1132 lines
43 KiB
C#
1132 lines
43 KiB
C#
/* Poly2Tri
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* Copyright (c) 2009-2010, Poly2Tri Contributors
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* http://code.google.com/p/poly2tri/
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*
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without modification,
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* are permitted provided that the following conditions are met:
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*
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* * Redistributions of source code must retain the above copyright notice,
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* this list of conditions and the following disclaimer.
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* * Redistributions in binary form must reproduce the above copyright notice,
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* this list of conditions and the following disclaimer in the documentation
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* and/or other materials provided with the distribution.
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* * Neither the name of Poly2Tri nor the names of its contributors may be
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* used to endorse or promote products derived from this software without specific
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* prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
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* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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* LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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/*
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* Sweep-line, Constrained Delauney Triangulation (CDT) See: Domiter, V. and
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* Zalik, B.(2008)'Sweep-line algorithm for constrained Delaunay triangulation',
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* International Journal of Geographical Information Science
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*
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* "FlipScan" Constrained Edge Algorithm invented by author of this code.
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*
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* Author: Thomas Åhlén, thahlen@gmail.com
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*/
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// Changes from the Java version
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// Turned DTSweep into a static class
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// Lots of deindentation via early bailout
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// Future possibilities
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// Comments!
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using System;
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using System.Collections.Generic;
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using System.Diagnostics;
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using FarseerPhysics.Common.Decomposition.CDT;
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namespace Poly2Tri.Triangulation.Delaunay.Sweep
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{
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public static class DTSweep
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{
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private const double PI_div2 = Math.PI/2;
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private const double PI_3div4 = 3*Math.PI/4;
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/// <summary>
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/// Triangulate simple polygon with holes
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/// </summary>
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public static void Triangulate(DTSweepContext tcx)
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{
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tcx.CreateAdvancingFront();
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Sweep(tcx);
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// Finalize triangulation
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if (tcx.TriangulationMode == TriangulationMode.Polygon)
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{
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FinalizationPolygon(tcx);
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}
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else
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{
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FinalizationConvexHull(tcx);
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}
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tcx.Done();
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}
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/// <summary>
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/// Start sweeping the Y-sorted point set from bottom to top
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/// </summary>
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private static void Sweep(DTSweepContext tcx)
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{
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List<TriangulationPoint> points = tcx.Points;
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TriangulationPoint point;
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AdvancingFrontNode node;
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for (int i = 1; i < points.Count; i++)
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{
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point = points[i];
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node = PointEvent(tcx, point);
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if (point.HasEdges)
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{
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foreach (DTSweepConstraint e in point.Edges)
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{
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EdgeEvent(tcx, e, node);
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}
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}
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tcx.Update(null);
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}
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}
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/// <summary>
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/// If this is a Delaunay Triangulation of a pointset we need to fill so the triangle mesh gets a ConvexHull
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/// </summary>
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private static void FinalizationConvexHull(DTSweepContext tcx)
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{
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AdvancingFrontNode n1, n2;
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DelaunayTriangle t1, t2;
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TriangulationPoint first, p1;
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n1 = tcx.aFront.Head.Next;
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n2 = n1.Next;
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first = n1.Point;
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TurnAdvancingFrontConvex(tcx, n1, n2);
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// TODO: implement ConvexHull for lower right and left boundary
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// Lets remove triangles connected to the two "algorithm" points
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// XXX: When the first the nodes are points in a triangle we need to do a flip before
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// removing triangles or we will lose a valid triangle.
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// Same for last three nodes!
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// !!! If I implement ConvexHull for lower right and left boundary this fix should not be
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// needed and the removed triangles will be added again by default
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n1 = tcx.aFront.Tail.Prev;
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if (n1.Triangle.Contains(n1.Next.Point) && n1.Triangle.Contains(n1.Prev.Point))
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{
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t1 = n1.Triangle.NeighborAcross(n1.Point);
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RotateTrianglePair(n1.Triangle, n1.Point, t1, t1.OppositePoint(n1.Triangle, n1.Point));
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tcx.MapTriangleToNodes(n1.Triangle);
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tcx.MapTriangleToNodes(t1);
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}
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n1 = tcx.aFront.Head.Next;
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if (n1.Triangle.Contains(n1.Prev.Point) && n1.Triangle.Contains(n1.Next.Point))
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{
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t1 = n1.Triangle.NeighborAcross(n1.Point);
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RotateTrianglePair(n1.Triangle, n1.Point, t1, t1.OppositePoint(n1.Triangle, n1.Point));
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tcx.MapTriangleToNodes(n1.Triangle);
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tcx.MapTriangleToNodes(t1);
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}
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// Lower right boundary
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first = tcx.aFront.Head.Point;
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n2 = tcx.aFront.Tail.Prev;
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t1 = n2.Triangle;
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p1 = n2.Point;
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n2.Triangle = null;
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do
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{
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tcx.RemoveFromList(t1);
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p1 = t1.PointCCW(p1);
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if (p1 == first) break;
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t2 = t1.NeighborCCW(p1);
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t1.Clear();
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t1 = t2;
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} while (true);
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// Lower left boundary
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first = tcx.aFront.Head.Next.Point;
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p1 = t1.PointCW(tcx.aFront.Head.Point);
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t2 = t1.NeighborCW(tcx.aFront.Head.Point);
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t1.Clear();
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t1 = t2;
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while (p1 != first) //TODO: Port note. This was do while before.
