/// <summary>
/// Exhaustive search to update neighbor pointers
/// </summary>
public void MarkNeighbor( DelaunayTriangle t )
{
// Points of this triangle also belonging to t
bool a = t.Contains(Points[0]);
bool b = t.Contains(Points[1]);
bool c = t.Contains(Points[2]);
if (b&&c) { Neighbors[0]=t; t.MarkNeighbor(Points[1],Points[2],this); }
else if (a&&c) { Neighbors[1]=t; t.MarkNeighbor(Points[0],Points[2],this); }
else if (a&&b) { Neighbors[2]=t; t.MarkNeighbor(Points[0],Points[1],this); }
else throw new Exception( "Failed to mark neighbor, doesn't share an edge!");
}
public void AddTriangle(DelaunayTriangle t)
{
Triangles.Add(t);
}
public void MarkEdge(DelaunayTriangle triangle)
{
for (int i = 0; i < 3; i++) if ( EdgeIsConstrained[i] ) {
triangle.MarkConstrainedEdge(Points[(i+1)%3], Points[(i+2)%3]);
}
}
/// <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>
/// 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);
}
public void RemoveFromList(DelaunayTriangle triangle)
{
base.Triangles.Remove(triangle);
}
/// <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 TriangulationPoint NextFlipPoint( TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle ot, TriangulationPoint op )
{
Orientation o2d = TriangulationUtil.Orient2d(eq, op, ep);
switch ( o2d ) {
case Orientation.CW: return ot.PointCCWFrom(op);
case Orientation.CCW: return ot.PointCWFrom(op);
case Orientation.Collinear:
// TODO: implement support for point on constraint edge
throw new PointOnEdgeException("Point on constrained edge not supported yet",eq,op,ep);
default:
throw new NotImplementedException("Orientation not handled");
}
}
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>
/// 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.EdgeIsConstrained[i] = 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;
}
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 = NextFlipPoint(ep, eq, ot, op);
FlipScanEdgeEvent(tcx, ep, eq, t, ot, newP);
EdgeEvent(tcx, ep, eq, t, p);
}
}
/// <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 {
newP = NextFlipPoint(ep, eq, ot, op);
FlipScanEdgeEvent(tcx, ep, eq, flipTriangle, ot, newP);
}
}
/// <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);
}
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) {
// TODO: Split edge in two
//// splitEdge( ep, eq, p1 );
// edgeEvent( tcx, p1, eq, triangle, point );
// edgeEvent( tcx, ep, p1, triangle, p1 );
// return;
throw new PointOnEdgeException("EdgeEvent - Point on constrained edge not supported yet",eq,p1,ep);
}
p2 = triangle.PointCWFrom(point);
Orientation o2 = TriangulationUtil.Orient2d(eq, p2, ep);
if (o2 == Orientation.Collinear) {
// TODO: Split edge in two
// edgeEvent( tcx, p2, eq, triangle, point );
// edgeEvent( tcx, ep, p2, triangle, p2 );
// return;
throw new PointOnEdgeException("EdgeEvent - Point on constrained edge not supported yet",eq,p2,ep);
}
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);
}
}
public void MeshClean(DelaunayTriangle triangle)
{
this.MeshCleanReq(triangle);
}
/// <param name="t">Opposite triangle</param>
/// <param name="p">The point in t that isn't shared between the triangles</param>
public TriangulationPoint OppositePoint(DelaunayTriangle t, TriangulationPoint p)
{
Debug.Assert(t != this, "self-pointer error");
return PointCWFrom(t.PointCWFrom(p));
}
/// <summary>
/// Creates a new front triangle and legalize it
/// </summary>
private static AdvancingFrontNode NewFrontTriangle( DTSweepContext tcx, TriangulationPoint point, AdvancingFrontNode node )
{
AdvancingFrontNode newNode;
DelaunayTriangle triangle;
triangle = new DelaunayTriangle(point, node.Point, node.Next.Point);
triangle.MarkNeighbor(node.Triangle);
tcx.Triangles.Add(triangle);
newNode = new AdvancingFrontNode(point);
newNode.Next = node.Next;
newNode.Prev = node;
node.Next.Prev = newNode;
node.Next = newNode;
tcx.AddNode(newNode); // XXX: BST
if (tcx.IsDebugEnabled) tcx.DTDebugContext.ActiveNode = newNode;
if (!Legalize(tcx, triangle)) tcx.MapTriangleToNodes(triangle);
return newNode;
}
/// <summary>
/// Update neighbor pointers
/// </summary>
/// <param name="p1">Point 1 of the shared edge</param>
/// <param name="p2">Point 2 of the shared edge</param>
/// <param name="t">This triangle's new neighbor</param>
private void MarkNeighbor( TriangulationPoint p1, TriangulationPoint p2, DelaunayTriangle t )
{
int i = EdgeIndex(p1,p2);
if ( i==-1 ) throw new Exception( "Error marking neighbors -- t doesn't contain edge p1-p2!" );
Neighbors[i] = t;
}
public void AddTriangle(DelaunayTriangle t)
{
_triangles.Add(t);
}