/// <summary>
/// Get convex hull for 2D point cloud.
/// Returns null if less than 2 points provided.
/// Returns two edges with surface area of 0 if exactly two points provided.
/// </summary>
/// <param name="points">Point cloud, list of Vector2 elements.</param>
/// <returns>List of Edges defining the convex hull. Edges are not sorted but will have normals pointing away from the convex hull.</returns>
public static List <Edge> GetHull(List <Vector2> points)
{
ReViewFeedManager debug = ReViewFeedManager.Instance;
if (points.Count < 2)
{
// Not enough points to create a convex hull -> return null
return(null);
}
// Final list of convex hull edges
List <Edge> edges = new List <Edge>();
List <int> pointIndicesToProcess = new List <int>();
// Find min and max vertex from X axis
int minIndex = -1;
int maxIndex = -1;
double maxX = -Double.MaxValue;
double minX = Double.MaxValue;
for (int i = 0; i < points.Count; i++)
{
pointIndicesToProcess.Add(i);
if (points[i].X > maxX)
{
maxX = points[i].X;
maxIndex = i;
}
if (points[i].X < minX)
{
minX = points[i].X;
minIndex = i;
}
}
// Random points -> Introduces a bug
/*
* minIndex = SRandom.Index(points.Count);
* maxIndex = SRandom.Index(points.Count);
* if (maxIndex == minIndex)
* {
* maxIndex = (maxIndex + 1) % points.Count;
* }
*/
// Add initial two edges to processing list
List <Edge> edgesToProcess = new List <Edge>();
edgesToProcess.Add(new Edge(minIndex, maxIndex));
edgesToProcess.Add(new Edge(maxIndex, minIndex));
pointIndicesToProcess.Remove(minIndex);
pointIndicesToProcess.Remove(maxIndex);
#region Debug_Region_1
//
// REVIEW DEBUG RENDERING
// Add boxes for vertices and for initial lines in the processing list
//
for (int i = 0; i < points.Count; i++)
{
debug.AddBox(0, -1, new Matrix4x4(), new Vector3(points[i].x, points[i].y, 0.0), new Vector3(0.005, 0.005, 0.005), new Color32(255, 255, 0, 255));
}
debug.AdvanceDebugTimer();
debug.MapID(edgesToProcess[0], debug.AddLine(debug.DebugTimer, -1, points[minIndex], points[maxIndex], new Color32(200, 255, 0, 255)));
debug.MapID(edgesToProcess[1], debug.AddLine(debug.DebugTimer, -1, points[maxIndex], points[minIndex], new Color32(200, 255, 0, 255)));
debug.AdvanceDebugTimer();
#endregion
// Iterate until no more edges to process
while (edgesToProcess.Count > 0)
{
// Remove edge from processing list (it will either end up in the final edges list or get ignored)
Edge edgeToProcess = edgesToProcess[0];
edgesToProcess.RemoveAt(0);
#region Debug_Region_2
//
// REVIEW DEBUG RENDERING
// Remove edge being processed and add it with different color for this frame
//
debug.RemovePrimitive(debug.FindID(edgeToProcess), debug.DebugTimer);
debug.AddLine(debug.DebugTimer, debug.DebugTimerStep, points[edgeToProcess.A], points[edgeToProcess.B], new Color32(0, 0, 0, 255));
#endregion
double furthestDistance = -1.0;
int candidateIndex = -1;
int pointsInFrontCount = 0;
for (int i = 0; i < pointIndicesToProcess.Count; i++)
{
int pointIndex = pointIndicesToProcess[i];
Vector2 point = points[pointIndex];
if (!edgeToProcess.Contains(pointIndex) && edgeToProcess.PointInFront(points, point))
{
#region Debug_Region_3
//
// REVIEW DEBUG RENDERING
// Color vertex being checked to be "in front"
//
debug.AddBox(debug.DebugTimer, debug.DebugTimerStep, new Matrix4x4(), new Vector3(point.x, point.y, 0.0), new Vector3(0.0075, 0.0075, 0.0075), new Color32(0, 255, 0, 255));
#endregion
