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    }