Negin Soltani 37239732ac Initial Push
- Globe Asset
- Spatial Anchors
- Photon Implementation
- Scripts for Globe Control and Initial Country Colorizing
- Script for Reading csv file
2024-05-16 14:41:23 +02:00

1063 lines
35 KiB
C#

/* Poly2Tri
* Copyright (c) 2009-2010, Poly2Tri Contributors
* http://code.google.com/p/poly2tri/
*
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without modification,
* are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
* * Neither the name of Poly2Tri nor the names of its contributors may be
* used to endorse or promote products derived from this software without specific
* prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
* LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/*
* Sweep-line, Constrained Delauney Triangulation (CDT) See: Domiter, V. and
* Zalik, B.(2008)'Sweep-line algorithm for constrained Delaunay triangulation',
* International Journal of Geographical Information Science
*
* "FlipScan" Constrained Edge Algorithm invented by author of this code.
*
* Author: Thomas Åhlén, thahlen@gmail.com
*/
/// Changes from the Java version
/// Turned DTSweep into a static class
/// Lots of deindentation via early bailout
/// Future possibilities
/// Comments!
using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
namespace WPM.Poly2Tri {
public static class DTSweep {
private const double PI_div2 = Math.PI / 2;
private const double PI_3div4 = 3 * Math.PI / 4;
/// <summary>
/// Triangulate simple polygon with holes
/// </summary>
public static void Triangulate (DTSweepContext tcx) {
tcx.CreateAdvancingFront ();
Sweep (tcx);
FixupConstrainedEdges (tcx);
// Finalize triangulation
if (tcx.TriangulationMode == TriangulationMode.Polygon) {
FinalizationPolygon (tcx);
} else {
FinalizationConvexHull (tcx);
if (tcx.TriangulationMode == TriangulationMode.Constrained) {
// work in progress. When it's done, call FinalizationConstraints INSTEAD of tcx.FinalizeTriangulation
//FinalizationConstraints(tcx);
tcx.FinalizeTriangulation ();
} else {
tcx.FinalizeTriangulation ();
}
}
tcx.Done ();
}
/// <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;
int pointsCount = points.Count;
for (int i = 1; i < pointsCount; i++) {
point = points [i];
node = PointEvent (tcx, point);
if (node != null && point.HasEdges) {
int pEdgesCount = point.Edges.Count;
for (int k=0;k<pEdgesCount;k++) {
DTSweepConstraint e = point.Edges[k];
EdgeEvent (tcx, e, node);
}
}
}
}
private static void FixupConstrainedEdges (DTSweepContext tcx) {
foreach (DelaunayTriangle t in tcx.Triangles) {
for (int i = 0; i < 3; ++i) {
bool isConstrained = t.GetConstrainedEdgeCCW (t.Points [i]);
if (!isConstrained) {
DTSweepConstraint edge = null;
bool hasConstrainedEdge = t.GetEdgeCCW (t.Points [i], out edge);
if (hasConstrainedEdge) {
t.MarkConstrainedEdge ((i + 2) % 3);
//t.MarkConstrainedEdgeCCW(t.Points[i]);
}
}
}
}
}
/// <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;
DelaunayTriangle t1, t2;
TriangulationPoint first, p1;
n1 = tcx.Front.Head.Next;
n2 = n1.Next;
first = n1.Point;
TurnAdvancingFrontConvex (tcx, n1, n2);
// Lets remove triangles connected to the two "algorithm" points
// XXX: When the first three 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.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);
}
// Lower right boundary
first = tcx.Front.Head.Point;
n2 = tcx.Front.Tail.Prev;
t1 = n2.Triangle;
p1 = n2.Point;
n2.Triangle = null;
do {
tcx.RemoveFromList (t1);
p1 = t1.PointCCWFrom (p1);
if (p1 == first) {
break;
}
t2 = t1.NeighborCCWFrom (p1);
t1.Clear ();
t1 = t2;
} while (true);
// Lower left boundary
first = tcx.Front.Head.Next.Point;
p1 = t1.PointCWFrom (tcx.Front.Head.Point);
t2 = t1.NeighborCWFrom (tcx.Front.Head.Point);
t1.Clear ();
t1 = t2;
while (p1 != first) {
tcx.RemoveFromList (t1);
p1 = t1.PointCCWFrom (p1);
t2 = t1.NeighborCCWFrom (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.Front.Head = tcx.Front.Head.Next;
tcx.Front.Head.Prev = null;
tcx.Front.Tail = tcx.Front.Tail.Prev;
tcx.Front.Tail.Next = null;
}
/// <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 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)) {
DelaunayTriangle tTmp = t.NeighborCCWFrom (p);
if (tTmp == null) {
break;
}
t = tTmp;
}
// Collect interior triangles constrained by edges
tcx.MeshClean (t);
}
/// <summary>
/// NOTE: WORK IN PROGRESS - for now this will just clean out all triangles from
/// inside the outermost holes without paying attention to holes within holes..