// This point is not part of edge and it is on the "front" side of the edge -> Check distance and mark as candidate
double distanceToEdge = edgeToProcess.DistanceToPoint(points, point);
if (distanceToEdge > furthestDistance)
{
furthestDistance = distanceToEdge;
candidateIndex = pointIndex;
}
pointsInFrontCount++;
}
#region Debug_Region_4
else
{
//
// REVIEW DEBUG RENDERING
// Color vertex being checked to not be "in front"
//
debug.AddBox(debug.DebugTimer, debug.DebugTimerStep, new Matrix4x4(), new Vector3(point.x, point.y, 0.0), new Vector3(0.0075, 0.0075, 0.0075), new Color32(255, 0, 0, 255));
}
#endregion
}
#region Debug_Region_5
debug.AdvanceDebugTimer();
#endregion
if (candidateIndex >= 0)
{
#region Debug_Region_6
//
// REVIEW DEBUG RENDERING
// Color vertex being selected as the furthest and "in front"
//
debug.AddBox(debug.DebugTimer, debug.DebugTimerStep, new Matrix4x4(), points[candidateIndex], new Vector3(0.0075, 0.0075, 0.0075), new Color32(0, 0, 0, 255));
#endregion
if (!edgeToProcess.PointInLine(points, points[candidateIndex]))
{
// Remove all points inside the new triangle
Triangle t = new Triangle(edgeToProcess.A, edgeToProcess.B, candidateIndex);
for (int i = 0; i < pointIndicesToProcess.Count; i++)
{
int pointIndex = pointIndicesToProcess[i];
if (t.Inside(points, points[pointIndex]))
{
pointIndicesToProcess.RemoveAt(i);
i--;
pointsInFrontCount--;
}
}
}
if (pointsInFrontCount == 0)
{
// New lines are part of the convex hull -> Don't add edgesToProcess
edges.Add(new Edge(edgeToProcess.A, candidateIndex));
edges.Add(new Edge(candidateIndex, edgeToProcess.B));
#region Debug_Region_7
//
// REVIEW DEBUG RENDERING
// Show convex hull lines added
//
long line_id_1 = debug.AddLine(debug.DebugTimer, -1, points[edgeToProcess.A], points[candidateIndex], new Color32(255, 255, 255, 255));
long line_id_2 = debug.AddLine(debug.DebugTimer, -1, points[candidateIndex], points[edgeToProcess.B], new Color32(255, 255, 255, 255));
debug.AddAnnotation(line_id_1, debug.DebugTimer, -1, "Hull Edge #" + (edges.Count - 1), new Color32(255, 255, 255, 255));
debug.AddAnnotation(line_id_2, debug.DebugTimer, -1, "Hull Edge #" + edges.Count, new Color32(255, 255, 255, 255));
#endregion
}
else
{
// Found point, add two new edges to process
edgesToProcess.Add(new Edge(edgeToProcess.A, candidateIndex));
edgesToProcess.Add(new Edge(candidateIndex, edgeToProcess.B));
#region Debug_Region_8
//
// REVIEW DEBUG RENDERING
// Show new lines added to be processed
//
debug.MapID(edgesToProcess[edgesToProcess.Count - 2], debug.AddLine(debug.DebugTimer, -1, points[edgeToProcess.A], points[candidateIndex], new Color32(200, 255, 0, 255)));
debug.MapID(edgesToProcess[edgesToProcess.Count - 1], debug.AddLine(debug.DebugTimer, -1, points[candidateIndex], points[edgeToProcess.B], new Color32(200, 255, 0, 255)));
#endregion
}
}
else
{
// No candidates found -> This is part of convex hull
edges.Add(new Edge(edgeToProcess.A, edgeToProcess.B));
#region Debug_Region_9
long line_id = debug.AddLine(debug.DebugTimer, -1, points[edgeToProcess.A], points[edgeToProcess.B], new Color32(255, 255, 255, 255));
debug.AddAnnotation(line_id, debug.DebugTimer, -1, "Hull Edge #" + edges.Count, new Color32(255, 255, 255, 255));
#endregion
}
#region Debug_Region_10
debug.AdvanceDebugTimer();
#endregion
}
#region Debug_Region_11
debug.RemoveAllAnnotations(debug.DebugTimer);
#endregion
return(edges);
}
/// <summary>
/// Delaunay triangulate point cloud with given convex hull.
