public static List<Vertices> ConvexPartition(Vertices vertices)
{
Polygon poly = new Polygon();
foreach (Vector2 vertex in vertices)
{
poly.Points.Add(new TriangulationPoint(vertex.X, vertex.Y));
}
DTSweepContext tcx = new DTSweepContext();
tcx.PrepareTriangulation(poly);
DTSweep.Triangulate(tcx);
List<Vertices> results = new List<Vertices>();
foreach (DelaunayTriangle triangle in poly.Triangles)
{
Vertices v = new Vertices();
foreach (TriangulationPoint p in triangle.Points)
{
v.Add(new Vector2((float)p.X, (float)p.Y));
}
results.Add(v);
}
return results;
}
/// <summary>
/// Triangulate simple polygon with holes
/// </summary>
public static void Triangulate(DTSweepContext tcx)
{
tcx.CreateAdvancingFront();
Sweep(tcx);
// Finalize triangulation
if (tcx.TriangulationMode == TriangulationMode.Polygon)
{
FinalizationPolygon(tcx);
}
else
{
FinalizationConvexHull(tcx);
}
tcx.Done();
}
/// <summary>
/// Start sweeping the Y-sorted point set from bottom to top
/// </summary>
static void Sweep( DTSweepContext tcx )
{
List<TriangulationPoint> points = tcx.Points;
for( int i = 1; i < points.Count; i++ )
{
TriangulationPoint point = points[i];
AdvancingFrontNode node = PointEvent( tcx, point );
if( point.HasEdges )
{
foreach( DTSweepConstraint e in point.Edges )
{
EdgeEvent( tcx, e, node );
}
}
tcx.Update( null );
}
}
/// <summary>
/// Decompose the polygon into several smaller non-concave polygon.
/// </summary>
public static List<Vertices> ConvexPartition(Vertices vertices)
{
if (vertices.Count <= 3)
return new List<Vertices> { vertices };
Polygon poly = new Polygon();
foreach (Vector2 vertex in vertices)
poly.Points.Add(new TriangulationPoint(vertex.X, vertex.Y));
if (vertices.Holes != null)
{
foreach (Vertices holeVertices in vertices.Holes)
{
Polygon hole = new Polygon();
foreach (Vector2 vertex in holeVertices)
hole.Points.Add(new TriangulationPoint(vertex.X, vertex.Y));
poly.AddHole(hole);
}
}
DTSweepContext tcx = new DTSweepContext();
tcx.PrepareTriangulation(poly);
DTSweep.Triangulate(tcx);
List<Vertices> results = new List<Vertices>();
foreach (DelaunayTriangle triangle in poly.Triangles)
{
Vertices v = new Vertices();
foreach (TriangulationPoint p in triangle.Points)
{
v.Add(new Vector2((float)p.X, (float)p.Y));
}
results.Add(v);
}
return results;
}
private static void FlipEdgeEvent(DTSweepContext tcx, TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle t, TriangulationPoint p)
{
DelaunayTriangle ot = t.NeighborAcross(p);
TriangulationPoint op = ot.OppositePoint(t, p);
if (ot == null)
{
// If we want to integrate the fillEdgeEvent do it here
// With current implementation we should never get here
throw new InvalidOperationException("[BUG:FIXME] FLIP failed due to missing triangle");
}
if (t.GetConstrainedEdgeAcross(p))
{
throw new Exception("Intersecting Constraints");
}
bool inScanArea = TriangulationUtil.InScanArea(p, t.PointCCW(p), t.PointCW(p), op);
if (inScanArea)
{
// Lets rotate shared edge one vertex CW
RotateTrianglePair(t, p, ot, op);
tcx.MapTriangleToNodes(t);
tcx.MapTriangleToNodes(ot);
if (p == eq && op == ep)
{
if (eq == tcx.EdgeEvent.ConstrainedEdge.Q &&
ep == tcx.EdgeEvent.ConstrainedEdge.P)
{
if (tcx.IsDebugEnabled)
{
Debug.WriteLine("[FLIP] - constrained edge done"); // TODO: remove
}
t.MarkConstrainedEdge(ep, eq);
ot.MarkConstrainedEdge(ep, eq);
Legalize(tcx, t);
Legalize(tcx, ot);
}
else
{
if (tcx.IsDebugEnabled)
{
Debug.WriteLine("[FLIP] - subedge done"); // TODO: remove
}
// XXX: I think one of the triangles should be legalized here?