/// hence the work in progress :)
///
/// Removes triangles inside "holes" (that are not inside of other holes already)
///
/// In the example below, assume that triangle ABC is a user-defined "hole". Thus
/// any triangles inside it (that aren't inside yet another user-defined hole inside
/// triangle ABC) should get removed. In this case, since there are no user-defined
/// holes inside ABC, we would remove triangles ADE, BCE, and CDE. We would also
/// need to combine the appropriate edges so that we end up with just triangle ABC
///
/// E
/// A +------+-----+ B A +-----------+ B
/// \ /| / \ /
/// \ / | / \ /
/// D + | / ======> \ /
/// \ | / \ /
/// \ |/ \ /
/// + +
/// C C
///
/// </summary>
private static void FinalizationConstraints (DTSweepContext tcx) {
// Get an Internal triangle to start with
DelaunayTriangle t = tcx.Front.Head.Triangle;
TriangulationPoint p = tcx.Front.Head.Point;
while (!t.GetConstrainedEdgeCW(p)) {
DelaunayTriangle tTmp = t.NeighborCCWFrom (p);
if (tTmp == null) {
break;
}
t = tTmp;
}
// Collect interior triangles constrained by edges
tcx.MeshClean (t);
}
/// <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;
// }
if (node == null || point == null) {
return null;
}
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) { // + Point2D.PRECISION) { // Changed by Kronnect Games MathUtil.EPSILON) {
Fill (tcx, node);
}
// tcx.AddNode (newNode);
FillAdvancingFront (tcx, newNode);
return newNode;
}
/// <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;
}
private static void EdgeEvent (DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node) {
try {
tcx.EdgeEvent.ConstrainedEdge = edge;
tcx.EdgeEvent.Right = edge.P.X > edge.Q.X; // + Point2D.PRECISION; // Changed by Kronnect Games
// 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) {
//Debug.WriteLine( String.Format( "Warning: Skipping Edge: {0}", e.Message ) );
throw;
}
}
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 FillRightConcaveEdgeEvent (DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node) {
Fill (tcx, node.Next);
if (node.Next.Point != edge.P) {
// Next above or below edge?
if (TriangulationUtil.Orient2d (edge.Q, node.Next.Point, edge.P) == Orientation.CCW) {
// Below
if (TriangulationUtil.Orient2d (node.Point, node.Next.Point, node.Next.Next.Point) == Orientation.CCW) {
// Next is concave
FillRightConcaveEdgeEvent (tcx, edge, node);
} else {
// Next is convex
}
}
}
}
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 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);
}
}
}
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;
}
}
}
private static void FillLeftConvexEdgeEvent (DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node) {
// Next concave or convex?
if (TriangulationUtil.Orient2d (node.Prev.Point, node.Prev.Prev.Point, node.Prev.Prev.Prev.Point) == Orientation.CW) {
// Concave
FillLeftConcaveEdgeEvent (tcx, edge, node.Prev);
} else {
// Convex
// Next above or below edge?
if (TriangulationUtil.Orient2d (edge.Q, node.Prev.Prev.Point, edge.P) == Orientation.CW) {
// Below
FillLeftConvexEdgeEvent (tcx, edge, node.Prev);
} else {
// Above
}
}
}
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
}
}
}
}
private static void FillLeftBelowEdgeEvent (DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node) {
// if (tcx.IsDebugEnabled)
// tcx.DTDebugContext.ActiveNode = 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 FillLeftAboveEdgeEvent (DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node) {
while (node.Prev.Point.X > edge.P.X) { // + Point2D.PRECISION) { // Changed by Kronnect Games
// if (tcx.IsDebugEnabled) {
// tcx.DTDebugContext.ActiveNode = node;
// }
// Check if next node is below the edge
Orientation o1 = TriangulationUtil.Orient2d (edge.Q, node.Prev.Point, edge.P);
if (o1 == Orientation.CW) {
FillLeftBelowEdgeEvent (tcx, edge, node);
} else {
node = node.Prev;
}
}
}
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;
}
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 (triangle==null) return; // Added by Kronnect Games
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");
}
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) {
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 {
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);
}
}
}
/// <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;
}
/// <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");
}
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>
/// 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 > PI_div2 || angle < -PI_div2) {
break;
}
Fill (tcx, node);
node = node.Next;
}
// Fill left holes
node = n.Prev;
while (node.HasPrev) {
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>
/// 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>
/// 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 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;
}
/// <summary>
/// ???
/// </summary>
/// <param name="node">middle node</param>
/// <returns>the angle between 3 front nodes</returns>
private static double HoleAngle (AdvancingFrontNode node) {
// XXX: do we really need a signed angle for holeAngle?
// could possible save some cycles here
/* Complex plane
* ab = cosA +i*sinA
* ab = (ax + ay*i)(bx + by*i) = (ax*bx + ay*by) + i(ax*by-ay*bx)
* atan2(y,x) computes the principal value of the argument function
* applied to the complex number x+iy
* Where x = ax*bx + ay*by
* y = ax*by - ay*bx
*/
double px = node.Point.X;
double py = node.Point.Y;
double ax = node.Next.Point.X - px;
double ay = node.Next.Point.Y - py;
double bx = node.Prev.Point.X - px;
double by = node.Prev.Point.Y - py;
return Math.Atan2 ((ax * by) - (ay * bx), (ax * bx) + (ay * by));
}
/// <summary>
/// The basin angle is decided against the horizontal line [1,0]
/// </summary>
private static double BasinAngle (AdvancingFrontNode node) {
double ax = node.Point.X - node.Next.Next.Point.X;
double ay = node.Point.Y - node.Next.Next.Point.Y;
return Math.Atan2 (ay, ax);
}
/// <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;
// If it was legalized the triangle has already been mapped
if (!Legalize (tcx, triangle)) {
tcx.MapTriangleToNodes (triangle);
}
}
/// <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>
/// 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);
}
}
}