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    }