}
}
else
{
if (tcx.IsDebugEnabled)
{
Debug.WriteLine("[FLIP] - flipping and continuing with triangle still crossing edge");
}
// TODO: remove
Orientation o = TriangulationUtil.Orient2d(eq, op, ep);
t = NextFlipTriangle(tcx, o, t, ot, p, op);
FlipEdgeEvent(tcx, ep, eq, t, p);
}
}
else
{
TriangulationPoint newP = NextFlipPoint(ep, eq, ot, op);
FlipScanEdgeEvent(tcx, ep, eq, t, ot, newP);
EdgeEvent(tcx, ep, eq, t, p);
}
}
/// <summary>
/// Creates a new front triangle and legalize it
/// </summary>
private static AdvancingFrontNode NewFrontTriangle(DTSweepContext tcx, TriangulationPoint point, AdvancingFrontNode node)
{
DelaunayTriangle triangle = new DelaunayTriangle(point, node.Point, node.Next.Point);
triangle.MarkNeighbor(node.Triangle);
tcx.Triangles.Add(triangle);
AdvancingFrontNode newNode = new AdvancingFrontNode(point);
newNode.Next = node.Next;
newNode.Prev = node;
node.Next.Prev = newNode;
node.Next = newNode;
tcx.AddNode(newNode); // XXX: BST
if (!Legalize(tcx, triangle))
{
tcx.MapTriangleToNodes(triangle);
}
return newNode;
}
private static bool IsShallow(DTSweepContext tcx, AdvancingFrontNode node)
{
double height;
if (tcx.Basin.leftHighest)
{
height = tcx.Basin.leftNode.Point.Y - node.Point.Y;
}
else
{
height = tcx.Basin.rightNode.Point.Y - node.Point.Y;
}
if (tcx.Basin.width > height)
{
return true;
}
return false;
}
private static void FinalizationPolygon(DTSweepContext tcx)
{
// Get an Internal triangle to start with
DelaunayTriangle t = tcx.aFront.Head.Next.Triangle;
TriangulationPoint p = tcx.aFront.Head.Next.Point;
while (!t.GetConstrainedEdgeCW(p))
{
t = t.NeighborCCW(p);
}
// Collect interior triangles constrained by edges
tcx.MeshClean(t);
}
private static void FillRightConvexEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
{
// Next concave or convex?
if (TriangulationUtil.Orient2d(node.Next.Point, node.Next.Next.Point, node.Next.Next.Next.Point) ==
Orientation.CCW)
{
// Concave
FillRightConcaveEdgeEvent(tcx, edge, node.Next);
}
else
{
// Convex
// Next above or below edge?
if (TriangulationUtil.Orient2d(edge.Q, node.Next.Next.Point, edge.P) == Orientation.CCW)
{
// Below
FillRightConvexEdgeEvent(tcx, edge, node.Next);
}
else
{
// Above
}
}
}
private static void FillRightAboveEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
{
while (node.Next.Point.X < edge.P.X)
{
// Check if next node is below the edge
Orientation o1 = TriangulationUtil.Orient2d(edge.Q, node.Next.Point, edge.P);
if (o1 == Orientation.CCW)
{
FillRightBelowEdgeEvent(tcx, edge, node);
}
else
{
node = node.Next;
}
}
}
/// <summary>
/// Find closes node to the left of the new point and
/// create a new triangle. If needed new holes and basins
/// will be filled to.
/// </summary>
private static AdvancingFrontNode PointEvent(DTSweepContext tcx, TriangulationPoint point)
{
AdvancingFrontNode node = tcx.LocateNode(point);
AdvancingFrontNode newNode = NewFrontTriangle(tcx, point, node);
// Only need to check +epsilon since point never have smaller
// x value than node due to how we fetch nodes from the front
if (point.X <= node.Point.X + TriangulationUtil.EPSILON)
{
Fill(tcx, node);
}
tcx.AddNode(newNode);
FillAdvancingFront(tcx, newNode);
return newNode;
}
static void FillLeftBelowEdgeEvent( DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node )
{
if( node.Point.X > edge.P.X )
{
if( TriangulationUtil.Orient2d( node.Point, node.Prev.Point, node.Prev.Prev.Point ) == Orientation.CW )
{
// Concave
FillLeftConcaveEdgeEvent( tcx, edge, node );
}
else
{
// Convex
FillLeftConvexEdgeEvent( tcx, edge, node );
// Retry this one
FillLeftBelowEdgeEvent( tcx, edge, node );
}
}
}
private static void EdgeEvent(DTSweepContext tcx, TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle triangle, TriangulationPoint point)
