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1   /*
2    * Licensed to the Apache Software Foundation (ASF) under one or more
3    * contributor license agreements.  See the NOTICE file distributed with
4    * this work for additional information regarding copyright ownership.
5    * The ASF licenses this file to You under the Apache License, Version 2.0
6    * (the "License"); you may not use this file except in compliance with
7    * the License.  You may obtain a copy of the License at
8    *
9    *      http://www.apache.org/licenses/LICENSE-2.0
10   *
11   * Unless required by applicable law or agreed to in writing, software
12   * distributed under the License is distributed on an "AS IS" BASIS,
13   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14   * See the License for the specific language governing permissions and
15   * limitations under the License.
16   */
17  package org.apache.commons.geometry.core.partitioning.bsp;
18  
19  import java.util.ArrayList;
20  import java.util.Comparator;
21  import java.util.HashSet;
22  import java.util.List;
23  import java.util.Set;
24  import java.util.function.BiConsumer;
25  
26  import org.apache.commons.geometry.core.Point;
27  import org.apache.commons.geometry.core.RegionLocation;
28  import org.apache.commons.geometry.core.partitioning.HyperplaneConvexSubset;
29  import org.apache.commons.geometry.core.partitioning.Split;
30  import org.apache.commons.geometry.core.partitioning.bsp.AbstractBSPTree.SubtreeInitializer;
31  import org.apache.commons.geometry.core.partitioning.bsp.AbstractRegionBSPTree.AbstractRegionNode;
32  
33  /** Class encapsulating logic for building regions by inserting boundaries into a BSP
34   * tree containing structural cuts, i.e. cuts where both sides of the cut have the same region
35   * location. This technique only produces accurate results when the inserted boundaries define
36   * the entire surface of the region. However, for valid input boundaries, significant performance
37   * improvements can be achieved due to the reduced height of the tree, especially where large
38   * numbers of boundaries are involved and/or the defined region is convex.
39   *
40   * <h2>Implementation Notes</h2>
41   *
42   * <p>This class constructs regions in two phases: (1) <em>partition insertion</em> and (2) <em>boundary insertion</em>.
43   * Instances begin in the <em>partition insertion</em> phase. Here, partitions can be inserted into the empty tree
44   * using the standard BSP insertion logic. The {@link RegionCutRule#INHERIT INHERIT} cut rule is used so that the
45   * represented region remains empty even as partitions are inserted.
46   * </p>
47   *
48   * <p>The instance moves into the <em>boundary insertion</em> phase when the caller inserts the first region boundary.
49   * Attempting to insert a partition after this point results in an {@code IllegalStateException}. This ensures that
50   * partitioning cuts are always located higher up the tree than boundary cuts.</p>
51   *
52   * <p>After all boundaries are inserted, the tree undergoes final processing to ensure that the region is consistent
53   * and that unnecessary nodes are removed.</p>
54   *
55   * <p>This class does not expose any public methods so that subclasses can present their own
56   * public API, tailored to the specific types being worked with. In particular, most subclasses
57   * will want to restrict the tree types used with the algorithm, which is difficult to implement
58   * cleanly at this level.</p>
59   * @param <P> Point implementation type
60   * @param <N> BSP tree node implementation type
61   */
62  public abstract class AbstractPartitionedRegionBuilder<
63      P extends Point<P>,
64      N extends AbstractRegionNode<P, N>> {
65  
66      /** Comparator for sorting nodes with the deepest nodes first. */
67      private static final Comparator<BSPTree.Node<?, ?>> DEEPEST_FIRST_ORDER =
68          (a, b) -> Integer.compare(b.depth(), a.depth());
69  
70      /** Tree being constructed. */
71      private final AbstractRegionBSPTree<P, N> tree;
72  
73      /** Subtree initializer for inserted boundaries. */
74      private final SubtreeInitializer<N> subtreeInit;
75  
76      /** Flag indicating whether or not partitions may still be inserted into the tree. */
77      private boolean insertingPartitions = true;
78  
79      /** Set of all internal nodes used as partitioning nodes. */
80      private final Set<N> partitionNodes = new HashSet<>();
81  
82      /** Construct a new instance that builds a partitioned region in the given tree. The tree must
83       * be empty.
