Embedding (Apache Commons Math 3.3 API)

org.apache.commons.math3.geometry.partitioning

## Interface Embedding<S extends Space,T extends Space>

- Type Parameters:
    `S` - Type of the embedding space.
    `T` - Type of the embedded sub-space.
  All Known Implementing Classes:
    Circle, Line, Line, Plane

      public interface Embedding<S extends Space,T extends 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<`Vector3D`, {link org.apache.commons.math3.geometry.euclidean.oned.Vector1D Vector1D>, 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.

  Since:
    3.0
  Version:
    $Id: Embedding.java 1591835 2014-05-02 09:04:01Z tn $
  See Also:
    `Hyperplane`

- - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `Point<S>` | `toSpace(Point<T> point)` Transform a sub-space point into a space point.
    `Point<T>` | `toSubSpace(Point<S> point)` Transform a space point into a sub-space point.

- - ### Method Detail

    - #### toSubSpace

          Point<T> toSubSpace(Point<S> point)

      Transform a space point into a sub-space point.
      Parameters:
        `point` - n-dimension point of the space
      Returns:
        (n-1)-dimension point of the sub-space corresponding to the specified space point
      See Also:
        `toSpace(org.apache.commons.math3.geometry.Point<T>)`

    - #### toSpace

          Point<S> toSpace(Point<T> point)

      Transform a sub-space point into a space point.
      Parameters:
        `point` - (n-1)-dimension point of the sub-space
      Returns:
        n-dimension point of the space corresponding to the specified sub-space point
      See Also:
        `toSubSpace(org.apache.commons.math3.geometry.Point<S>)`

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