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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 inversible affine transform in a space.
Inversible affine transform include for example scalings,
translations, rotations.
Transforms are dimension-specific. The consistency rules between the three apply methods are the following ones for a transformed defined for dimension D:

  
 the transform can be applied to a point in the D-dimension space using its apply(Point) method 
  
 the transform can be applied to a (D-1)-dimension hyperplane in the D-dimension space using its apply(Hyperplane) method 
  
 the transform can be applied to a (D-2)-dimension sub-hyperplane in a (D-1)-dimension hyperplane using its apply(SubHyperplane, Hyperplane, Hyperplane) method 

Type parameters:
<S> – Type of the embedding space.
<T> – Type of the embedded sub-space.
Since:
3.0/** This interface represents an inversible affine transform in a space.
 * <p>Inversible affine transform include for example scalings,
 * translations, rotations.</p>

 * <p>Transforms are dimension-specific. The consistency rules between
 * the three {@code apply} methods are the following ones for a
 * transformed defined for dimension D:</p>
 * <ul>
 *   <li>
 *     the transform can be applied to a point in the
 *     D-dimension space using its {@link #apply(Point)}
 *     method
 *   </li>
 *   <li>
 *     the transform can be applied to a (D-1)-dimension
 *     hyperplane in the D-dimension space using its
 *     {@link #apply(Hyperplane)} method
 *   </li>
 *   <li>
 *     the transform can be applied to a (D-2)-dimension
 *     sub-hyperplane in a (D-1)-dimension hyperplane using
 *     its {@link #apply(SubHyperplane, Hyperplane, Hyperplane)}
 *     method
 *   </li>
 * </ul>

 * @param <S> Type of the embedding space.
 * @param <T> Type of the embedded sub-space.

 * @since 3.0
 */
public interface Transform<S extends Space, T extends Space> {

    
Transform a point of a space.
Params:
point – point to transform
Returns:
a new object representing the transformed point/** Transform a point of a space.
     * @param point point to transform
     * @return a new object representing the transformed point
     */
    Point<S> apply(Point<S> point);

    
Transform an hyperplane of a space.
Params:
hyperplane – hyperplane to transform
Returns:
a new object representing the transformed hyperplane/** Transform an hyperplane of a space.
     * @param hyperplane hyperplane to transform
     * @return a new object representing the transformed hyperplane
     */
    Hyperplane<S> apply(Hyperplane<S> hyperplane);

    
Transform a sub-hyperplane embedded in an hyperplane.
Params:
sub – sub-hyperplane to transform
original – hyperplane in which the sub-hyperplane is
defined (this is the original hyperplane, the transform has
not been applied to it)
transformed – hyperplane in which the sub-hyperplane is
defined (this is the transformed hyperplane, the transform
has been applied to it)
Returns:
a new object representing the transformed sub-hyperplane/** Transform a sub-hyperplane embedded in an hyperplane.
     * @param sub sub-hyperplane to transform
     * @param original hyperplane in which the sub-hyperplane is
     * defined (this is the original hyperplane, the transform has
     * <em>not</em> been applied to it)
     * @param transformed hyperplane in which the sub-hyperplane is
     * defined (this is the transformed hyperplane, the transform
     * <em>has</em> been applied to it)
     * @return a new object representing the transformed sub-hyperplane
     */
    SubHyperplane<T> apply(SubHyperplane<T> sub, Hyperplane<S> original, Hyperplane<S> transformed);

}