{
if (IsEdgeSideOfTriangle(triangle, ep, eq))
{
return;
}
TriangulationPoint p1 = triangle.PointCCW(point);
Orientation o1 = TriangulationUtil.Orient2d(eq, p1, ep);
if (o1 == Orientation.Collinear)
{
if (triangle.Contains(eq, p1))
{
triangle.MarkConstrainedEdge(eq, p1);
// We are modifying the constraint maybe it would be better to
// not change the given constraint and just keep a variable for the new constraint
tcx.EdgeEvent.ConstrainedEdge.Q = p1;
triangle = triangle.NeighborAcross(point);
EdgeEvent(tcx, ep, p1, triangle, p1);
}
else
{
throw new PointOnEdgeException("EdgeEvent - Point on constrained edge not supported yet");
}
if (tcx.IsDebugEnabled)
{
Debug.WriteLine("EdgeEvent - Point on constrained edge");
}
return;
}
TriangulationPoint p2 = triangle.PointCW(point);
Orientation o2 = TriangulationUtil.Orient2d(eq, p2, ep);
if (o2 == Orientation.Collinear)
{
if (triangle.Contains(eq, p2))
{
triangle.MarkConstrainedEdge(eq, p2);
// We are modifying the constraint maybe it would be better to
// not change the given constraint and just keep a variable for the new constraint
tcx.EdgeEvent.ConstrainedEdge.Q = p2;
triangle = triangle.NeighborAcross(point);
EdgeEvent(tcx, ep, p2, triangle, p2);
}
else
{
throw new PointOnEdgeException("EdgeEvent - Point on constrained edge not supported yet");
}
if (tcx.IsDebugEnabled)
{
Debug.WriteLine("EdgeEvent - Point on constrained edge");
}
return;
}
if (o1 == o2)
{
// Need to decide if we are rotating CW or CCW to get to a triangle
// that will cross edge
if (o1 == Orientation.CW)
{
triangle = triangle.NeighborCCW(point);
}
else
{
triangle = triangle.NeighborCW(point);
}
EdgeEvent(tcx, ep, eq, triangle, point);
}
else
{
// This triangle crosses constraint so lets flippin start!
FlipEdgeEvent(tcx, ep, eq, triangle, point);
}
}
/// <summary>
/// If this is a Delaunay Triangulation of a pointset we need to fill so the triangle mesh gets a ConvexHull
/// </summary>
private static void FinalizationConvexHull(DTSweepContext tcx)
{
DelaunayTriangle t1, t2;
AdvancingFrontNode n1 = tcx.aFront.Head.Next;
AdvancingFrontNode n2 = n1.Next;
TurnAdvancingFrontConvex(tcx, n1, n2);
// TODO: implement ConvexHull for lower right and left boundary
// Lets remove triangles connected to the two "algorithm" points
// XXX: When the first the nodes are points in a triangle we need to do a flip before
// removing triangles or we will lose a valid triangle.
// Same for last three nodes!
// !!! If I implement ConvexHull for lower right and left boundary this fix should not be
// needed and the removed triangles will be added again by default
n1 = tcx.aFront.Tail.Prev;
if (n1.Triangle.Contains(n1.Next.Point) && n1.Triangle.Contains(n1.Prev.Point))
{
t1 = n1.Triangle.NeighborAcross(n1.Point);
RotateTrianglePair(n1.Triangle, n1.Point, t1, t1.OppositePoint(n1.Triangle, n1.Point));
tcx.MapTriangleToNodes(n1.Triangle);
tcx.MapTriangleToNodes(t1);
}
n1 = tcx.aFront.Head.Next;
if (n1.Triangle.Contains(n1.Prev.Point) && n1.Triangle.Contains(n1.Next.Point))
{
t1 = n1.Triangle.NeighborAcross(n1.Point);
RotateTrianglePair(n1.Triangle, n1.Point, t1, t1.OppositePoint(n1.Triangle, n1.Point));
tcx.MapTriangleToNodes(n1.Triangle);
tcx.MapTriangleToNodes(t1);
}
// Lower right boundary
TriangulationPoint first = tcx.aFront.Head.Point;
n2 = tcx.aFront.Tail.Prev;
t1 = n2.Triangle;
TriangulationPoint p1 = n2.Point;
n2.Triangle = null;
do
{
tcx.RemoveFromList(t1);
p1 = t1.PointCCW(p1);
if (p1 == first)
{
break;
}
t2 = t1.NeighborCCW(p1);
t1.Clear();
t1 = t2;
} while (true);
// Lower left boundary
first = tcx.aFront.Head.Next.Point;
p1 = t1.PointCW(tcx.aFront.Head.Point);
t2 = t1.NeighborCW(tcx.aFront.Head.Point);
t1.Clear();
t1 = t2;
while (p1 != first) //TODO: Port note. This was do while before.
