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/*******************************************************************************
* Copyright 2011 See AUTHORS file.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
******************************************************************************/
package com.badlogic.gdx.math;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
/** A simple implementation of the ear cutting algorithm to triangulate simple polygons without holes. For more information:
* http://cgm.cs.mcgill.ca/~godfried/teaching/cg-projects/97/Ian/algorithm2.html
* http://www.geometrictools.com/Documentation/TriangulationByEarClipping.pdf
*
* @author [email protected]
* @author Nicolas Gramlich (Improved performance. Collinear edges are now supported.)
* @author Eric Spitz */
public final class EarClippingTriangulator {
private static final int CONCAVE = 1;
private static final int CONVEX = -1;
private int concaveVertexCount;
/** Triangulates the given (concave) polygon to a list of triangles. The resulting triangles have clockwise order.
*
* @param polygon the polygon
* @return the triangles */
public List computeTriangles (final List polygon) {
// TODO Check if LinkedList performs better
final ArrayList triangles = new ArrayList();
final ArrayList vertices = new ArrayList(polygon.size());
vertices.addAll(polygon);
/*
* ESpitz: For the sake of performance, we only need to test for eartips while the polygon has more than three verts. If
* there are only three verts left to test, or there were only three verts to begin with, there is no need to continue with
* this loop.
*/
while (vertices.size() > 3) {
// TODO Usually(Always?) only the Types of the vertices next to the
// ear change! --> Improve
final int vertexTypes[] = this.classifyVertices(vertices);
final int vertexCount = vertices.size();
for (int index = 0; index < vertexCount; index++) {
if (this.isEarTip(vertices, index, vertexTypes)) {
this.cutEarTip(vertices, index, triangles);
break;
}
}
}
/*
* ESpitz: If there are only three verts left to test, or there were only three verts to begin with, we have the final
* triangle.
*/
if (vertices.size() == 3) {
triangles.addAll(vertices);
}
return triangles;
}
private static boolean areVerticesClockwise (final ArrayList pVertices) {
final int vertexCount = pVertices.size();
float area = 0;
for (int i = 0; i < vertexCount; i++) {
final Vector2 p1 = pVertices.get(i);
final Vector2 p2 = pVertices.get(EarClippingTriangulator.computeNextIndex(pVertices, i));
area += p1.x * p2.y - p2.x * p1.y;
}
if (area < 0) {
return true;
} else {
return false;
}
}
/** @param pVertices
* @return An array of length pVertices.size() filled with either {@link EarClippingTriangulator#CONCAVE} or
* {@link EarClippingTriangulator#CONVEX}. */
private int[] classifyVertices (final ArrayList pVertices) {
final int vertexCount = pVertices.size();
final int[] vertexTypes = new int[vertexCount];
this.concaveVertexCount = 0;
/* Ensure vertices are in clockwise order. */
if (!EarClippingTriangulator.areVerticesClockwise(pVertices)) {
Collections.reverse(pVertices);
}
for (int index = 0; index < vertexCount; index++) {
final int previousIndex = EarClippingTriangulator.computePreviousIndex(pVertices, index);
final int nextIndex = EarClippingTriangulator.computeNextIndex(pVertices, index);
final Vector2 previousVertex = pVertices.get(previousIndex);
final Vector2 currentVertex = pVertices.get(index);
final Vector2 nextVertex = pVertices.get(nextIndex);
if (EarClippingTriangulator.isTriangleConvex(previousVertex.x, previousVertex.y, currentVertex.x, currentVertex.y,
nextVertex.x, nextVertex.y)) {
vertexTypes[index] = CONVEX;
} else {
vertexTypes[index] = CONCAVE;
this.concaveVertexCount++;
}
}
return vertexTypes;
}
private static boolean isTriangleConvex (final float pX1, final float pY1, final float pX2, final float pY2, final float pX3,
final float pY3) {
if (EarClippingTriangulator.computeSpannedAreaSign(pX1, pY1, pX2, pY2, pX3, pY3) < 0) {
return false;
} else {
return true;
}
}
private static int computeSpannedAreaSign (final float pX1, final float pY1, final float pX2, final float pY2,
final float pX3, final float pY3) {
/*
* Espitz: using doubles corrects for very rare cases where we run into floating point imprecision in the area test, causing
* the method to return a 0 when it should have returned -1 or 1.
