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.partitioning;
018
019 import org.apache.commons.math3.geometry.Vector;
020 import org.apache.commons.math3.geometry.Space;
021
022 /** This interface defines mappers between a space and one of its sub-spaces.
023
024 * <p>Sub-spaces are the lower dimensions subsets of a n-dimensions
025 * space. The (n-1)-dimension sub-spaces are specific sub-spaces known
026 * as {@link Hyperplane hyperplanes}. This interface can be used regardless
027 * of the dimensions differences. As an example, {@link
028 * org.apache.commons.math3.geometry.euclidean.threed.Line Line} in 3D
029 * implements Embedding<{@link
030 * org.apache.commons.math3.geometry.euclidean.threed.Vector3D Vector3D}, {link
031 * org.apache.commons.math3.geometry.euclidean.oned.Vector1D Vector1D>, i.e. it
032 * maps directly dimensions 3 and 1.</p>
033
034 * <p>In the 3D euclidean space, hyperplanes are 2D planes, and the 1D
035 * sub-spaces are lines.</p>
036
037 * @param <S> Type of the embedding space.
038 * @param <T> Type of the embedded sub-space.
039
040 * @see Hyperplane
041 * @version $Id: Embedding.java 1416643 2012-12-03 19:37:14Z tn $
042 * @since 3.0
043 */
044 public interface Embedding<S extends Space, T extends Space> {
045
046 /** Transform a space point into a sub-space point.
047 * @param point n-dimension point of the space
048 * @return (n-1)-dimension point of the sub-space corresponding to
049 * the specified space point
050 * @see #toSpace
051 */
052 Vector<T> toSubSpace(Vector<S> point);
053
054 /** Transform a sub-space point into a space point.
055 * @param point (n-1)-dimension point of the sub-space
056 * @return n-dimension point of the space corresponding to the
057 * specified sub-space point
058 * @see #toSubSpace
059 */
060 Vector<S> toSpace(Vector<T> point);
061
062 }