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{
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tcx.RemoveFromList(t1);
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p1 = t1.PointCCW(p1);
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t2 = t1.NeighborCCW(p1);
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t1.Clear();
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t1 = t2;
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}
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// Remove current head and tail node now that we have removed all triangles attached
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// to them. Then set new head and tail node points
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tcx.aFront.Head = tcx.aFront.Head.Next;
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tcx.aFront.Head.Prev = null;
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tcx.aFront.Tail = tcx.aFront.Tail.Prev;
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tcx.aFront.Tail.Next = null;
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tcx.FinalizeTriangulation();
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}
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/// <summary>
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/// We will traverse the entire advancing front and fill it to form a convex hull.
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/// </summary>
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private static void TurnAdvancingFrontConvex(DTSweepContext tcx, AdvancingFrontNode b, AdvancingFrontNode c)
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{
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AdvancingFrontNode first = b;
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while (c != tcx.aFront.Tail)
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{
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if (TriangulationUtil.Orient2d(b.Point, c.Point, c.Next.Point) == Orientation.CCW)
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{
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// [b,c,d] Concave - fill around c
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Fill(tcx, c);
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c = c.Next;
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}
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else
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{
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// [b,c,d] Convex
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if (b != first && TriangulationUtil.Orient2d(b.Prev.Point, b.Point, c.Point) == Orientation.CCW)
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{
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// [a,b,c] Concave - fill around b
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Fill(tcx, b);
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b = b.Prev;
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}
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else
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{
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// [a,b,c] Convex - nothing to fill
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b = c;
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c = c.Next;
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}
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}
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}
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}
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private static void FinalizationPolygon(DTSweepContext tcx)
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{
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// Get an Internal triangle to start with
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DelaunayTriangle t = tcx.aFront.Head.Next.Triangle;
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TriangulationPoint p = tcx.aFront.Head.Next.Point;
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while (!t.GetConstrainedEdgeCW(p))
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{
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t = t.NeighborCCW(p);
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}
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// Collect interior triangles constrained by edges
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tcx.MeshClean(t);
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}
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/// <summary>
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/// Find closes node to the left of the new point and
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/// create a new triangle. If needed new holes and basins
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/// will be filled to.
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/// </summary>
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private static AdvancingFrontNode PointEvent(DTSweepContext tcx, TriangulationPoint point)
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{
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AdvancingFrontNode node, newNode;
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node = tcx.LocateNode(point);
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newNode = NewFrontTriangle(tcx, point, node);
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// Only need to check +epsilon since point never have smaller
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// x value than node due to how we fetch nodes from the front
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if (point.X <= node.Point.X + TriangulationUtil.EPSILON)
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{
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Fill(tcx, node);
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}
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tcx.AddNode(newNode);
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FillAdvancingFront(tcx, newNode);
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return newNode;
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}
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/// <summary>
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/// Creates a new front triangle and legalize it
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/// </summary>
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private static AdvancingFrontNode NewFrontTriangle(DTSweepContext tcx, TriangulationPoint point,
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AdvancingFrontNode node)
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{
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AdvancingFrontNode newNode;
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DelaunayTriangle triangle;
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triangle = new DelaunayTriangle(point, node.Point, node.Next.Point);
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triangle.MarkNeighbor(node.Triangle);
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tcx.Triangles.Add(triangle);
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newNode = new AdvancingFrontNode(point);
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newNode.Next = node.Next;
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newNode.Prev = node;
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node.Next.Prev = newNode;
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node.Next = newNode;
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tcx.AddNode(newNode); // XXX: BST
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if (!Legalize(tcx, triangle))
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{
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tcx.MapTriangleToNodes(triangle);
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}
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return newNode;
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}
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private static void EdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
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{
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try
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{
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tcx.EdgeEvent.ConstrainedEdge = edge;
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tcx.EdgeEvent.Right = edge.P.X > edge.Q.X;
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if (IsEdgeSideOfTriangle(node.Triangle, edge.P, edge.Q))
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{
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return;
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}
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// For now we will do all needed filling
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// TODO: integrate with flip process might give some better performance
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// but for now this avoid the issue with cases that needs both flips and fills
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FillEdgeEvent(tcx, edge, node);
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EdgeEvent(tcx, edge.P, edge.Q, node.Triangle, edge.Q);
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}
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catch (PointOnEdgeException e)
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{
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Debug.WriteLine(String.Format("Skipping Edge: {0}", e.Message));
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}
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}
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private static void FillEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
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{
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if (tcx.EdgeEvent.Right)
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{
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FillRightAboveEdgeEvent(tcx, edge, node);
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}
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else
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{
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FillLeftAboveEdgeEvent(tcx, edge, node);
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}
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}
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private static void FillRightConcaveEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge,
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AdvancingFrontNode node)
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{
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Fill(tcx, node.Next);
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if (node.Next.Point != edge.P)
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{
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// Next above or below edge?