84       * @param tree tree to build the region in; must be empty
85       * @throws IllegalArgumentException if the tree is not empty
86       */
87      protected AbstractPartitionedRegionBuilder(final AbstractRegionBSPTree<P, N> tree) {
88          if (!tree.isEmpty()) {
89              throw new IllegalArgumentException("Tree must be empty");
90          }
91  
92          this.tree = tree;
93          this.subtreeInit = tree.getSubtreeInitializer(RegionCutRule.MINUS_INSIDE);
94      }
95  
96      /** Internal method to build and return the tree representing the final partitioned region.
97       * @return the partitioned region
98       */
99      protected AbstractRegionBSPTree<P, N> buildInternal() {
100         // condense to combine homogenous leaf nodes
101         tree.condense();
102 
103         // propagate region interiors to partitioned nodes that have not received
104         // a boundary
105         if (propagateRegionInterior()) {
106             // condense again since some leaf nodes changed
107             tree.condense();
108         }
109 
110         return tree;
111     }
112 
113     /** Internal method to insert a partition into the tree.
114      * @param partition partition to insert
115      * @throws IllegalStateException if a boundary has previously been inserted
116      */
117     protected void insertPartitionInternal(final HyperplaneConvexSubset<P> partition) {
118         ensureInsertingPartitions();
119 
120         tree.insert(partition, RegionCutRule.INHERIT);
121     }
122 
123     /** Internal method to insert a region boundary into the tree.
124      * @param boundary boundary to insert
125      */
126     protected void insertBoundaryInternal(final HyperplaneConvexSubset<P> boundary) {
127         if (insertingPartitions) {
128             // switch to inserting boundaries; place all current internal nodes into
129             // a set for easy identification
130             for (final N node : tree.nodes()) {
131                 if (node.isInternal()) {
132                     partitionNodes.add(node);
133                 }
134             }
135 
136             insertingPartitions = false;
137         }
138 
139         insertBoundaryRecursive(tree.getRoot(), boundary, boundary.getHyperplane().span(),
140             (leaf, cut) -> tree.setNodeCut(leaf, cut, subtreeInit));
141     }
142 
143     /** Insert a region boundary into the tree.
144      * @param node node to insert into
145      * @param insert the hyperplane convex subset to insert
146      * @param trimmed version of the hyperplane convex subset filling the entire space of {@code node}
147      * @param leafFn function to apply to leaf nodes
148      */
149     private void insertBoundaryRecursive(final N node, final HyperplaneConvexSubset<P> insert,
150             final HyperplaneConvexSubset<P> trimmed, final BiConsumer<N, HyperplaneConvexSubset<P>> leafFn) {
151         if (node.isLeaf()) {
152             leafFn.accept(node, trimmed);
153         } else {
154             insertBoundaryRecursiveInternalNode(node, insert, trimmed, leafFn);
155         }
156     }
157 
158     /** Recursive boundary insertion method for internal nodes.
159      * @param node node to insert into
160      * @param insert the hyperplane convex subset to insert
161      * @param trimmed version of the hyperplane convex subset filling the entire space of {@code node}
162      * @param leafFn function to apply to leaf nodes
163      * @see #insertBoundaryRecursive(AbstractRegionNode, HyperplaneConvexSubset, HyperplaneConvexSubset, BiConsumer)
164      */
165     private void insertBoundaryRecursiveInternalNode(final N node, final HyperplaneConvexSubset<P> insert,
166             final HyperplaneConvexSubset<P> trimmed, final BiConsumer<N, HyperplaneConvexSubset<P>> leafFn) {
167 
168         final Split<? extends HyperplaneConvexSubset<P>> insertSplit =
169                 insert.split(node.getCutHyperplane());
170 
171         final HyperplaneConvexSubset<P> minus = insertSplit.getMinus();
172         final HyperplaneConvexSubset<P> plus = insertSplit.getPlus();
173 
174         if (minus == null && plus == null && isPartitionNode(node)) {
175             // the inserted boundary lies directly on a partition; proceed down the tree with the
176             // rest of the insertion algorithm but instead of cutting the final leaf nodes, just
177             // set the location
178 
179             // remove this node from the set of partition nodes since this is now a boundary cut
180             partitionNodes.remove(node);
181 
182             final boolean sameOrientation = node.getCutHyperplane().similarOrientation(insert.getHyperplane());
183             final N insertMinus = sameOrientation ? node.getMinus() : node.getPlus();
184             final N insertPlus = sameOrientation ? node.getPlus() : node.getMinus();
185 
186             insertBoundaryRecursive(insertMinus, insert, trimmed,
187                 (leaf, cut) -> leaf.setLocation(RegionLocation.INSIDE));
188 
189             insertBoundaryRecursive(insertPlus, insert, trimmed,
190                 (leaf, cut) -> leaf.setLocation(RegionLocation.OUTSIDE));
191 
192         } else if (minus != null || plus != null) {
193             final Split<? extends HyperplaneConvexSubset<P>> trimmedSplit =
194                     trimmed.split(node.getCutHyperplane());
195 
196             final HyperplaneConvexSubset<P> trimmedMinus = trimmedSplit.getMinus();
197             final HyperplaneConvexSubset<P> trimmedPlus = trimmedSplit.getPlus();
198 
199             if (minus != null) {
200                 insertBoundaryRecursive(node.getMinus(), minus, trimmedMinus, leafFn);
201             }
202             if (plus != null) {
203                 insertBoundaryRecursive(node.getPlus(), plus, trimmedPlus, leafFn);
204             }
205         }
206     }
207 
208     /** Propagate the region interior to partitioned leaf nodes that have not had a boundary
209      * inserted.
