View Javadoc
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;
18  
19  import org.apache.commons.geometry.core.Point;
20  import org.apache.commons.geometry.core.Transform;
21  
22  /** Interface representing a hyperplane, which in a space of dimension {@code n} is
23   * a subspace of dimension {@code n - 1}. (A hyperplane in Euclidean 3D space,
24   * for example, is a 2 dimensional plane.)
25   *
26   * <p>
27   * Hyperplanes partition their surrounding space into 3 distinct sets: (1) points
28   * lying on one side of the hyperplane, (2) points lying on the opposite side, and
29   * (3) points lying on the hyperplane itself. One side of the hyperplane is labeled
30   * as the <em>plus</em> side and the other as the <em>minus</em> side. The
31   * {@link #offset(Point) offset} of a point in relation to a hyperplane is the distance
32   * from the point to the hyperplane combined with the sign of the side that the point
33   * lies on: points lying on the plus side of the hyperplane have a positive offsets,
34   * those on the minus side have a negative offset, and those lying directly on the
35   * hyperplane have an offset of zero.
36   *
37   * @param <P> Point implementation type
38   * @see HyperplaneLocation
39   * @see HyperplaneSubset
40   */
41  public interface Hyperplane<P extends Point<P>> {
42  
43      /** Get the offset (oriented distance) of a point with respect
44       * to this instance. Points with an offset of zero lie on the
45       * hyperplane itself.
46       * @param point the point to compute the offset for
47       * @return the offset of the point
48       */
49      double offset(P point);
50  
51      /** Classify a point with respect to this hyperplane.
52       * @param point the point to classify
53       * @return the relative location of the point with
54       *      respect to this instance
55       */
56      HyperplaneLocation classify(P point);
57  
58      /** Return true if the given point lies on the hyperplane.
59       * @param point the point to test
60       * @return true if the point lies on the hyperplane
61       */
62      boolean contains(P point);
63  
64      /** Project a point onto this instance.
65       * @param point the point to project
66       * @return the projection of the point onto this instance. The returned
67       *      point lies on the hyperplane.
68       */
69      P project(P point);
70  
71      /** Return a hyperplane that has the opposite orientation as this instance.
72       * That is, the plus side of this instance is the minus side of the returned
73       * instance and vice versa.
74       * @return a hyperplane with the opposite orientation
75       */
76      Hyperplane<P> reverse();
77  
78      /** Transform this instance using the given {@link Transform}.
79       * @param transform object to transform this instance with
80       * @return a new, transformed hyperplane
81       */
82      Hyperplane<P> transform(Transform<P> transform);
83  
84      /** Return true if this instance has a similar orientation to the given hyperplane,
85       * meaning that they point in generally the same direction. This method is not
86       * used to determine exact equality of hyperplanes, but rather to determine whether
87       * two hyperplanes that contain the same points are parallel (point in the same direction)
88       * or anti-parallel (point in opposite directions).
89       * @param other the hyperplane to compare with
90       * @return true if the hyperplanes point in generally the same direction and could
91       *      possibly be parallel
92       */
93      boolean similarOrientation(Hyperplane<P> other);
94  
95      /** Return a {@link HyperplaneConvexSubset} spanning this entire hyperplane. The returned
96       * subset contains all points lying in this hyperplane and no more.
97       * @return a {@link HyperplaneConvexSubset} containing all points lying in this hyperplane
98       */
99      HyperplaneConvexSubset<P> span();
100 }