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if (TriangulationUtil.Orient2d(edge.Q, node.Next.Point, edge.P) == Orientation.CCW)
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{
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// Below
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if (TriangulationUtil.Orient2d(node.Point, node.Next.Point, node.Next.Next.Point) == Orientation.CCW)
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{
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// Next is concave
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FillRightConcaveEdgeEvent(tcx, edge, node);
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}
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else
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{
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// Next is convex
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}
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}
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}
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}
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private static void FillRightConvexEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
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{
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// Next concave or convex?
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if (TriangulationUtil.Orient2d(node.Next.Point, node.Next.Next.Point, node.Next.Next.Next.Point) ==
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Orientation.CCW)
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{
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// Concave
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FillRightConcaveEdgeEvent(tcx, edge, node.Next);
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}
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else
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{
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// Convex
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// Next above or below edge?
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if (TriangulationUtil.Orient2d(edge.Q, node.Next.Next.Point, edge.P) == Orientation.CCW)
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{
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// Below
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FillRightConvexEdgeEvent(tcx, edge, node.Next);
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}
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else
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{
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// Above
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}
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}
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}
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private static void FillRightBelowEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
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{
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if (node.Point.X < edge.P.X) // needed?
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{
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if (TriangulationUtil.Orient2d(node.Point, node.Next.Point, node.Next.Next.Point) == Orientation.CCW)
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{
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// Concave
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FillRightConcaveEdgeEvent(tcx, edge, node);
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}
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else
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{
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// Convex
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FillRightConvexEdgeEvent(tcx, edge, node);
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// Retry this one
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FillRightBelowEdgeEvent(tcx, edge, node);
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}
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}
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}
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private static void FillRightAboveEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
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{
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while (node.Next.Point.X < edge.P.X)
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{
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// Check if next node is below the edge
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Orientation o1 = TriangulationUtil.Orient2d(edge.Q, node.Next.Point, edge.P);
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if (o1 == Orientation.CCW)
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{
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FillRightBelowEdgeEvent(tcx, edge, node);
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}
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else
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{
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node = node.Next;
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}
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}
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}
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private static void FillLeftConvexEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
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{
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// Next concave or convex?
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if (TriangulationUtil.Orient2d(node.Prev.Point, node.Prev.Prev.Point, node.Prev.Prev.Prev.Point) ==
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Orientation.CW)
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{
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// Concave
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FillLeftConcaveEdgeEvent(tcx, edge, node.Prev);
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}
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else
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{
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// Convex
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// Next above or below edge?
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if (TriangulationUtil.Orient2d(edge.Q, node.Prev.Prev.Point, edge.P) == Orientation.CW)
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{
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// Below
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FillLeftConvexEdgeEvent(tcx, edge, node.Prev);
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}
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else
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{
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// Above
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}
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}
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}
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private static void FillLeftConcaveEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
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{
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Fill(tcx, node.Prev);
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if (node.Prev.Point != edge.P)
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{
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// Next above or below edge?
