001 /* 002 * Licensed to the Apache Software Foundation (ASF) under one or more 003 * contributor license agreements. See the NOTICE file distributed with 004 * this work for additional information regarding copyright ownership. 005 * The ASF licenses this file to You under the Apache License, Version 2.0 006 * (the "License"); you may not use this file except in compliance with 007 * the License. You may obtain a copy of the License at 008 * 009 * http://www.apache.org/licenses/LICENSE-2.0 010 * 011 * Unless required by applicable law or agreed to in writing, software 012 * distributed under the License is distributed on an "AS IS" BASIS, 013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 014 * See the License for the specific language governing permissions and 015 * limitations under the License. 016 */ 017 package org.apache.commons.math3.geometry.euclidean.threed; 018 019 import java.util.ArrayList; 020 021 import org.apache.commons.math3.geometry.euclidean.twod.Euclidean2D; 022 import org.apache.commons.math3.geometry.euclidean.twod.PolygonsSet; 023 import org.apache.commons.math3.geometry.euclidean.twod.Vector2D; 024 import org.apache.commons.math3.geometry.partitioning.AbstractSubHyperplane; 025 import org.apache.commons.math3.geometry.partitioning.BSPTree; 026 import org.apache.commons.math3.geometry.partitioning.BSPTreeVisitor; 027 import org.apache.commons.math3.geometry.partitioning.BoundaryAttribute; 028 import org.apache.commons.math3.geometry.partitioning.RegionFactory; 029 import org.apache.commons.math3.geometry.partitioning.SubHyperplane; 030 import org.apache.commons.math3.util.FastMath; 031 032 /** Extractor for {@link PolygonsSet polyhedrons sets} outlines. 033 * <p>This class extracts the 2D outlines from {{@link PolygonsSet 034 * polyhedrons sets} in a specified projection plane.</p> 035 * @version $Id: OutlineExtractor.java 1416643 2012-12-03 19:37:14Z tn $ 036 * @since 3.0 037 */ 038 public class OutlineExtractor { 039 040 /** Abscissa axis of the projection plane. */ 041 private Vector3D u; 042 043 /** Ordinate axis of the projection plane. */ 044 private Vector3D v; 045 046 /** Normal of the projection plane (viewing direction). */ 047 private Vector3D w; 048 049 /** Build an extractor for a specific projection plane. 050 * @param u abscissa axis of the projection point 051 * @param v ordinate axis of the projection point 052 */ 053 public OutlineExtractor(final Vector3D u, final Vector3D v) { 054 this.u = u; 055 this.v = v; 056 w = Vector3D.crossProduct(u, v); 057 } 058 059 /** Extract the outline of a polyhedrons set. 060 * @param polyhedronsSet polyhedrons set whose outline must be extracted 061 * @return an outline, as an array of loops. 062 */ 063 public Vector2D[][] getOutline(final PolyhedronsSet polyhedronsSet) { 064 065 // project all boundary facets into one polygons set 066 final BoundaryProjector projector = new BoundaryProjector(); 067 polyhedronsSet.getTree(true).visit(projector); 068 final PolygonsSet projected = projector.getProjected(); 069 070 // Remove the spurious intermediate vertices from the outline 071 final Vector2D[][] outline = projected.getVertices(); 072 for (int i = 0; i < outline.length; ++i) { 073 final Vector2D[] rawLoop = outline[i]; 074 int end = rawLoop.length; 075 int j = 0; 076 while (j < end) { 077 if (pointIsBetween(rawLoop, end, j)) { 078 // the point should be removed 079 for (int k = j; k < (end - 1); ++k) { 080 rawLoop[k] = rawLoop[k + 1]; 081 } 082 --end; 083 } else { 084 // the point remains in the loop 085 ++j; 086 } 087 } 088 if (end != rawLoop.length) { 089 // resize the array 090 outline[i] = new Vector2D[end]; 091 System.arraycopy(rawLoop, 0, outline[i], 0, end); 092 } 093 } 094 095 return outline; 096 097 } 098 099 /** Check if a point is geometrically between its neighbour in an array. 100 * <p>The neighbours are computed considering the array is a loop 101 * (i.e. point at index (n-1) is before point at index 0)</p> 102 * @param loop points array 103 * @param n number of points to consider in the array 104 * @param i index of the point to check (must be between 0 and n-1) 105 * @return true if the point is exactly between its neighbours 106 */ 107 private boolean pointIsBetween(final Vector2D[] loop, final int n, final int i) { 108 final Vector2D previous = loop[(i + n - 1) % n]; 109 final Vector2D current = loop[i]; 110 final Vector2D next = loop[(i + 1) % n]; 111 final double dx1 = current.getX() - previous.getX(); 112 final double dy1 = current.getY() - previous.getY(); 113 final double dx2 = next.getX() - current.getX(); 114 final double dy2 = next.getY() - current.getY(); 115 final double cross = dx1 * dy2 - dx2 * dy1; 116 final double dot = dx1 * dx2 + dy1 * dy2; 117 final double d1d2 = FastMath.sqrt((dx1 * dx1 + dy1 * dy1) * (dx2 * dx2 + dy2 * dy2)); 118 return (FastMath.abs(cross) <= (1.0e-6 * d1d2)) && (dot >= 0.0); 119 } 120 121 /** Visitor projecting the boundary facets on a plane. */ 122 private class BoundaryProjector implements BSPTreeVisitor<Euclidean3D> { 123 124 /** Projection of the polyhedrons set on the plane. */ 125 private PolygonsSet projected; 126 127 /** Simple constructor. 