/// Returns null if less than 3 points provided.
/// Using Tenamura-Merriam algorithm which does 'advancing front' starting with convexHull edges.
/// UNOPTIMAL IMPLEMENTATION! This will not deal with regular grids.
/// </summary>
/// <param name="points">Point cloud, list of Vector2 elements.</param>
/// <param name="points">Edge list, convex hull for point cloud.</param>
/// <returns>List of Edges defining the convex hull. Edges are not sorted but will have normals pointing away from the convex hull.</returns>
public static List <Triangle> Triangulate(List <Vector2> points, List <Edge> convexHull)
{
if (points.Count < 3)
{
// Not enough points to create triangulation -> return null
return(null);
}
#region Debug_Region_1
Vector3 LINE_ZOFFS = new Vector3(0, 0, 0.002);
int triCount = 0;
ReViewFeedManager debug = ReViewFeedManager.Instance;
long mesh_id = debug.AddMesh(debug.DebugTimer, -1, new Matrix4x4(), new Vector3(0, 0, 0.001), true);
#endregion
// Final list of convex hull edges
List <Triangle> triangles = new List <Triangle>();
List <Edge> edgesToProcess = new List <Edge>();
foreach (Edge edge in convexHull)
{
edgesToProcess.Add(edge.GetFlipped());
}
while (edgesToProcess.Count > 0)
{
Edge edgeToProcess = edgesToProcess[0];
edgesToProcess.RemoveAt(0);
int circumCircleFailCount = 0;
bool triangleAdded = false;
// Try to find third vertex for the edgeToProcess to form a triangle
List <int> testedCandidates = new List <int>();
for (int i = 0; i < points.Count; i++)
{
if (edgeToProcess.Contains(i))
{
// This point is part of the edge already -> Skip
continue;
}
if (!edgeToProcess.PointInFront(points, points[i]))
{
// This point is not in front -> Skip
continue;
}
if (testedCandidates.Contains(i))
{
// Already processed -> Skip
continue;
}
testedCandidates.Add(i);
Triangle t = new Triangle(edgeToProcess.A, edgeToProcess.B, i);
if (GeometryMath.IsTriangleDegenerate(points[t.A], points[t.B], points[t.C]))
{
// Degenerate triangle (no surface area so points are all in a line) -> Ignore this and continue
continue;
}
// Check circumcircle validity for this triangle
bool pointsInCircumCircle = false;
for (int j = 0; j < points.Count; j++)
{
if (i == j || edgeToProcess.Contains(j))
{
continue;
}
Vector2 otherPoint = points[j];
// Some other point -> Check if in circumcircle
if (t.PointInCircumcircle(points, otherPoint))
{
#region Debug_Region_2
// Add debug drawing for failed circumcircle tests
Vector2 center;
double radius;
if (GeometryMath.GetCircumcircle(points[edgeToProcess.A], points[edgeToProcess.B], points[i], out center, out radius))
{
Color32 debugColor = Color32.FromHSVA((double)circumCircleFailCount / 16.0 % 1.0, 0.9, 1.0, 1.0);
// Circumcircle
debug.AddCircle(debug.DebugTimer, debug.DebugTimerStep, (Vector3)center + LINE_ZOFFS, radius, new Vector3(0, 0, 1), 64, debugColor);
// Point that was inside (fails the test)
debug.AddBox(debug.DebugTimer, debug.DebugTimerStep, new Matrix4x4(new Quaternion(new Vector3(0, 0, 1), Math.PI * 0.25)), new Vector3(points[j].x, points[j].y, 0.0), new Vector3(0.015, 0.015, 0.015), debugColor);
// Lines to show triangle tested
debug.AddLine(debug.DebugTimer, debug.DebugTimerStep, (Vector3)points[edgeToProcess.A] + LINE_ZOFFS, (Vector3)points[edgeToProcess.B] + LINE_ZOFFS, new Color32(0, 0, 0, 255));