{
tcx.RemoveFromList(t1);
p1 = t1.PointCCW(p1);
t2 = t1.NeighborCCW(p1);
t1.Clear();
t1 = t2;
}
// Remove current head and tail node now that we have removed all triangles attached
// to them. Then set new head and tail node points
tcx.aFront.Head = tcx.aFront.Head.Next;
tcx.aFront.Head.Prev = null;
tcx.aFront.Tail = tcx.aFront.Tail.Prev;
tcx.aFront.Tail.Next = null;
tcx.FinalizeTriangulation();
}
/// <summary>
/// Returns true if triangle was legalized
/// </summary>
private static bool Legalize(DTSweepContext tcx, DelaunayTriangle t)
{
// To legalize a triangle we start by finding if any of the three edges
// violate the Delaunay condition
for (int i = 0; i < 3; i++)
{
// TODO: fix so that cEdge is always valid when creating new triangles then we can check it here
// instead of below with ot
if (t.EdgeIsDelaunay[i])
{
continue;
}
DelaunayTriangle ot = t.Neighbors[i];
if (ot != null)
{
TriangulationPoint p = t.Points[i];
TriangulationPoint op = ot.OppositePoint(t, p);
int oi = ot.IndexOf(op);
// If this is a Constrained Edge or a Delaunay Edge(only during recursive legalization)
// then we should not try to legalize
if (ot.EdgeIsConstrained[oi] || ot.EdgeIsDelaunay[oi])
{
t.EdgeIsConstrained[i] = ot.EdgeIsConstrained[oi];
// XXX: have no good way of setting this property when creating new triangles so lets set it here
continue;
}
bool inside = TriangulationUtil.SmartIncircle(p, t.PointCCW(p), t.PointCW(p), op);
if (inside)
{
// Lets mark this shared edge as Delaunay
t.EdgeIsDelaunay[i] = true;
ot.EdgeIsDelaunay[oi] = true;
// Lets rotate shared edge one vertex CW to legalize it
RotateTrianglePair(t, p, ot, op);
// We now got one valid Delaunay Edge shared by two triangles
// This gives us 4 new edges to check for Delaunay
// Make sure that triangle to node mapping is done only one time for a specific triangle
bool notLegalized = !Legalize(tcx, t);
if (notLegalized)
{
tcx.MapTriangleToNodes(t);
}
notLegalized = !Legalize(tcx, ot);
if (notLegalized)
{
tcx.MapTriangleToNodes(ot);
}
// Reset the Delaunay edges, since they only are valid Delaunay edges
// until we add a new triangle or point.
// XXX: need to think about this. Can these edges be tried after we
// return to previous recursive level?
t.EdgeIsDelaunay[i] = false;
ot.EdgeIsDelaunay[oi] = false;
// If triangle have been legalized no need to check the other edges since
// the recursive legalization will handles those so we can end here.
return(true);
}
}
}
return(false);
}
private static void FillEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
{
if (tcx.EdgeEvent.Right)
{
FillRightAboveEdgeEvent(tcx, edge, node);
}
else
{
FillLeftAboveEdgeEvent(tcx, edge, node);
}
}
private static void FillLeftConcaveEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
{
Fill(tcx, node.Prev);
if (node.Prev.Point != edge.P)
{
// Next above or below edge?
if (TriangulationUtil.Orient2d(edge.Q, node.Prev.Point, edge.P) == Orientation.CW)
{
// Below
if (TriangulationUtil.Orient2d(node.Point, node.Prev.Point, node.Prev.Prev.Point) == Orientation.CW)
{
// Next is concave
FillLeftConcaveEdgeEvent(tcx, edge, node);
}
else
{
// Next is convex
}
}
}
}
/// <summary>
/// We will traverse the entire advancing front and fill it to form a convex hull.
/// </summary>
private static void TurnAdvancingFrontConvex(DTSweepContext tcx, AdvancingFrontNode b, AdvancingFrontNode c)
{
AdvancingFrontNode first = b;
while (c != tcx.aFront.Tail)
{
if (TriangulationUtil.Orient2d(b.Point, c.Point, c.Next.Point) == Orientation.CCW)
{
// [b,c,d] Concave - fill around c
Fill(tcx, c);
c = c.Next;
}
else
{
// [b,c,d] Convex
if (b != first && TriangulationUtil.Orient2d(b.Prev.Point, b.Point, c.Point) == Orientation.CCW)
{
// [a,b,c] Concave - fill around b
Fill(tcx, b);
b = b.Prev;
}
else
{
// [a,b,c] Convex - nothing to fill
b = c;
c = c.Next;
}
}
}
}
private static void FillRightBelowEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
{
if (node.Point.X < edge.P.X) // needed?
