org.apache.commons.math3.geometry.partitioning

## Interface Hyperplane<S extends Space>

- Type Parameters:
    `S` - Type of the space.
  All Known Implementing Classes:
    Circle, LimitAngle, Line, OrientedPoint, Plane

      public interface Hyperplane<S extends Space>

  This interface represents an hyperplane of a space.

  The most prominent place where hyperplane appears in space partitioning is as cutters. Each partitioning node in a `BSP tree` has a cut `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.

  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: Hyperplane.java 1566416 2014-02-09 20:56:55Z luc $

- - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `Hyperplane<S>` | `copySelf()` Copy the instance.
    `double` | `getOffset(Point<S> point)` Get the offset (oriented distance) of a point.
    `double` | `getTolerance()` Get the tolerance below which points are considered to belong to the hyperplane.
    `Point<S>` | `project(Point<S> point)` Project a point to the hyperplane.
    `boolean` | `sameOrientationAs(Hyperplane<S> other)` Check if the instance has the same orientation as another hyperplane.
    `SubHyperplane<S>` | `wholeHyperplane()` Build a sub-hyperplane covering the whole hyperplane.
    `Region<S>` | `wholeSpace()` Build a region covering the whole space.

- - ### Method Detail

    - #### copySelf

          Hyperplane<S> copySelf()

      Copy the instance.

      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).

      Returns:
        a new hyperplane, copy of the instance

    - #### getOffset

          double getOffset(Point<S> point)

      Get the offset (oriented distance) of a point.

      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.

      Parameters:
        `point` - point to check
      Returns:
        offset of the point

    - #### project

          Point<S> project(Point<S> point)

      Project a point to the hyperplane.
      Parameters:
        `point` - point to project
      Returns:
        projected point
      Since:
        3.3

    - #### getTolerance

          double getTolerance()

      Get the tolerance below which points are considered to belong to the hyperplane.
      Returns:
        tolerance below which points are considered to belong to the hyperplane
      Since:
        3.3

    - #### sameOrientationAs

          boolean sameOrientationAs(Hyperplane<S> other)

      Check if the instance has the same orientation as another hyperplane.

      This method is expected to be called on parallel hyperplanes. The method should not re-check for parallelism, only for orientation, typically by testing something like the sign of the dot-products of normals.

      Parameters:
        `other` - other hyperplane to check against the instance
      Returns:
        true if the instance and the other hyperplane have the same orientation

    - #### wholeHyperplane

          SubHyperplane<S> wholeHyperplane()

      Build a sub-hyperplane covering the whole hyperplane.
      Returns:
        a sub-hyperplane covering the whole hyperplane

    - #### wholeSpace

          Region<S> wholeSpace()

      Build a region covering the whole space.
      Returns:
        a region containing the instance

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