Hyperplane.java

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 *      http://www.apache.org/licenses/LICENSE-2.0
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package org.apache.commons.math3.geometry.partitioning;

import org.apache.commons.math3.geometry.Point;
import org.apache.commons.math3.geometry.Space;

/** This interface represents an hyperplane of a space.

 * <p>The most prominent place where hyperplane appears in space
 * partitioning is as cutters. Each partitioning node in a {@link
 * BSPTree BSP tree} has a cut {@link SubHyperplane sub-hyperplane}
 * which is either an hyperplane or a part of an hyperplane. In an
 * n-dimensions euclidean space, an hyperplane is an (n-1)-dimensions
 * hyperplane (for example a traditional plane in the 3D euclidean
 * space). They can be more exotic objects in specific fields, for
 * example a circle on the surface of the unit sphere.</p>

 * <p>
 * Note that this interface is <em>not</em> intended to be implemented
 * by Apache Commons Math users, it is only intended to be implemented
 * within the library itself. New methods may be added even for minor
 * versions, which breaks compatibility for external implementations.
 * </p>

 * @param <S> Type of the space.

 * @since 3.0
 */
public interface Hyperplane<S extends Space> {

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

    /** Get the offset (oriented distance) of a point.
     * <p>The offset is 0 if the point is on the underlying hyperplane,
     * it is positive if the point is on one particular side of the
     * hyperplane, and it is negative if the point is on the other side,
     * according to the hyperplane natural orientation.</p>
     * @param point point to check
     * @return offset of the point
     */
    double getOffset(Point<S> point);

    /** Project a point to the hyperplane.
     * @param point point to project
     * @return projected point
     * @since 3.3
     */
    Point<S> project(Point<S> point);

    /** Get the tolerance below which points are considered to belong to the hyperplane.
     * @return tolerance below which points are considered to belong to the hyperplane
     * @since 3.3
     */
    double getTolerance();

    /** Check if the instance has the same orientation as another hyperplane.
     * <p>This method is expected to be called on parallel hyperplanes. The
     * method should <em>not</em> re-check for parallelism, only for
     * orientation, typically by testing something like the sign of the
     * dot-products of normals.</p>
     * @param other other hyperplane to check against the instance
     * @return true if the instance and the other hyperplane have
     * the same orientation
     */
    boolean sameOrientationAs(Hyperplane<S> other);

    /** Build a sub-hyperplane covering the whole hyperplane.
     * @return a sub-hyperplane covering the whole hyperplane
     */
    SubHyperplane<S> wholeHyperplane();

    /** Build a region covering the whole space.
     * @return a region containing the instance
     */
    Region<S> wholeSpace();

}