{
if (TriangulationUtil.Orient2d(node.Point, node.Next.Point, node.Next.Next.Point) == Orientation.CCW)
{
// Concave
FillRightConcaveEdgeEvent(tcx, edge, node);
}
else
{
// Convex
FillRightConvexEdgeEvent(tcx, edge, node);
// Retry this one
FillRightBelowEdgeEvent(tcx, edge, node);
}
}
}
private static void EdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
{
try
{
tcx.EdgeEvent.ConstrainedEdge = edge;
tcx.EdgeEvent.Right = edge.P.X > edge.Q.X;
if (IsEdgeSideOfTriangle(node.Triangle, edge.P, edge.Q))
{
return;
}
// For now we will do all needed filling
// TODO: integrate with flip process might give some better performance
// but for now this avoid the issue with cases that needs both flips and fills
FillEdgeEvent(tcx, edge, node);
EdgeEvent(tcx, edge.P, edge.Q, node.Triangle, edge.Q);
}
catch (PointOnEdgeException e)
{
Debug.WriteLine("Skipping Edge: {0}", e.Message);
}
}
/// <summary>
/// If this is a Delaunay Triangulation of a pointset we need to fill so the triangle mesh gets a ConvexHull
/// </summary>
private static void FinalizationConvexHull(DTSweepContext tcx)
{
DelaunayTriangle t1, t2;
AdvancingFrontNode n1 = tcx.aFront.Head.Next;
AdvancingFrontNode n2 = n1.Next;
TurnAdvancingFrontConvex(tcx, n1, n2);
// TODO: implement ConvexHull for lower right and left boundary
// Lets remove triangles connected to the two "algorithm" points
// XXX: When the first the nodes are points in a triangle we need to do a flip before
// removing triangles or we will lose a valid triangle.
// Same for last three nodes!
// !!! If I implement ConvexHull for lower right and left boundary this fix should not be
// needed and the removed triangles will be added again by default
n1 = tcx.aFront.Tail.Prev;
if (n1.Triangle.Contains(n1.Next.Point) && n1.Triangle.Contains(n1.Prev.Point))
{
t1 = n1.Triangle.NeighborAcross(n1.Point);
RotateTrianglePair(n1.Triangle, n1.Point, t1, t1.OppositePoint(n1.Triangle, n1.Point));
tcx.MapTriangleToNodes(n1.Triangle);
tcx.MapTriangleToNodes(t1);
}
n1 = tcx.aFront.Head.Next;
if (n1.Triangle.Contains(n1.Prev.Point) && n1.Triangle.Contains(n1.Next.Point))
{
t1 = n1.Triangle.NeighborAcross(n1.Point);
RotateTrianglePair(n1.Triangle, n1.Point, t1, t1.OppositePoint(n1.Triangle, n1.Point));
tcx.MapTriangleToNodes(n1.Triangle);
tcx.MapTriangleToNodes(t1);
}
// Lower right boundary
TriangulationPoint first = tcx.aFront.Head.Point;
n2 = tcx.aFront.Tail.Prev;
t1 = n2.Triangle;
TriangulationPoint p1 = n2.Point;
n2.Triangle = null;
do
{
tcx.RemoveFromList(t1);
p1 = t1.PointCCW(p1);
if (p1 == first) break;
t2 = t1.NeighborCCW(p1);
t1.Clear();
t1 = t2;
} while (true);
// Lower left boundary
first = tcx.aFront.Head.Next.Point;
p1 = t1.PointCW(tcx.aFront.Head.Point);
t2 = t1.NeighborCW(tcx.aFront.Head.Point);
t1.Clear();
t1 = t2;
while (p1 != first) //TODO: Port note. This was do while before.
