/// <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;
TriangulationPoint op, newP;
bool inScanArea;
ot = t.NeighborAcrossFrom(p);
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");
}
if (tcx.IsDebugEnabled)
{
//Console.WriteLine("[FLIP:SCAN] - scan next point"); // TODO: remove
tcx.DTDebugContext.PrimaryTriangle = t;
tcx.DTDebugContext.SecondaryTriangle = ot;
}
inScanArea = TriangulationUtil.InScanArea(eq, flipTriangle.PointCCWFrom(eq), flipTriangle.PointCWFrom(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
{
if (NextFlipPoint(ep, eq, ot, op, out newP))
{
FlipScanEdgeEvent(tcx, ep, eq, flipTriangle, ot, newP);
}
//newP = NextFlipPoint(ep, eq, ot, op);
}
}
/// <summary>
/// When we need to traverse from one triangle to the next we need
/// the point in current triangle that is the opposite point to the next
/// triangle.
/// </summary>
private static bool NextFlipPoint(TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle ot, TriangulationPoint op, out TriangulationPoint newP)
{
newP = null;
Orientation o2d = TriangulationUtil.Orient2d(eq, op, ep);
switch (o2d)
{
case Orientation.CW:
newP = ot.PointCCWFrom(op);
return(true);
case Orientation.CCW:
newP = ot.PointCWFrom(op);
return(true);
case Orientation.Collinear:
// TODO: implement support for point on constraint edge
//throw new PointOnEdgeException("Point on constrained edge not supported yet", eq, op, ep);
return(false);
default:
throw new NotImplementedException("Orientation not handled");
}
}
/// <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);
}
private static void EdgeEvent(DTSweepContext tcx, TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle triangle, TriangulationPoint point)
{
TriangulationPoint p1, p2;
if (tcx.IsDebugEnabled)
{
tcx.DTDebugContext.PrimaryTriangle = triangle;
}
if (IsEdgeSideOfTriangle(triangle, ep, eq))
{
return;
}
p1 = triangle.PointCCWFrom(point);
Orientation o1 = TriangulationUtil.Orient2d(eq, p1, ep);
if (o1 == Orientation.Collinear)
{
if (triangle.Contains(eq) && triangle.Contains(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.NeighborAcrossFrom(point);
EdgeEvent(tcx, ep, p1, triangle, p1);
}
else
{
throw new PointOnEdgeException("EdgeEvent - Point on constrained edge not supported yet", ep, eq, p1);
}
if (tcx.IsDebugEnabled)
{
//Console.WriteLine("EdgeEvent - Point on constrained edge");
}
return;
}
p2 = triangle.PointCWFrom(point);
Orientation o2 = TriangulationUtil.Orient2d(eq, p2, ep);
if (o2 == Orientation.Collinear)
{
if (triangle.Contains(eq) && triangle.Contains(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.NeighborAcrossFrom(point);
EdgeEvent(tcx, ep, p2, triangle, p2);
}
else
{
throw new PointOnEdgeException("EdgeEvent - Point on constrained edge not supported yet", ep, eq, p2);
}
if (tcx.IsDebugEnabled)
{
//Console.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.NeighborCCWFrom(point);
}
else
{
triangle = triangle.NeighborCWFrom(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.NeighborAcrossFrom(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 (tcx.IsDebugEnabled)
{
tcx.DTDebugContext.PrimaryTriangle = t;
tcx.DTDebugContext.SecondaryTriangle = ot;
} // TODO: remove
bool inScanArea = TriangulationUtil.InScanArea(p, t.PointCCWFrom(p), t.PointCWFrom(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)
{
//Console.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)
{
//Console.WriteLine("[FLIP] - subedge done"); // TODO: remove
}
// XXX: I think one of the triangles should be legalized here?
