/// <summary>
/// Triangulate simple polygon with holes
/// </summary>
public static void Triangulate( DTSweepContext tcx )
{
tcx.CreateAdvancingFront();
Sweep(tcx);
// TODO: remove temporary
// Check if the sweep algorithm is legalize robust
// By doing a legalize on all triangles and see if anything happens
// we know if the sweep algorithm missed some legalizations
// Console.WriteLine("============================");
// foreach ( DelaunayTriangle t in tcx.Triangles )
// {
// if( Legalize( tcx, t ) )
// {
// tcx.getDebugContext().setPrimaryTriangle( t );
// Console.WriteLine("[FIX] Triangle needed legalization after sweep");
// }
// }
// Finalize triangulation
if (tcx.TriangulationMode == TriangulationMode.Polygon) {
FinalizationPolygon(tcx);
} else {
FinalizationConvexHull(tcx);
}
tcx.Done();
}
/// <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);
}
}
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);
}
}
private static void FinalizationPolygon( DTSweepContext tcx )
{
// Get an Internal triangle to start with
DelaunayTriangle t = tcx.Front.Head.Next.Triangle;
TriangulationPoint p = tcx.Front.Head.Next.Point;
while (!t.GetConstrainedEdgeCW(p)) t = t.NeighborCCWFrom(p);
// Collect interior triangles constrained by edges
tcx.MeshClean(t);
}
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);
}
}
/// <summary>
/// Start sweeping the Y-sorted point set from bottom to top
/// </summary>
private static void Sweep( DTSweepContext tcx )
{
var points = tcx.Points;
TriangulationPoint point;
AdvancingFrontNode node;
for (int i = 1; i < points.Count; i++) {
point = points[i];
node = PointEvent(tcx, point);
if (point.HasEdges) foreach (DTSweepConstraint e in point.Edges) {
if (tcx.IsDebugEnabled) tcx.DTDebugContext.ActiveConstraint = e;
EdgeEvent(tcx, e, node);
}
tcx.Update(null);
}
}
/// <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 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>
/// Recursive algorithm to fill a Basin with triangles
/// </summary>
private static void FillBasinReq( DTSweepContext tcx, AdvancingFrontNode node )
{
if (IsShallow(tcx, node)) return; // if shallow stop filling
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);
}
private static void FillEdgeEvent( DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node )
{
if (tcx.EdgeEvent.Right) {
FillRightAboveEdgeEvent(tcx, edge, node);
} else {
FillLeftAboveEdgeEvent(tcx, edge, node);
}
}
/// <summary>
/// Fills a basin that has formed on the Advancing Front to the right
/// of given node.<br>
/// 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) return; // No valid basin
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) return; // No valid basins
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>
/// Fills holes in the Advancing Front
/// </summary>
private static void FillAdvancingFront( DTSweepContext tcx, AdvancingFrontNode n )
{
AdvancingFrontNode node;
double angle;
// Fill right holes
node = n.Next;
while (node.HasNext) {
angle = HoleAngle(node);
if (angle > PiDiv2 || angle < -PiDiv2) break;
Fill(tcx, node);
node = node.Next;
}
// Fill left holes
node = n.Prev;
while (node.HasPrev) {
angle = HoleAngle(node);
if (angle > PiDiv2 || angle < -PiDiv2) 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>
/// 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 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 FillRightAboveEdgeEvent( DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node )
{
while (node.Next.Point.X < edge.P.X) {
if (tcx.IsDebugEnabled) { tcx.DTDebugContext.ActiveNode = node; }
// 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>
/// 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 FillRightBelowEdgeEvent( DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node )
{
if (tcx.IsDebugEnabled) tcx.DTDebugContext.ActiveNode = 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);
}
}
}
/// <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) {Next = node.Next, 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;
}
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
}
}
}
/// <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, newNode;
node = tcx.LocateNode(point);
if (tcx.IsDebugEnabled) tcx.DTDebugContext.ActiveNode = node;
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;
}
/// <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 )
{
AdvancingFrontNode n1, n2, n3;
DelaunayTriangle t1;
TriangulationPoint first, p1;
n1 = tcx.Front.Head.Next;
n2 = n1.Next;
n3 = n2.Next;
first = n1.Point;
TurnAdvancingFrontConvex(tcx, n1, n2);
n1 = tcx.Front.Tail.Prev;
if (n1.Triangle.Contains(n1.Next.Point) && n1.Triangle.Contains(n1.Prev.Point)) {
t1 = n1.Triangle.NeighborAcrossFrom(n1.Point);
RotateTrianglePair(n1.Triangle, n1.Point, t1, t1.OppositePoint(n1.Triangle, n1.Point));
tcx.MapTriangleToNodes(n1.Triangle);
tcx.MapTriangleToNodes(t1);
}
n1 = tcx.Front.Head.Next;
if (n1.Triangle.Contains(n1.Prev.Point) && n1.Triangle.Contains(n1.Next.Point)) {
t1 = n1.Triangle.NeighborAcrossFrom(n1.Point);
RotateTrianglePair(n1.Triangle, n1.Point, t1, t1.OppositePoint(n1.Triangle, n1.Point));
tcx.MapTriangleToNodes(n1.Triangle);
tcx.MapTriangleToNodes(t1);
}
// TODO: implement ConvexHull for lower right and left boundary
// Lower right boundary
first = tcx.Front.Head.Point;
n2 = tcx.Front.Tail.Prev;
t1 = n2.Triangle;
p1 = n2.Point;
do {
tcx.RemoveFromList(t1);
p1 = t1.PointCCWFrom(p1);
if (p1 == first) break;
t1 = t1.NeighborCCWFrom(p1);
} while (true);
// Lower left boundary
first = tcx.Front.Head.Next.Point;
p1 = t1.PointCWFrom(tcx.Front.Head.Point);
t1 = t1.NeighborCWFrom(tcx.Front.Head.Point);
do {
tcx.RemoveFromList(t1);
p1 = t1.PointCCWFrom(p1);
t1 = t1.NeighborCCWFrom(p1);
} while (p1 != first);
tcx.FinalizeTriangulation();
}
/// <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.Front.Tail) {
if (tcx.IsDebugEnabled) tcx.DTDebugContext.ActiveNode = c;
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 EdgeEvent( DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node )
{
try {
tcx.EdgeEvent.ConstrainedEdge = edge;
tcx.EdgeEvent.Right = edge.P.X > edge.Q.X;
if (tcx.IsDebugEnabled) { tcx.DTDebugContext.PrimaryTriangle = node.Triangle; }
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( String.Format( "Warning: Skipping Edge: {0}", e.Message ) );
throw;
}
}