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if (TriangulationUtil.Orient2d(edge.Q, node.Prev.Point, edge.P) == Orientation.CW)
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{
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// Below
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if (TriangulationUtil.Orient2d(node.Point, node.Prev.Point, node.Prev.Prev.Point) == Orientation.CW)
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{
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// Next is concave
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FillLeftConcaveEdgeEvent(tcx, edge, node);
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}
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else
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{
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// Next is convex
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}
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}
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}
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}
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private static void FillLeftBelowEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
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{
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if (node.Point.X > edge.P.X)
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{
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if (TriangulationUtil.Orient2d(node.Point, node.Prev.Point, node.Prev.Prev.Point) == Orientation.CW)
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{
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// Concave
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FillLeftConcaveEdgeEvent(tcx, edge, node);
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}
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else
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{
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// Convex
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FillLeftConvexEdgeEvent(tcx, edge, node);
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// Retry this one
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FillLeftBelowEdgeEvent(tcx, edge, node);
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}
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}
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}
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private static void FillLeftAboveEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
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{
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while (node.Prev.Point.X > edge.P.X)
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{
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// Check if next node is below the edge
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Orientation o1 = TriangulationUtil.Orient2d(edge.Q, node.Prev.Point, edge.P);
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if (o1 == Orientation.CW)
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{
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FillLeftBelowEdgeEvent(tcx, edge, node);
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}
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else
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{
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node = node.Prev;
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}
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}
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}
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//TODO: Port note: There were some structural differences here.
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private static bool IsEdgeSideOfTriangle(DelaunayTriangle triangle, TriangulationPoint ep, TriangulationPoint eq)
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{
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int index;
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index = triangle.EdgeIndex(ep, eq);
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if (index != -1)
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{
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triangle.MarkConstrainedEdge(index);
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triangle = triangle.Neighbors[index];
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if (triangle != null)
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{
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triangle.MarkConstrainedEdge(ep, eq);
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}
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return true;
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}
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return false;
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}
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private static void EdgeEvent(DTSweepContext tcx, TriangulationPoint ep, TriangulationPoint eq,
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DelaunayTriangle triangle, TriangulationPoint point)
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{
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TriangulationPoint p1, p2;
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if (IsEdgeSideOfTriangle(triangle, ep, eq))
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{
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return;
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}
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p1 = triangle.PointCCW(point);
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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;
|
|
}
|
|
|
|
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);
|
|
}
|
|
}
|
|
|
|
private static void FlipEdgeEvent(DTSweepContext tcx, TriangulationPoint ep, TriangulationPoint eq,
|
|
DelaunayTriangle t, TriangulationPoint p)
|
|
{
|
|
TriangulationPoint op, newP;
|
|
DelaunayTriangle ot;
|
|
bool inScanArea;
|
|
|
|
ot = t.NeighborAcross(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 InvalidOperationException("[BUG:FIXME] FLIP failed due to missing triangle");
|
|
}
|
|
|
|
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) 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
|
|
{
|
|
newP = NextFlipPoint(ep, eq, ot, op);
|
|
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 TriangulationPoint NextFlipPoint(TriangulationPoint ep, TriangulationPoint eq,
|
|
DelaunayTriangle ot, TriangulationPoint op)
|
|
{
|
|
Orientation o2d = TriangulationUtil.Orient2d(eq, op, ep);
|
|
if (o2d == Orientation.CW)
|
|
{
|
|
// Right
|
|
return ot.PointCCW(op);
|
|
}
|
|
else if (o2d == Orientation.CCW)
|
|
{
|
|
// Left
|
|
return ot.PointCW(op);
|
|
}
|
|
else
|
|
{
|
|
// TODO: implement support for point on constraint edge
|
|
throw new PointOnEdgeException("Point on constrained edge not supported yet");
|
|
}
|
|
}
|
|
|
|
/// <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.NeighborAcross(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.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
|
|
{
|
|
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)
|
|
{
|
|
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)
|
|
{
|
|
// 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>
|
|
/// 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);
|
|
}
|
|
|
|
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;
|
|
tcx.RemoveNode(node);
|
|
|
|
// 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)
|
|
{
|
|
int oi;
|
|
bool inside;
|
|
TriangulationPoint p, op;
|
|
DelaunayTriangle ot;
|
|
|
|
// 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;
|
|
}
|
|
|
|
ot = t.Neighbors[i];
|
|
if (ot != null)
|
|
{
|
|
p = t.Points[i];
|
|
op = ot.OppositePoint(t, p);
|
|
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;
|
|
}
|
|
|
|
inside = TriangulationUtil.SmartIncircle(p,
|
|
t.PointCCW(p),
|
|
t.PointCW(p),
|
|
op);
|
|
|
|
if (inside)
|
|
{
|
|
bool notLegalized;
|
|
|
|
// 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
|
|
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>
|
|
/// 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.NeighborCCW(p);
|
|
n2 = t.NeighborCW(p);
|
|
n3 = ot.NeighborCCW(op);
|
|
n4 = ot.NeighborCW(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);
|
|
}
|
|
}
|
|
} |