debug.AddLine(debug.DebugTimer, debug.DebugTimerStep, (Vector3)points[edgeToProcess.B] + LINE_ZOFFS, (Vector3)points[i] + LINE_ZOFFS, debugColor);
debug.AddLine(debug.DebugTimer, debug.DebugTimerStep, (Vector3)points[i] + LINE_ZOFFS, (Vector3)points[edgeToProcess.A] + LINE_ZOFFS, debugColor);
debug.AdvanceDebugTimer();
}
#endregion
circumCircleFailCount++;
if (!testedCandidates.Contains(j))
{
i = j - 1;
}
pointsInCircumCircle = true;
break;
}
}
if (pointsInCircumCircle)
{
// Points in circumcircle -> Skip
continue;
}
// Update edgesToProcess list by adding two new edges if they are not one of the convex hull edges
Edge newEdgeA = new Edge(edgeToProcess.A, i);
Edge newEdgeB = new Edge(i, edgeToProcess.B);
// Check if new edges would be the same as unprocessed convex-hull edges
for (int j = 0; j < edgesToProcess.Count; j++)
{
Edge convexEdge = edgesToProcess[j];
if (convexEdge == newEdgeA)
{
// Don't add newEdgeA and remove convexEdge
newEdgeA = null;
edgesToProcess.RemoveAt(j);
j--;
}
else if (convexEdge == newEdgeB)
{
// Don't add newEdgeA and remove convexEdge
newEdgeB = null;
edgesToProcess.RemoveAt(j);
j--;
}
}
// Check if new edges would be shared with existing triangle edges
for (int j = 0; j < triangles.Count; j++)
{
if (triangles[j].Contains(newEdgeA))
{
newEdgeA = null;
}
if (triangles[j].Contains(newEdgeB))
{
newEdgeB = null;
}
if (newEdgeA == null && newEdgeB == null)
{
break;
}
}
if (newEdgeA != null)
{
edgesToProcess.Add(newEdgeA);
}
if (newEdgeB != null)
{
edgesToProcess.Add(newEdgeB);
}
// Valid triangle -> Add to delaunay set
triangles.Add(t);
#region Debug_Region_3
// Debug graphics for triangle to be added
Vector2 triCenter;
double triRadius;
// Add circumcircle
GeometryMath.GetCircumcircle(points[t.A], points[t.B], points[t.C], out triCenter, out triRadius);
debug.AddCircle(debug.DebugTimer, debug.DebugTimerStep, (Vector3)triCenter + LINE_ZOFFS, triRadius, new Vector3(0, 0, 1), 64, new Color32(255, 255, 0, 255));
// Add triangle lines
debug.AddLine(debug.DebugTimer, -1, (Vector3)points[t.A] + LINE_ZOFFS, (Vector3)points[t.B] + LINE_ZOFFS, new Color32(0, 0, 0, 255));
debug.AddLine(debug.DebugTimer, -1, (Vector3)points[t.B] + LINE_ZOFFS, (Vector3)points[t.C] + LINE_ZOFFS, new Color32(0, 0, 0, 255));
debug.AddLine(debug.DebugTimer, -1, (Vector3)points[t.C] + LINE_ZOFFS, (Vector3)points[t.A] + LINE_ZOFFS, new Color32(0, 0, 0, 255));
// Add triangle
debug.AddTriangle(mesh_id, debug.DebugTimer, points[t.A], points[t.B], points[t.C], new Color32(32, 255, 32, 128));
// Progress for console window
triCount++;
if (triCount % 100 == 0)
{
Console.WriteLine("TriCount {0}", triCount);
}
debug.AdvanceDebugTimer();
#endregion
triangleAdded = true;
// Processed 'edgeToProcess' -> Proceed to next in the list
break;
}
#region Debug_Region_4
// Debug graphics for the case when no triangle could be added for given edge
if (!triangleAdded)
{
long line_id = debug.AddLine(debug.DebugTimer, debug.DebugTimerStep, (Vector3)points[edgeToProcess.A] + LINE_ZOFFS * 2, (Vector3)points[edgeToProcess.B] + LINE_ZOFFS * 2, new Color32(255, 0, 0, 255));
debug.AddAnnotation(line_id, debug.DebugTimer, debug.DebugTimerStep, "No valid triangle could be generated!", new Color32(255, 255, 255, 255));
debug.AdvanceDebugTimer();
}
#endregion
}
Console.WriteLine("Done triangles");
return(triangles);
}