/*
 * 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 org.apache.commons.math3.geometry.Space;

/** This interface represents the remaining parts of an hyperplane after
 * other parts have been chopped off.

 * <p>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.</p>

 * @param <S> Type of the embedding space.

 * @version $Id: SubHyperplane.java 1416643 2012-12-03 19:37:14Z tn $
 * @since 3.0
 */
public interface SubHyperplane<S extends Space> {

    /** Copy the instance.
     * <p>The instance created is completely independent of the original
     * one. A deep copy is used, none of the underlying objects are
     * shared (except for the nodes attributes and immutable
     * objects).</p>
     * @return a new sub-hyperplane, copy of the instance
     */
    SubHyperplane<S> copySelf();

    /** Get the underlying hyperplane.
     * @return underlying hyperplane
     */
    Hyperplane<S> getHyperplane();

    /** Check if the instance is empty.
     * @return true if the instance is empty
     */
    boolean isEmpty();

    /** Get the size of the instance.
     * @return the size of the instance (this is a length in 1D, an area
     * in 2D, a volume in 3D ...)
     */
    double getSize();

    /** Compute the relative position of the instance with respect
     * to an hyperplane.
     * @param hyperplane hyperplane to check instance against
     * @return one of {@link Side#PLUS}, {@link Side#MINUS}, {@link Side#BOTH},
     * {@link Side#HYPER}
     */
    Side side(Hyperplane<S> hyperplane);

    /** Split the instance in two parts by an hyperplane.
     * @param hyperplane splitting hyperplane
     * @return an object containing both the part of the instance
     * on the plus side of the instance and the part of the
     * instance on the minus side of the instance
     */
    SplitSubHyperplane<S> split(Hyperplane<S> hyperplane);

    /** Compute the union of the instance and another sub-hyperplane.
     * @param other other sub-hyperplane to union (<em>must</em> be in the
     * same hyperplane as the instance)
     * @return a new sub-hyperplane, union of the instance and other
     */
    SubHyperplane<S> reunite(SubHyperplane<S> other);

    /** Class holding the results of the {@link #split split} method.
     * @param <U> Type of the embedding space.
     */
    public static class SplitSubHyperplane<U extends Space> {

        /** Part of the sub-hyperplane on the plus side of the splitting hyperplane. */
        private final SubHyperplane<U> plus;

        /** Part of the sub-hyperplane on the minus side of the splitting hyperplane. */
        private final SubHyperplane<U> minus;

        /** Build a SplitSubHyperplane from its parts.
         * @param plus part of the sub-hyperplane on the plus side of the
         * splitting hyperplane
         * @param minus part of the sub-hyperplane on the minus side of the
         * splitting hyperplane
         */
        public SplitSubHyperplane(final SubHyperplane<U> plus,
                                  final SubHyperplane<U> minus) {
            this.plus  = plus;
            this.minus = minus;
        }

        /** Get the part of the sub-hyperplane on the plus side of the splitting hyperplane.
         * @return part of the sub-hyperplane on the plus side of the splitting hyperplane
         */
        public SubHyperplane<U> getPlus() {
            return plus;
        }

        /** Get the part of the sub-hyperplane on the minus side of the splitting hyperplane.
         * @return part of the sub-hyperplane on the minus side of the splitting hyperplane
         */
        public SubHyperplane<U> getMinus() {
            return minus;
        }

    }

}
