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The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.
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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* 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.
*/
package org.apache.commons.math3.geometry.partitioning;
import java.util.HashMap;
import java.util.Map;
import org.apache.commons.math3.geometry.Space;
/** This class implements the dimension-independent parts of {@link SubHyperplane}.
* sub-hyperplanes are obtained when parts of an {@link
* Hyperplane hyperplane} are chopped off by other hyperplanes that
* intersect it. The remaining part is a convex region. Such objects
* appear in {@link BSPTree BSP trees} as the intersection of a cut
* hyperplane with the convex region which it splits, the chopping
* hyperplanes are the cut hyperplanes closer to the tree root.
* @param Type of the embedding space.
* @param Type of the embedded sub-space.
* @since 3.0
*/
public abstract class AbstractSubHyperplane
implements SubHyperplane {
/** Underlying hyperplane. */
private final Hyperplane hyperplane;
/** Remaining region of the hyperplane. */
private final Region remainingRegion;
/** Build a sub-hyperplane from an hyperplane and a region.
* @param hyperplane underlying hyperplane
* @param remainingRegion remaining region of the hyperplane
*/
protected AbstractSubHyperplane(final Hyperplane hyperplane,
final Region remainingRegion) {
this.hyperplane = hyperplane;
this.remainingRegion = remainingRegion;
}
/** Build a sub-hyperplane from an hyperplane and a region.
* @param hyper underlying hyperplane
* @param remaining remaining region of the hyperplane
* @return a new sub-hyperplane
*/
protected abstract AbstractSubHyperplane buildNew(final Hyperplane hyper,
final Region remaining);
/** {@inheritDoc} */
public AbstractSubHyperplane copySelf() {
return buildNew(hyperplane.copySelf(), remainingRegion);
}
/** Get the underlying hyperplane.
* @return underlying hyperplane
*/
public Hyperplane getHyperplane() {
return hyperplane;
}
/** Get the remaining region of the hyperplane.
* The returned region is expressed in the canonical hyperplane
* frame and has the hyperplane dimension. For example a chopped
* hyperplane in the 3D euclidean is a 2D plane and the
* corresponding region is a convex 2D polygon.
* @return remaining region of the hyperplane
*/
public Region getRemainingRegion() {
return remainingRegion;
}
/** {@inheritDoc} */
public double getSize() {
return remainingRegion.getSize();
}
/** {@inheritDoc} */
public AbstractSubHyperplane reunite(final SubHyperplane other) {
@SuppressWarnings("unchecked")
AbstractSubHyperplane o = (AbstractSubHyperplane) other;
return buildNew(hyperplane,
new RegionFactory().union(remainingRegion, o.remainingRegion));
}
/** Apply a transform to the instance.
* The instance must be a (D-1)-dimension sub-hyperplane with
* respect to the transform not a (D-2)-dimension
* sub-hyperplane the transform knows how to transform by
* itself. The transform will consist in transforming first the
* hyperplane and then the all region using the various methods
* provided by the transform.
* @param transform D-dimension transform to apply
* @return the transformed instance
*/
public AbstractSubHyperplane applyTransform(final Transform transform) {
final Hyperplane tHyperplane = transform.apply(hyperplane);
// transform the tree, except for boundary attribute splitters
final Map, BSPTree> map = new HashMap, BSPTree>();
final BSPTree tTree =
recurseTransform(remainingRegion.getTree(false), tHyperplane, transform, map);
// set up the boundary attributes splitters
for (final Map.Entry, BSPTree> entry : map.entrySet()) {
if (entry.getKey().getCut() != null) {
@SuppressWarnings("unchecked")
BoundaryAttribute original = (BoundaryAttribute) entry.getKey().getAttribute();
if (original != null) {
@SuppressWarnings("unchecked")
BoundaryAttribute transformed = (BoundaryAttribute) entry.getValue().getAttribute();
for (final BSPTree splitter : original.getSplitters()) {
transformed.getSplitters().add(map.get(splitter));
}
}
}
}
return buildNew(tHyperplane, remainingRegion.buildNew(tTree));
}
/** Recursively transform a BSP-tree from a sub-hyperplane.
* @param node current BSP tree node
* @param transformed image of the instance hyperplane by the transform
* @param transform transform to apply
* @param map transformed nodes map
* @return a new tree
*/
private BSPTree recurseTransform(final BSPTree node,
final Hyperplane transformed,
final Transform transform,
final Map, BSPTree> map) {
final BSPTree transformedNode;
if (node.getCut() == null) {
transformedNode = new BSPTree(node.getAttribute());
} else {
@SuppressWarnings("unchecked")
BoundaryAttribute attribute = (BoundaryAttribute) node.getAttribute();
if (attribute != null) {
final SubHyperplane tPO = (attribute.getPlusOutside() == null) ?
null : transform.apply(attribute.getPlusOutside(), hyperplane, transformed);
final SubHyperplane tPI = (attribute.getPlusInside() == null) ?
null : transform.apply(attribute.getPlusInside(), hyperplane, transformed);
// we start with an empty list of splitters, it will be filled in out of recursion
attribute = new BoundaryAttribute(tPO, tPI, new NodesSet());
}
transformedNode = new BSPTree(transform.apply(node.getCut(), hyperplane, transformed),
recurseTransform(node.getPlus(), transformed, transform, map),
recurseTransform(node.getMinus(), transformed, transform, map),
attribute);
}
map.put(node, transformedNode);
return transformedNode;
}
/** {@inheritDoc} */
@Deprecated
public Side side(Hyperplane hyper) {
return split(hyper).getSide();
}
/** {@inheritDoc} */
public abstract SplitSubHyperplane split(Hyperplane hyper);
/** {@inheritDoc} */
public boolean isEmpty() {
return remainingRegion.isEmpty();
}
}