128 */ 129 public BoundaryProjector() { 130 projected = new PolygonsSet(new BSPTree<Euclidean2D>(Boolean.FALSE)); 131 } 132 133 /** {@inheritDoc} */ 134 public Order visitOrder(final BSPTree<Euclidean3D> node) { 135 return Order.MINUS_SUB_PLUS; 136 } 137 138 /** {@inheritDoc} */ 139 public void visitInternalNode(final BSPTree<Euclidean3D> node) { 140 @SuppressWarnings("unchecked") 141 final BoundaryAttribute<Euclidean3D> attribute = 142 (BoundaryAttribute<Euclidean3D>) node.getAttribute(); 143 if (attribute.getPlusOutside() != null) { 144 addContribution(attribute.getPlusOutside(), false); 145 } 146 if (attribute.getPlusInside() != null) { 147 addContribution(attribute.getPlusInside(), true); 148 } 149 } 150 151 /** {@inheritDoc} */ 152 public void visitLeafNode(final BSPTree<Euclidean3D> node) { 153 } 154 155 /** Add he contribution of a boundary facet. 156 * @param facet boundary facet 157 * @param reversed if true, the facet has the inside on its plus side 158 */ 159 private void addContribution(final SubHyperplane<Euclidean3D> facet, final boolean reversed) { 160 161 // extract the vertices of the facet 162 @SuppressWarnings("unchecked") 163 final AbstractSubHyperplane<Euclidean3D, Euclidean2D> absFacet = 164 (AbstractSubHyperplane<Euclidean3D, Euclidean2D>) facet; 165 final Plane plane = (Plane) facet.getHyperplane(); 166 167 final double scal = plane.getNormal().dotProduct(w); 168 if (FastMath.abs(scal) > 1.0e-3) { 169 Vector2D[][] vertices = 170 ((PolygonsSet) absFacet.getRemainingRegion()).getVertices(); 171 172 if ((scal < 0) ^ reversed) { 173 // the facet is seen from the inside, 174 // we need to invert its boundary orientation 175 final Vector2D[][] newVertices = new Vector2D[vertices.length][]; 176 for (int i = 0; i < vertices.length; ++i) { 177 final Vector2D[] loop = vertices[i]; 178 final Vector2D[] newLoop = new Vector2D[loop.length]; 179 if (loop[0] == null) { 180 newLoop[0] = null; 181 for (int j = 1; j < loop.length; ++j) { 182 newLoop[j] = loop[loop.length - j]; 183 } 184 } else { 185 for (int j = 0; j < loop.length; ++j) { 186 newLoop[j] = loop[loop.length - (j + 1)]; 187 } 188 } 189 newVertices[i] = newLoop; 190 } 191 192 // use the reverted vertices 193 vertices = newVertices; 194 195 } 196 197 // compute the projection of the facet in the outline plane 198 final ArrayList<SubHyperplane<Euclidean2D>> edges = new ArrayList<SubHyperplane<Euclidean2D>>(); 199 for (Vector2D[] loop : vertices) { 200 final boolean closed = loop[0] != null; 201 int previous = closed ? (loop.length - 1) : 1; 202 Vector3D previous3D = plane.toSpace(loop[previous]); 203 int current = (previous + 1) % loop.length; 204 Vector2D pPoint = new Vector2D(previous3D.dotProduct(u), 205 previous3D.dotProduct(v)); 206 while (current < loop.length) { 207 208 final Vector3D current3D = plane.toSpace(loop[current]); 209 final Vector2D cPoint = new Vector2D(current3D.dotProduct(u), 210 current3D.dotProduct(v)); 211 final org.apache.commons.math3.geometry.euclidean.twod.Line line = 212 new org.apache.commons.math3.geometry.euclidean.twod.Line(pPoint, cPoint); 213 SubHyperplane<Euclidean2D> edge = line.wholeHyperplane(); 214 215 if (closed || (previous != 1)) { 216 // the previous point is a real vertex 217 // it defines one bounding point of the edge 218 final double angle = line.getAngle() + 0.5 * FastMath.PI; 219 final org.apache.commons.math3.geometry.euclidean.twod.Line l = 220 new org.apache.commons.math3.geometry.euclidean.twod.Line(pPoint, angle); 221 edge = edge.split(l).getPlus(); 222 } 223 224 if (closed || (current != (loop.length - 1))) { 225 // the current point is a real vertex 226 // it defines one bounding point of the edge 227 final double angle = line.getAngle() + 0.5 * FastMath.PI; 228 final org.apache.commons.math3.geometry.euclidean.twod.Line l = 229 new org.apache.commons.math3.geometry.euclidean.twod.Line(cPoint, angle); 230 edge = edge.split(l).getMinus(); 231 } 232 233 edges.add(edge); 234 235 previous = current++; 236 previous3D = current3D; 237 pPoint = cPoint; 238 239 } 240 } 241 final PolygonsSet projectedFacet = new PolygonsSet(edges); 242 243 // add the contribution of the facet to the global outline 244 projected = (PolygonsSet) new RegionFactory<Euclidean2D>().union(projected, projectedFacet); 245 246 } 247 } 248 249 /** Get the projection of the polyhedrons set on the plane. 250 * @return projection of the polyhedrons set on the plane 251 */ 252 public PolygonsSet getProjected() { 253 return projected; 254 } 255 256 } 257 258 }