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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 defines mappers between a space and one of its sub-spaces.
Sub-spaces are the lower dimensions subsets of a n-dimensions space. The (n-1)-dimension sub-spaces are specific sub-spaces known as hyperplanes. This interface can be used regardless of the dimensions differences. As an example, Line in 3D implements Embedding, i.e. it
maps directly dimensions 3 and 1.
In the 3D euclidean space, hyperplanes are 2D planes, and the 1D
sub-spaces are lines.

Note that this interface is not 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.

Type parameters:
<S> – Type of the embedding space.
<T> – Type of the embedded sub-space.
See Also:
Hyperplane
Since:
3.0/** This interface defines mappers between a space and one of its sub-spaces.

 * <p>Sub-spaces are the lower dimensions subsets of a n-dimensions
 * space. The (n-1)-dimension sub-spaces are specific sub-spaces known
 * as {@link Hyperplane hyperplanes}. This interface can be used regardless
 * of the dimensions differences. As an example, {@link
 * org.apache.commons.math3.geometry.euclidean.threed.Line Line} in 3D
 * implements Embedding<{@link
 * org.apache.commons.math3.geometry.euclidean.threed.Vector3D Vector3D}, {link
 * org.apache.commons.math3.geometry.euclidean.oned.Vector1D Vector1D>, i.e. it
 * maps directly dimensions 3 and 1.</p>

 * <p>In the 3D euclidean space, hyperplanes are 2D planes, and the 1D
 * sub-spaces are lines.</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 embedding space.
 * @param <T> Type of the embedded sub-space.

 * @see Hyperplane
 * @since 3.0
 */
public interface Embedding<S extends Space, T extends Space> {

    
Transform a space point into a sub-space point.
Params:
point – n-dimension point of the space
See Also:
toSpace
Returns:
(n-1)-dimension point of the sub-space corresponding to
the specified space point/** Transform a space point into a sub-space point.
     * @param point n-dimension point of the space
     * @return (n-1)-dimension point of the sub-space corresponding to
     * the specified space point
     * @see #toSpace
     */
    Point<T> toSubSpace(Point<S> point);

    
Transform a sub-space point into a space point.
Params:
point – (n-1)-dimension point of the sub-space
See Also:
toSubSpace
Returns:
n-dimension point of the space corresponding to the
specified sub-space point/** Transform a sub-space point into a space point.
     * @param point (n-1)-dimension point of the sub-space
     * @return n-dimension point of the space corresponding to the
     * specified sub-space point
     * @see #toSubSpace
     */
    Point<S> toSpace(Point<T> point);

}