{
tcx.RemoveFromList(t1);
p1 = t1.PointCCW(p1);
t2 = t1.NeighborCCW(p1);
t1.Clear();
t1 = t2;
}
// Remove current head and tail node now that we have removed all triangles attached
// to them. Then set new head and tail node points
tcx.aFront.Head = tcx.aFront.Head.Next;
tcx.aFront.Head.Prev = null;
tcx.aFront.Tail = tcx.aFront.Tail.Prev;
tcx.aFront.Tail.Next = null;
tcx.FinalizeTriangulation();
}
private static void EdgeEvent(DTSweepContext tcx, TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle triangle, TriangulationPoint point)
{
if (IsEdgeSideOfTriangle(triangle, ep, eq))
return;
TriangulationPoint p1 = triangle.PointCCW(point);
Orientation o1 = TriangulationUtil.Orient2d(eq, p1, ep);
if (o1 == Orientation.Collinear)
{
if (triangle.Contains(eq, p1))
{
triangle.MarkConstrainedEdge(eq, p1);
// We are modifying the constraint maybe it would be better to
// not change the given constraint and just keep a variable for the new constraint
tcx.EdgeEvent.ConstrainedEdge.Q = p1;
triangle = triangle.NeighborAcross(point);
EdgeEvent(tcx, ep, p1, triangle, p1);
}
else
{
throw new PointOnEdgeException("EdgeEvent - Point on constrained edge not supported yet");
}
return;
}
TriangulationPoint p2 = triangle.PointCW(point);
Orientation o2 = TriangulationUtil.Orient2d(eq, p2, ep);
if (o2 == Orientation.Collinear)
{
if (triangle.Contains(eq, p2))
{
triangle.MarkConstrainedEdge(eq, p2);
// We are modifying the constraint maybe it would be better to
// not change the given constraint and just keep a variable for the new constraint
tcx.EdgeEvent.ConstrainedEdge.Q = p2;
triangle = triangle.NeighborAcross(point);
EdgeEvent(tcx, ep, p2, triangle, p2);
}
else
{
throw new PointOnEdgeException("EdgeEvent - Point on constrained edge not supported yet");
}
return;
}
if (o1 == o2)
{
// Need to decide if we are rotating CW or CCW to get to a triangle
// that will cross edge
if (o1 == Orientation.CW)
{
triangle = triangle.NeighborCCW(point);
}
else
{
triangle = triangle.NeighborCW(point);
}
EdgeEvent(tcx, ep, eq, triangle, point);
}
else
{
// This triangle crosses constraint so lets flippin start!
FlipEdgeEvent(tcx, ep, eq, triangle, point);
}
}
private static void FlipEdgeEvent(DTSweepContext tcx, TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle t, TriangulationPoint p)
{
DelaunayTriangle ot = t.NeighborAcross(p);
TriangulationPoint op = ot.OppositePoint(t, p);
if (ot == null)
{
// If we want to integrate the fillEdgeEvent do it here
// With current implementation we should never get here
throw new InvalidOperationException("[BUG:FIXME] FLIP failed due to missing triangle");
}
if (t.GetConstrainedEdgeAcross(p))
{
throw new Exception("Intersecting Constraints");
}
bool inScanArea = TriangulationUtil.InScanArea(p, t.PointCCW(p), t.PointCW(p), op);
if (inScanArea)
{
// Lets rotate shared edge one vertex CW
RotateTrianglePair(t, p, ot, op);
tcx.MapTriangleToNodes(t);
tcx.MapTriangleToNodes(ot);
if (p == eq && op == ep)
{
if (eq == tcx.EdgeEvent.ConstrainedEdge.Q
&& ep == tcx.EdgeEvent.ConstrainedEdge.P)
{
t.MarkConstrainedEdge(ep, eq);
ot.MarkConstrainedEdge(ep, eq);
Legalize(tcx, t);
Legalize(tcx, ot);
}
else
{
// XXX: I think one of the triangles should be legalized here?
}
}
else
{
// TODO: remove
Orientation o = TriangulationUtil.Orient2d(eq, op, ep);
t = NextFlipTriangle(tcx, o, t, ot, p, op);
FlipEdgeEvent(tcx, ep, eq, t, p);
}
}
else
{
TriangulationPoint newP = NextFlipPoint(ep, eq, ot, op);
FlipScanEdgeEvent(tcx, ep, eq, t, ot, newP);
EdgeEvent(tcx, ep, eq, t, p);
}
}
/// <summary>
/// Adds a triangle to the advancing front to fill a hole.
