point on the convex hull
//then we are not allowed to pick it as next point, so we have to try again
if (previousPoint.Equals(pointsOnConvexHull[0]) && nextPoint.Equals(pointsOnConvexHull[0]))
{
counter += 1;
continue;
}
//VISUALIZE
ShowHull(pointsOnConvexHull, new List <MyVector2>()
{
nextPoint
});
//ShowActivePoint(nextPoint);
yield return(new WaitForSeconds(controller.pauseTime));
//This point is assumed to be on the convex hull
pointsToAddToTheHull.Add(nextPoint);
//But this randomly selected point might not be the best next point, so we have to see if we can improve
//by finding a point that is more to the right
//We also have to check if this point has colinear points if it happens to be on the hull
for (int i = 0; i < points.Count; i++)
{
MyVector2 testPoint = points[i];
//Dont test the point we picked randomly
//Or the point we are coming from which might happen when we move from the first point on the hull
if (testPoint.Equals(nextPoint) || testPoint.Equals(previousPoint))
{
continue;
}
//VISUALIZE
//ShowHull(pointsOnConvexHull, new List<MyVector2>() { testPoint });
ShowActivePoint(testPoint);
yield return(new WaitForSeconds(controller.pauseTime));
//Where is the test point in relation to the line between the point we are coming from
//which we know is on the hull, and the point we think is on the hull
LeftOnRight pointRelation = _Geometry.IsPoint_Left_On_Right_OfVector(previousPoint, nextPoint, testPoint);
//The test point is on the line, so we have found a colinear point
if (pointRelation == LeftOnRight.On)
{
pointsToAddToTheHull.Add(testPoint);
}
//To the right = better point, so pick it as next point we want to test if it is on the hull
else if (pointRelation == LeftOnRight.Right)
{
nextPoint = testPoint;
//Clear colinear points because they belonged to the old point which was worse
pointsToAddToTheHull.Clear();
pointsToAddToTheHull.Add(nextPoint);
//We dont have to start over because the previous points weve gone through were worse
//VISUALIZE
ShowHull(pointsOnConvexHull, pointsToAddToTheHull);
yield return(new WaitForSeconds(controller.pauseTime));
}
//To the left = worse point so do nothing
}
//Sort this list, so we can add the colinear points in correct order
pointsToAddToTheHull = pointsToAddToTheHull.OrderBy(n => MyVector2.SqrMagnitude(n - previousPoint)).ToList();
pointsOnConvexHull.AddRange(pointsToAddToTheHull);
//Remove the points that are now on the convex hull, which should speed up the algorithm
//Or will it be slower because it also takes some time to remove points?
for (int i = 0; i < pointsToAddToTheHull.Count; i++)
{
points.Remove(pointsToAddToTheHull[i]);
}
//The point we are coming from in the next iteration
previousPoint = pointsOnConvexHull[pointsOnConvexHull.Count - 1];
//Have we found the first point on the hull? If so we have completed the hull
if (previousPoint.Equals(pointsOnConvexHull[0]))
{
//Then remove it because it is the same as the first point, and we want a convex hull with no duplicates
pointsOnConvexHull.RemoveAt(pointsOnConvexHull.Count - 1);
//Stop the loop!
break;
}
//Safety
if (counter > 100000)
{
Debug.Log("Stuck in endless loop when generating convex hull with jarvis march");
break;
}
counter += 1;
}
//Dont forget to unnormalize the points!
//VISUALIZE
ShowHull(pointsOnConvexHull, new List <MyVector2>()
{
pointsOnConvexHull[0]
});
yield return(null);
}