}
}
else
{
if (tcx.IsDebugEnabled)
{
//Console.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 = null;
if (NextFlipPoint(ep, eq, ot, op, out newP))
{
FlipScanEdgeEvent(tcx, ep, eq, t, ot, newP);
EdgeEvent(tcx, ep, eq, t, p);
}
}
}
private static bool IsEdgeSideOfTriangle(DelaunayTriangle triangle, TriangulationPoint ep, TriangulationPoint eq)
{
int index = triangle.EdgeIndex(ep, eq);
if (index == -1)
{
return(false);
}
triangle.MarkConstrainedEdge(index);
triangle = triangle.Neighbors[index];
if (triangle != null)
{
triangle.MarkConstrainedEdge(ep, eq);
}
return(true);
}
/// <summary>
/// Rotates a triangle pair one vertex CW
/// n2 n2
/// P +-----+ P +-----+
/// | t /| |\ t |
/// | / | | \ |
/// n1| / |n3 n1| \ |n3
/// | / | after CW | \ |
/// |/ oT | | oT \|
/// +-----+ oP +-----+
/// n4 n4
/// </summary>
private static void RotateTrianglePair(DelaunayTriangle t, TriangulationPoint p, DelaunayTriangle ot, TriangulationPoint op)
{
DelaunayTriangle n1, n2, n3, n4;
n1 = t.NeighborCCWFrom(p);
n2 = t.NeighborCWFrom(p);
n3 = ot.NeighborCCWFrom(op);
n4 = ot.NeighborCWFrom(op);
bool ce1, ce2, ce3, ce4;
ce1 = t.GetConstrainedEdgeCCW(p);
ce2 = t.GetConstrainedEdgeCW(p);
ce3 = ot.GetConstrainedEdgeCCW(op);
ce4 = ot.GetConstrainedEdgeCW(op);
bool de1, de2, de3, de4;
de1 = t.GetDelaunayEdgeCCW(p);
de2 = t.GetDelaunayEdgeCW(p);
de3 = ot.GetDelaunayEdgeCCW(op);
de4 = ot.GetDelaunayEdgeCW(op);
t.Legalize(p, op);
ot.Legalize(op, p);
// Remap dEdge
ot.SetDelaunayEdgeCCW(p, de1);
t.SetDelaunayEdgeCW(p, de2);
t.SetDelaunayEdgeCCW(op, de3);
ot.SetDelaunayEdgeCW(op, de4);
// Remap cEdge
ot.SetConstrainedEdgeCCW(p, ce1);
t.SetConstrainedEdgeCW(p, ce2);
t.SetConstrainedEdgeCCW(op, ce3);
ot.SetConstrainedEdgeCW(op, ce4);
// Remap neighbors
// XXX: might optimize the markNeighbor by keeping track of
// what side should be assigned to what neighbor after the
// rotation. Now mark neighbor does lots of testing to find
// the right side.
t.Neighbors.Clear();
ot.Neighbors.Clear();
if (n1 != null)
{
ot.MarkNeighbor(n1);
}
if (n2 != null)
{
t.MarkNeighbor(n2);
}
if (n3 != null)
{
t.MarkNeighbor(n3);
}
if (n4 != null)
{
ot.MarkNeighbor(n4);
}
t.MarkNeighbor(ot);
}
/// <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)
{
continue;
}
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.SetConstrainedEdgeAcross(p, ot.EdgeIsConstrained[oi]); // XXX: have no good way of setting this property when creating new triangles so lets set it here
continue;
}
if (!TriangulationUtil.SmartIncircle(p, t.PointCCWFrom(p), t.PointCWFrom(p), op))
{
continue;
}
// 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
if (!Legalize(tcx, t))
{
tcx.MapTriangleToNodes(t);
}
if (!Legalize(tcx, ot))
{
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>
/// Give two points in any order. Will always be ordered so
/// that q.y > p.y and q.x > p.x if same y value
/// </summary>
public DTSweepConstraint(TriangulationPoint p1, TriangulationPoint p2)
: base(p1, p2)
{
Q.AddEdge(this);
}
/// <summary>
/// We use a balancing tree to locate a node smaller or equal to given key value (in theory)
/// </summary>
public AdvancingFrontNode LocateNode(TriangulationPoint point)
{
return(LocateNode(point.X));
}