/// </summary>
/// <param name="tcx"></param>
/// <param name="node">middle node, that is the bottom of the hole</param>
private static void Fill(DTSweepContext tcx, AdvancingFrontNode node)
{
DelaunayTriangle triangle = new DelaunayTriangle(node.Prev.Point, node.Point, node.Next.Point);
// TODO: should copy the cEdge value from neighbor triangles
// for now cEdge values are copied during the legalize
triangle.MarkNeighbor(node.Prev.Triangle);
triangle.MarkNeighbor(node.Triangle);
tcx.Triangles.Add(triangle);
// Update the advancing front
node.Prev.Next = node.Next;
node.Next.Prev = node.Prev;
tcx.RemoveNode(node);
// If it was legalized the triangle has already been mapped
if (!Legalize(tcx, triangle))
{
tcx.MapTriangleToNodes(triangle);
}
}
/// <summary>
/// Scan part of the FlipScan algorithm<br>
/// When a triangle pair isn't flippable we will scan for the next
/// point that is inside the flip triangle scan area. When found
/// we generate a new flipEdgeEvent
/// </summary>
/// <param name="tcx"></param>
/// <param name="ep">last point on the edge we are traversing</param>
/// <param name="eq">first point on the edge we are traversing</param>
/// <param name="flipTriangle">the current triangle sharing the point eq with edge</param>
/// <param name="t"></param>
/// <param name="p"></param>
private static void FlipScanEdgeEvent(DTSweepContext tcx, TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle flipTriangle, DelaunayTriangle t, TriangulationPoint p)
{
DelaunayTriangle ot = t.NeighborAcross(p);
TriangulationPoint op = ot.OppositePoint(t, p);
if (ot == null)
{
// If we want to integrate the fillEdgeEvent do it here
// With current implementation we should never get here
throw new Exception("[BUG:FIXME] FLIP failed due to missing triangle");
}
bool inScanArea = TriangulationUtil.InScanArea(eq, flipTriangle.PointCCW(eq), flipTriangle.PointCW(eq), op);
if (inScanArea)
{
// flip with new edge op->eq
FlipEdgeEvent(tcx, eq, op, ot, op);
// TODO: Actually I just figured out that it should be possible to
// improve this by getting the next ot and op before the the above
// flip and continue the flipScanEdgeEvent here
// set new ot and op here and loop back to inScanArea test
// also need to set a new flipTriangle first
// Turns out at first glance that this is somewhat complicated
// so it will have to wait.
}
else
{
TriangulationPoint newP = NextFlipPoint(ep, eq, ot, op);
FlipScanEdgeEvent(tcx, ep, eq, flipTriangle, ot, newP);
}
}
/// <summary>
/// Fills holes in the Advancing Front
/// </summary>
private static void FillAdvancingFront(DTSweepContext tcx, AdvancingFrontNode n)
{
double angle;
// Fill right holes
AdvancingFrontNode node = n.Next;
while (node.HasNext)
{
// if HoleAngle exceeds 90 degrees then break.
if (LargeHole_DontFill(node))
break;
Fill(tcx, node);
node = node.Next;
}
// Fill left holes
node = n.Prev;
while (node.HasPrev)
{
// if HoleAngle exceeds 90 degrees then break.
if (LargeHole_DontFill(node))
break;
angle = HoleAngle(node);
if (angle > PI_div2 || angle < -PI_div2)
{
break;
}
Fill(tcx, node);
node = node.Prev;
}
// Fill right basins
if (n.HasNext && n.Next.HasNext)
{
angle = BasinAngle(n);
if (angle < PI_3div4)
{
FillBasin(tcx, n);
}
}
}
/// <summary>
/// Returns true if triangle was legalized
/// </summary>
private static bool Legalize(DTSweepContext tcx, DelaunayTriangle t)
{
// To legalize a triangle we start by finding if any of the three edges
// violate the Delaunay condition
for (int i = 0; i < 3; i++)
{
// TODO: fix so that cEdge is always valid when creating new triangles then we can check it here
// instead of below with ot
if (t.EdgeIsDelaunay[i])
{
continue;
}
DelaunayTriangle ot = t.Neighbors[i];
if (ot != null)
{
TriangulationPoint p = t.Points[i];
TriangulationPoint op = ot.OppositePoint(t, p);
int oi = ot.IndexOf(op);
// If this is a Constrained Edge or a Delaunay Edge(only during recursive legalization)
// then we should not try to legalize
if (ot.EdgeIsConstrained[oi] || ot.EdgeIsDelaunay[oi])
{
t.EdgeIsConstrained[i] = ot.EdgeIsConstrained[oi];
// XXX: have no good way of setting this property when creating new triangles so lets set it here
continue;
}
bool inside = TriangulationUtil.SmartIncircle(p, t.PointCCW(p), t.PointCW(p), op);
if (inside)
{
// Lets mark this shared edge as Delaunay
t.EdgeIsDelaunay[i] = true;
ot.EdgeIsDelaunay[oi] = true;
// Lets rotate shared edge one vertex CW to legalize it
RotateTrianglePair(t, p, ot, op);
// We now got one valid Delaunay Edge shared by two triangles
// This gives us 4 new edges to check for Delaunay
// Make sure that triangle to node mapping is done only one time for a specific triangle
bool notLegalized = !Legalize(tcx, t);
if (notLegalized)
{
tcx.MapTriangleToNodes(t);
}
notLegalized = !Legalize(tcx, ot);
if (notLegalized)
{
tcx.MapTriangleToNodes(ot);
}
// Reset the Delaunay edges, since they only are valid Delaunay edges
// until we add a new triangle or point.
