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    * Licensed to the Apache Software Foundation (ASF) under one or more
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    * this work for additional information regarding copyright ownership.
    * The ASF licenses this file to You 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.
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  package org.apache.commons.geometry.core.partitioning.bsp;
  
  import java.util.ArrayList;
  import java.util.Comparator;
  import java.util.HashSet;
  import java.util.List;
  import java.util.Set;
  import java.util.function.BiConsumer;
  
  import org.apache.commons.geometry.core.Point;
  import org.apache.commons.geometry.core.RegionLocation;
  import org.apache.commons.geometry.core.partitioning.HyperplaneConvexSubset;
  import org.apache.commons.geometry.core.partitioning.Split;
  import org.apache.commons.geometry.core.partitioning.bsp.AbstractBSPTree.SubtreeInitializer;
  import org.apache.commons.geometry.core.partitioning.bsp.AbstractRegionBSPTree.AbstractRegionNode;
  
  /** Class encapsulating logic for building regions by inserting boundaries into a BSP
   * tree containing structural cuts, i.e. cuts where both sides of the cut have the same region
   * location. This technique only produces accurate results when the inserted boundaries define
   * the entire surface of the region. However, for valid input boundaries, significant performance
   * improvements can be achieved due to the reduced height of the tree, especially where large
   * numbers of boundaries are involved and/or the defined region is convex.
   *
   * <h2>Implementation Notes</h2>
   *
   * <p>This class constructs regions in two phases: (1) <em>partition insertion</em> and (2) <em>boundary insertion</em>.
   * Instances begin in the <em>partition insertion</em> phase. Here, partitions can be inserted into the empty tree
   * using the standard BSP insertion logic. The {@link RegionCutRule#INHERIT INHERIT} cut rule is used so that the
   * represented region remains empty even as partitions are inserted.
   * </p>
   *
   * <p>The instance moves into the <em>boundary insertion</em> phase when the caller inserts the first region boundary.
   * Attempting to insert a partition after this point results in an {@code IllegalStateException}. This ensures that
   * partitioning cuts are always located higher up the tree than boundary cuts.</p>
   *
   * <p>After all boundaries are inserted, the tree undergoes final processing to ensure that the region is consistent
   * and that unnecessary nodes are removed.</p>
   *
   * <p>This class does not expose any public methods so that subclasses can present their own
   * public API, tailored to the specific types being worked with. In particular, most subclasses
   * will want to restrict the tree types used with the algorithm, which is difficult to implement
   * cleanly at this level.</p>
   * @param <P> Point implementation type
   * @param <N> BSP tree node implementation type
   */
  public abstract class AbstractPartitionedRegionBuilder<
      P extends Point<P>,
      N extends AbstractRegionNode<P, N>> {
  
      /** Comparator for sorting nodes with the deepest nodes first. */
      private static final Comparator<BSPTree.Node<?, ?>> DEEPEST_FIRST_ORDER =
          (a, b) -> Integer.compare(b.depth(), a.depth());
  
      /** Tree being constructed. */
      private final AbstractRegionBSPTree<P, N> tree;
  
      /** Subtree initializer for inserted boundaries. */
      private final SubtreeInitializer<N> subtreeInit;
  
      /** Flag indicating whether or not partitions may still be inserted into the tree. */
      private boolean insertingPartitions = true;
  
      /** Set of all internal nodes used as partitioning nodes. */
      private final Set<N> partitionNodes = new HashSet<>();
  
      /** Construct a new instance that builds a partitioned region in the given tree. The tree must
       * be empty.
       * @param tree tree to build the region in; must be empty
       * @throws IllegalArgumentException if the tree is not empty
       */
      protected AbstractPartitionedRegionBuilder(final AbstractRegionBSPTree<P, N> tree) {
          if (!tree.isEmpty()) {
              throw new IllegalArgumentException("Tree must be empty");
          }
  
          this.tree = tree;
          this.subtreeInit = tree.getSubtreeInitializer(RegionCutRule.MINUS_INSIDE);
      }
  
      /** Internal method to build and return the tree representing the final partitioned region.
       * @return the partitioned region
       */
      protected AbstractRegionBSPTree<P, N> buildInternal() {
         // condense to combine homogenous leaf nodes
         tree.condense();
 
         // propagate region interiors to partitioned nodes that have not received
         // a boundary
         if (propagateRegionInterior()) {
             // condense again since some leaf nodes changed
             tree.condense();
         }
 
         return tree;
     }
 
     /** Internal method to insert a partition into the tree.
      * @param partition partition to insert
      * @throws IllegalStateException if a boundary has previously been inserted
      */
     protected void insertPartitionInternal(final HyperplaneConvexSubset<P> partition) {
         ensureInsertingPartitions();
 
         tree.insert(partition, RegionCutRule.INHERIT);
     }
 
     /** Internal method to insert a region boundary into the tree.
      * @param boundary boundary to insert
      */
     protected void insertBoundaryInternal(final HyperplaneConvexSubset<P> boundary) {
         if (insertingPartitions) {
             // switch to inserting boundaries; place all current internal nodes into
             // a set for easy identification
             for (final N node : tree.nodes()) {
                 if (node.isInternal()) {
                     partitionNodes.add(node);
                 }
             }
 
             insertingPartitions = false;
         }
 
         insertBoundaryRecursive(tree.getRoot(), boundary, boundary.getHyperplane().span(),
             (leaf, cut) -> tree.setNodeCut(leaf, cut, subtreeInit));
     }
 