210      * @return true if any nodes were changed
211      */
212     private boolean propagateRegionInterior() {
213         final List<N> outsidePartitionedLeaves = getOutsidePartitionedLeaves();
214         outsidePartitionedLeaves.sort(DEEPEST_FIRST_ORDER);
215 
216         int changeCount = 0;
217 
218         N parent;
219         N sibling;
220         for (final N leaf : outsidePartitionedLeaves) {
221             parent = leaf.getParent();
222 
223             // check if the parent cut touches the inside anywhere on the side opposite of
224             // this leaf; if so, then this node should also be inside
225             sibling = leaf.isMinus() ?
226                     parent.getPlus() :
227                     parent.getMinus();
228 
229             if (touchesInside(parent.getCut(), sibling)) {
230                 leaf.setLocation(RegionLocation.INSIDE);
231 
232                 ++changeCount;
233             }
234         }
235 
236         return changeCount > 0;
237     }
238 
239     /** Return a list containing all outside leaf nodes that have a parent marked as a partition node.
240      * @return a list containing all outside leaf nodes that have a parent marked as a partition node
241      */
242     private List<N> getOutsidePartitionedLeaves() {
243         final List<N> result = new ArrayList<>();
244 
245         final N root = tree.getRoot();
246         collectOutsidePartitionedLeavesRecursive(root, false, result);
247 
248         return result;
249     }
250 
251    /** Recursively collect all outside leaf nodes that have a parent marked as a partition node.
252     * @param node root of the subtree to collect nodes from
253     * @param parentIsPartitionNode true if the parent of {@code node} is a partition node
254     * @param result list of accumulated results
255     */
256     private void collectOutsidePartitionedLeavesRecursive(final N node, final boolean parentIsPartitionNode,
257             final List<N> result) {
258         if (node != null) {
259             if (parentIsPartitionNode && node.isOutside()) {
260                 result.add(node);
261             }
262 
263             final boolean partitionNode = isPartitionNode(node);
264 
265             collectOutsidePartitionedLeavesRecursive(node.getMinus(), partitionNode, result);
266             collectOutsidePartitionedLeavesRecursive(node.getPlus(), partitionNode, result);
267         }
268     }
269 
270     /** Return true if {@code sub} touches an inside leaf node anywhere in the subtree rooted at {@code node}.
271      * @param sub convex subset to check
272      * @param node root node of the subtree to test against
273      * @return true if {@code sub} touches an inside leaf node anywhere in the subtree rooted at {@code node}
274      */
275     private boolean touchesInside(final HyperplaneConvexSubset<P> sub, final N node) {
276         if (sub != null) {
277             if (node.isLeaf()) {
278                 return node.isInside();
279             } else {
280                 final Split<? extends HyperplaneConvexSubset<P>> split = sub.split(node.getCutHyperplane());
281 
282                 return touchesInside(split.getMinus(), node.getMinus()) ||
283                         touchesInside(split.getPlus(), node.getPlus());
284 
285             }
286         }
287 
288         return false;
289     }
290 
291     /** Return true if the given node is marked as a partition node.
292      * @param node node to check
293      * @return true if the given node is marked as a partition node
294      */
295     private boolean isPartitionNode(final N node) {
296         return partitionNodes.contains(node);
297     }
298 
299     /** Throw an exception if the instance is no longer accepting partitions.
300      * @throws IllegalStateException if the instance is no longer accepting partitions
301      */
302     private void ensureInsertingPartitions() {
303         if (!insertingPartitions) {
304             throw new IllegalStateException("Cannot insert partitions after boundaries have been inserted");
305         }
306     }
307 }