// XXX: need to think about this. Can these edges be tried after we
// return to previous recursive level?
t.EdgeIsDelaunay[i] = false;
ot.EdgeIsDelaunay[oi] = false;
// If triangle have been legalized no need to check the other edges since
// the recursive legalization will handles those so we can end here.
return true;
}
}
}
return false;
}
/// <summary>
/// Fills a basin that has formed on the Advancing Front to the right
/// of given node.
/// First we decide a left,bottom and right node that forms the
/// boundaries of the basin. Then we do a reqursive fill.
/// </summary>
/// <param name="tcx"></param>
/// <param name="node">starting node, this or next node will be left node</param>
private static void FillBasin(DTSweepContext tcx, AdvancingFrontNode node)
{
if (TriangulationUtil.Orient2d(node.Point, node.Next.Point, node.Next.Next.Point) == Orientation.CCW)
{
// tcx.basin.leftNode = node.next.next;
tcx.Basin.leftNode = node;
}
else
{
tcx.Basin.leftNode = node.Next;
}
// Find the bottom and right node
tcx.Basin.bottomNode = tcx.Basin.leftNode;
while (tcx.Basin.bottomNode.HasNext && tcx.Basin.bottomNode.Point.Y >= tcx.Basin.bottomNode.Next.Point.Y)
{
tcx.Basin.bottomNode = tcx.Basin.bottomNode.Next;
}
if (tcx.Basin.bottomNode == tcx.Basin.leftNode)
{
// No valid basins
return;
}
tcx.Basin.rightNode = tcx.Basin.bottomNode;
while (tcx.Basin.rightNode.HasNext && tcx.Basin.rightNode.Point.Y < tcx.Basin.rightNode.Next.Point.Y)
{
tcx.Basin.rightNode = tcx.Basin.rightNode.Next;
}
if (tcx.Basin.rightNode == tcx.Basin.bottomNode)
{
// No valid basins
return;
}
tcx.Basin.width = tcx.Basin.rightNode.Point.X - tcx.Basin.leftNode.Point.X;
tcx.Basin.leftHighest = tcx.Basin.leftNode.Point.Y > tcx.Basin.rightNode.Point.Y;
FillBasinReq(tcx, tcx.Basin.bottomNode);
}
/// <summary>
/// After a flip we have two triangles and know that only one will still be
/// intersecting the edge. So decide which to contiune with and legalize the other
/// </summary>
/// <param name="tcx"></param>
/// <param name="o">should be the result of an TriangulationUtil.orient2d( eq, op, ep )</param>
/// <param name="t">triangle 1</param>
/// <param name="ot">triangle 2</param>
/// <param name="p">a point shared by both triangles</param>
/// <param name="op">another point shared by both triangles</param>
/// <returns>returns the triangle still intersecting the edge</returns>
private static DelaunayTriangle NextFlipTriangle(DTSweepContext tcx, Orientation o, DelaunayTriangle t, DelaunayTriangle ot, TriangulationPoint p, TriangulationPoint op)
{
int edgeIndex;
if (o == Orientation.CCW)
{
// ot is not crossing edge after flip
edgeIndex = ot.EdgeIndex(p, op);
ot.EdgeIsDelaunay[edgeIndex] = true;
Legalize(tcx, ot);
ot.EdgeIsDelaunay.Clear();
return t;
}
// t is not crossing edge after flip
edgeIndex = t.EdgeIndex(p, op);
t.EdgeIsDelaunay[edgeIndex] = true;
Legalize(tcx, t);
t.EdgeIsDelaunay.Clear();
return ot;
}
/// <summary>
/// Recursive algorithm to fill a Basin with triangles
/// </summary>
private static void FillBasinReq(DTSweepContext tcx, AdvancingFrontNode node)
{
// if shallow stop filling
if (IsShallow(tcx, node))
{
return;
}
Fill(tcx, node);
if (node.Prev == tcx.Basin.leftNode && node.Next == tcx.Basin.rightNode)
{
return;
}
else if (node.Prev == tcx.Basin.leftNode)
{
Orientation o = TriangulationUtil.Orient2d(node.Point, node.Next.Point, node.Next.Next.Point);
if (o == Orientation.CW)
{
return;
}
node = node.Next;
}
else if (node.Next == tcx.Basin.rightNode)
{
Orientation o = TriangulationUtil.Orient2d(node.Point, node.Prev.Point, node.Prev.Prev.Point);
if (o == Orientation.CCW)
{
return;
}
node = node.Prev;
}
else
{
// Continue with the neighbor node with lowest Y value
if (node.Prev.Point.Y < node.Next.Point.Y)
{
node = node.Prev;
}
else
{
node = node.Next;
}
}
FillBasinReq(tcx, node);
}