     /** Insert a region boundary into the tree.
      * @param node node to insert into
      * @param insert the hyperplane convex subset to insert
      * @param trimmed version of the hyperplane convex subset filling the entire space of {@code node}
      * @param leafFn function to apply to leaf nodes
      */
     private void insertBoundaryRecursive(final N node, final HyperplaneConvexSubset<P> insert,
             final HyperplaneConvexSubset<P> trimmed, final BiConsumer<N, HyperplaneConvexSubset<P>> leafFn) {
         if (node.isLeaf()) {
             leafFn.accept(node, trimmed);
         } else {
             final Split<? extends HyperplaneConvexSubset<P>> insertSplit =
                     insert.split(node.getCutHyperplane());
 
             final HyperplaneConvexSubset<P> minus = insertSplit.getMinus();
             final HyperplaneConvexSubset<P> plus = insertSplit.getPlus();
 
             if (minus == null && plus == null && isPartitionNode(node)) {
                 // the inserted boundary lies directly on a partition; proceed down the tree with the
                 // rest of the insertion algorithm but instead of cutting the final leaf nodes, just
                 // set the location
 
                 // remove this node from the set of partition nodes since this is now a boundary cut
                 partitionNodes.remove(node);
 
                 final boolean sameOrientation = node.getCutHyperplane().similarOrientation(insert.getHyperplane());
                 final N insertMinus = sameOrientation ? node.getMinus() : node.getPlus();
                 final N insertPlus = sameOrientation ? node.getPlus() : node.getMinus();
 
                 insertBoundaryRecursive(insertMinus, insert, trimmed,
                     (leaf, cut) -> leaf.setLocation(RegionLocation.INSIDE));
 
                 insertBoundaryRecursive(insertPlus, insert, trimmed,
                     (leaf, cut) -> leaf.setLocation(RegionLocation.OUTSIDE));
 
             } else if (minus != null || plus != null) {
                 final Split<? extends HyperplaneConvexSubset<P>> trimmedSplit =
                         trimmed.split(node.getCutHyperplane());
 
                 final HyperplaneConvexSubset<P> trimmedMinus = trimmedSplit.getMinus();
                 final HyperplaneConvexSubset<P> trimmedPlus = trimmedSplit.getPlus();
 
                 if (minus != null) {
                     insertBoundaryRecursive(node.getMinus(), minus, trimmedMinus, leafFn);
                 }
                 if (plus != null) {
                     insertBoundaryRecursive(node.getPlus(), plus, trimmedPlus, leafFn);
                 }
             }
         }
     }
 
     /** Propagate the region interior to partitioned leaf nodes that have not had a boundary
      * inserted.
      * @return true if any nodes were changed
      */
     private boolean propagateRegionInterior() {
         final List<N> outsidePartitionedLeaves = getOutsidePartitionedLeaves();
         outsidePartitionedLeaves.sort(DEEPEST_FIRST_ORDER);
 
         int changeCount = 0;
 
         N parent;
         N sibling;
         for (final N leaf : outsidePartitionedLeaves) {
             parent = leaf.getParent();
 
             // check if the parent cut touches the inside anywhere on the side opposite of
             // this leaf; if so, then this node should also be inside
             sibling = leaf.isMinus() ?
                     parent.getPlus() :
                     parent.getMinus();
 
             if (touchesInside(parent.getCut(), sibling)) {
                 leaf.setLocation(RegionLocation.INSIDE);
 
                 ++changeCount;
             }
         }
 
         return changeCount > 0;
     }
 
     /** Return a list containing all outside leaf nodes that have a parent marked as a partition node.
      * @return a list containing all outside leaf nodes that have a parent marked as a partition node
      */
     private List<N> getOutsidePartitionedLeaves() {
         final List<N> result = new ArrayList<>();
 
         final N root = tree.getRoot();
         collectOutsidePartitionedLeavesRecursive(root, false, result);
 
         return result;
     }
 
    /** Recursively collect all outside leaf nodes that have a parent marked as a partition node.
     * @param node root of the subtree to collect nodes from
     * @param parentIsPartitionNode true if the parent of {@code node} is a partition node
     * @param result list of accumulated results
     */
     private void collectOutsidePartitionedLeavesRecursive(final N node, final boolean parentIsPartitionNode,
             final List<N> result) {
         if (node != null) {
             if (parentIsPartitionNode && node.isOutside()) {
                 result.add(node);
             }
 
             final boolean partitionNode = isPartitionNode(node);
 
             collectOutsidePartitionedLeavesRecursive(node.getMinus(), partitionNode, result);
             collectOutsidePartitionedLeavesRecursive(node.getPlus(), partitionNode, result);
         }
     }
 
     /** Return true if {@code sub} touches an inside leaf node anywhere in the subtree rooted at {@code node}.
      * @param sub convex subset to check
      * @param node root node of the subtree to test against
      * @return true if {@code sub} touches an inside leaf node anywhere in the subtree rooted at {@code node}
      */
     private boolean touchesInside(final HyperplaneConvexSubset<P> sub, final N node) {
         if (sub != null) {
             if (node.isLeaf()) {
                 return node.isInside();
             } else {
                 final Split<? extends HyperplaneConvexSubset<P>> split = sub.split(node.getCutHyperplane());
 
                 return touchesInside(split.getMinus(), node.getMinus()) ||
                         touchesInside(split.getPlus(), node.getPlus());
 
             }
         }
 
         return false;
     }
 
     /** Return true if the given node is marked as a partition node.
      * @param node node to check
      * @return true if the given node is marked as a partition node
      */
     private boolean isPartitionNode(final N node) {
         return partitionNodes.contains(node);
     }
 
     /** Throw an exception if the instance is no longer accepting partitions.
      * @throws IllegalStateException if the instance is no longer accepting partitions
      */
     private void ensureInsertingPartitions() {
         if (!insertingPartitions) {
             throw new IllegalStateException("Cannot insert partitions after boundaries have been inserted");
         }
     }
 }