*/
double area = 0;
area += (double)pX1 * (pY3 - pY2);
area += (double)pX2 * (pY1 - pY3);
area += (double)pX3 * (pY2 - pY1);
return (int)Math.signum(area);
}
/** @return true when the Triangles contains one or more vertices, false otherwise. */
private static boolean isAnyVertexInTriangle (final ArrayList pVertices, final int[] pVertexTypes, final float pX1,
final float pY1, final float pX2, final float pY2, final float pX3, final float pY3) {
int i = 0;
final int vertexCount = pVertices.size();
while (i < vertexCount - 1) {
if ((pVertexTypes[i] == CONCAVE)) {
final Vector2 currentVertex = pVertices.get(i);
final float currentVertexX = currentVertex.x;
final float currentVertexY = currentVertex.y;
final int areaSign1 = EarClippingTriangulator.computeSpannedAreaSign(pX1, pY1, pX2, pY2, currentVertexX,
currentVertexY);
final int areaSign2 = EarClippingTriangulator.computeSpannedAreaSign(pX2, pY2, pX3, pY3, currentVertexX,
currentVertexY);
final int areaSign3 = EarClippingTriangulator.computeSpannedAreaSign(pX3, pY3, pX1, pY1, currentVertexX,
currentVertexY);
if (areaSign1 > 0 && areaSign2 > 0 && areaSign3 > 0) {
return true;
} else if (areaSign1 <= 0 && areaSign2 <= 0 && areaSign3 <= 0) {
return true;
}
}
i++;
}
return false;
}
private boolean isEarTip (final ArrayList pVertices, final int pEarTipIndex, final int[] pVertexTypes) {
if (this.concaveVertexCount != 0) {
final Vector2 previousVertex = pVertices.get(EarClippingTriangulator.computePreviousIndex(pVertices, pEarTipIndex));
final Vector2 currentVertex = pVertices.get(pEarTipIndex);
final Vector2 nextVertex = pVertices.get(EarClippingTriangulator.computeNextIndex(pVertices, pEarTipIndex));
if (EarClippingTriangulator.isAnyVertexInTriangle(pVertices, pVertexTypes, previousVertex.x, previousVertex.y,
currentVertex.x, currentVertex.y, nextVertex.x, nextVertex.y)) {
return false;
} else {
return true;
}
} else {
return true;
}
}
private void cutEarTip (final ArrayList pVertices, final int pEarTipIndex, final ArrayList pTriangles) {
final int previousIndex = EarClippingTriangulator.computePreviousIndex(pVertices, pEarTipIndex);
final int nextIndex = EarClippingTriangulator.computeNextIndex(pVertices, pEarTipIndex);
if (!EarClippingTriangulator.isCollinear(pVertices, previousIndex, pEarTipIndex, nextIndex)) {
pTriangles.add(new Vector2(pVertices.get(previousIndex)));
pTriangles.add(new Vector2(pVertices.get(pEarTipIndex)));
pTriangles.add(new Vector2(pVertices.get(nextIndex)));
}
pVertices.remove(pEarTipIndex);
if (pVertices.size() >= 3) {
EarClippingTriangulator.removeCollinearNeighborEarsAfterRemovingEarTip(pVertices, pEarTipIndex);
}
}
private static void removeCollinearNeighborEarsAfterRemovingEarTip (final ArrayList pVertices,
final int pEarTipCutIndex) {
final int collinearityCheckNextIndex = pEarTipCutIndex % pVertices.size();
int collinearCheckPreviousIndex = EarClippingTriangulator.computePreviousIndex(pVertices, collinearityCheckNextIndex);
if (EarClippingTriangulator.isCollinear(pVertices, collinearityCheckNextIndex)) {
pVertices.remove(collinearityCheckNextIndex);
if (pVertices.size() > 3) {
/* Update */
collinearCheckPreviousIndex = EarClippingTriangulator.computePreviousIndex(pVertices, collinearityCheckNextIndex);
if (EarClippingTriangulator.isCollinear(pVertices, collinearCheckPreviousIndex)) {
pVertices.remove(collinearCheckPreviousIndex);
}
}
} else if (EarClippingTriangulator.isCollinear(pVertices, collinearCheckPreviousIndex)) {
pVertices.remove(collinearCheckPreviousIndex);
}
}
private static boolean isCollinear (final ArrayList pVertices, final int pIndex) {
final int previousIndex = EarClippingTriangulator.computePreviousIndex(pVertices, pIndex);
final int nextIndex = EarClippingTriangulator.computeNextIndex(pVertices, pIndex);
return EarClippingTriangulator.isCollinear(pVertices, previousIndex, pIndex, nextIndex);
}
private static boolean isCollinear (final ArrayList pVertices, final int pPreviousIndex, final int pIndex,
final int pNextIndex) {
final Vector2 previousVertex = pVertices.get(pPreviousIndex);
final Vector2 vertex = pVertices.get(pIndex);
final Vector2 nextVertex = pVertices.get(pNextIndex);
return EarClippingTriangulator.computeSpannedAreaSign(previousVertex.x, previousVertex.y, vertex.x, vertex.y, nextVertex.x,
nextVertex.y) == 0;
}
private static int computePreviousIndex (final List pVertices, final int pIndex) {
return pIndex == 0 ? pVertices.size() - 1 : pIndex - 1;
}
private static int computeNextIndex (final List pVertices, final int pIndex) {
return pIndex == pVertices.size() - 1 ? 0 : pIndex + 1;
}
}
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