Plane (Apache Commons Math 3.6.1 API)

java.lang.Object
- org.apache.commons.math3.geometry.euclidean.threed.Plane

All Implemented Interfaces:

Embedding<Euclidean3D,Euclidean2D>, Hyperplane<Euclidean3D>
```
public class Plane
extends Object
implements Hyperplane<Euclidean3D>, Embedding<Euclidean3D,Euclidean2D>
```
The class represent planes in a three dimensional space.

Since:

3.0

Constructor Summary

Constructors
Constructor and Description
`Plane(Plane plane)` Copy constructor.
`Plane(Vector3D normal)` Deprecated. as of 3.3, replaced with `Plane(Vector3D, double)`
`Plane(Vector3D normal, double tolerance)` Build a plane normal to a given direction and containing the origin.
`Plane(Vector3D p, Vector3D normal)` Deprecated. as of 3.3, replaced with `Plane(Vector3D, Vector3D, double)`
`Plane(Vector3D p, Vector3D normal, double tolerance)` Build a plane from a point and a normal.
`Plane(Vector3D p1, Vector3D p2, Vector3D p3)` Deprecated. as of 3.3, replaced with `Plane(Vector3D, Vector3D, Vector3D, double)`
`Plane(Vector3D p1, Vector3D p2, Vector3D p3, double tolerance)` Build a plane from three points.

Method Summary

Methods
Modifier and Type	Method and Description
`boolean`	`contains(Vector3D p)` Check if the instance contains a point.
`Plane`	`copySelf()` Copy the instance.
`Vector3D`	`getNormal()` Get the normalized normal vector.
`double`	`getOffset(Plane plane)` Get the offset (oriented distance) of a parallel plane.
`double`	`getOffset(Point<Euclidean3D> point)` Get the offset (oriented distance) of a point.
`double`	`getOffset(Vector<Euclidean3D> vector)` Get the offset (oriented distance) of a vector.
`Vector3D`	`getOrigin()` Get the origin point of the plane frame.
`Vector3D`	`getPointAt(Vector2D inPlane, double offset)` Get one point from the 3D-space.
`double`	`getTolerance()` Get the tolerance below which points are considered to belong to the hyperplane.
`Vector3D`	`getU()` Get the plane first canonical vector.
`Vector3D`	`getV()` Get the plane second canonical vector.
`Vector3D`	`intersection(Line line)` Get the intersection of a line with the instance.
`Line`	`intersection(Plane other)` Build the line shared by the instance and another plane.
`static Vector3D`	`intersection(Plane plane1, Plane plane2, Plane plane3)` Get the intersection point of three planes.
`boolean`	`isSimilarTo(Plane plane)` Check if the instance is similar to another plane.
`Point<Euclidean3D>`	`project(Point<Euclidean3D> point)` Project a point to the hyperplane.
`void`	`reset(Plane original)` Reset the instance from another one.
`void`	`reset(Vector3D p, Vector3D normal)` Reset the instance as if built from a point and a normal.
`void`	`revertSelf()` Revert the plane.
`Plane`	`rotate(Vector3D center, Rotation rotation)` Rotate the plane around the specified point.
`boolean`	`sameOrientationAs(Hyperplane<Euclidean3D> other)` Check if the instance has the same orientation as another hyperplane.
`Vector3D`	`toSpace(Point<Euclidean2D> point)` Transform an in-plane point into a 3D space point.
`Vector3D`	`toSpace(Vector<Euclidean2D> vector)` Transform a sub-space point into a space point.
`Vector2D`	`toSubSpace(Point<Euclidean3D> point)` Transform a 3D space point into an in-plane point.
`Vector2D`	`toSubSpace(Vector<Euclidean3D> vector)` Transform a space point into a sub-space point.
`Plane`	`translate(Vector3D translation)` Translate the plane by the specified amount.
`SubPlane`	`wholeHyperplane()` Build a region covering the whole hyperplane.
`PolyhedronsSet`	`wholeSpace()` Build a region covering the whole space.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - Plane
```
public Plane(Vector3D normal,
     double tolerance)
      throws MathArithmeticException
```
    Build a plane normal to a given direction and containing the origin.
    
    Parameters:
    normal - normal direction to the plane
    tolerance - tolerance below which points are considered identical
    
    Throws:
    
    MathArithmeticException - if the normal norm is too small
    Since:
    
    3.3
  - Plane
```
public Plane(Vector3D p,
     Vector3D normal,
     double tolerance)
      throws MathArithmeticException
```
    Build a plane from a point and a normal.
    
    Parameters:
    p - point belonging to the plane
    normal - normal direction to the plane
    tolerance - tolerance below which points are considered identical
    
    Throws:
    
    MathArithmeticException - if the normal norm is too small
    Since:
    
    3.3
  - Plane
```
public Plane(Vector3D p1,
     Vector3D p2,
     Vector3D p3,
     double tolerance)
      throws MathArithmeticException
```
    Build a plane from three points.
    The plane is oriented in the direction of (p2-p1) ^ (p3-p1)
    
    Parameters:
    p1 - first point belonging to the plane
    p2 - second point belonging to the plane
    p3 - third point belonging to the plane
    tolerance - tolerance below which points are considered identical
    
    Throws:
    
    MathArithmeticException - if the points do not constitute a plane
    Since:
    
    3.3
  - Plane
```
@Deprecated
public Plane(Vector3D normal)
      throws MathArithmeticException
```
    Deprecated. as of 3.3, replaced with Plane(Vector3D, double)
    
    Build a plane normal to a given direction and containing the origin.
    
    Parameters:
    normal - normal direction to the plane
    
    Throws:
    
    MathArithmeticException - if the normal norm is too small
  - Plane
```
@Deprecated
public Plane(Vector3D p,
                Vector3D normal)
      throws MathArithmeticException
```
    Deprecated. as of 3.3, replaced with Plane(Vector3D, Vector3D, double)
    
    Build a plane from a point and a normal.
    
    Parameters:
    p - point belonging to the plane
    normal - normal direction to the plane
    
    Throws:
    
    MathArithmeticException - if the normal norm is too small
  - Plane
```
@Deprecated
public Plane(Vector3D p1,
                Vector3D p2,
                Vector3D p3)
      throws MathArithmeticException
```
    Deprecated. as of 3.3, replaced with Plane(Vector3D, Vector3D, Vector3D, double)
    
    Build a plane from three points.
    The plane is oriented in the direction of (p2-p1) ^ (p3-p1)
    
    Parameters:
    p1 - first point belonging to the plane
    p2 - second point belonging to the plane
    p3 - third point belonging to the plane
    
    Throws:
    
    MathArithmeticException - if the points do not constitute a plane
  - Plane
```
public Plane(Plane plane)
```
    Copy constructor.
    The instance created is completely independant of the original one. A deep copy is used, none of the underlying object are shared.
    
    Parameters:
    plane - plane to copy
- Method Detail
  - copySelf
```
public Plane 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).
    
    Specified by:
    
    copySelf in interface Hyperplane<Euclidean3D>
    
    Returns:
    a new hyperplane, copy of the instance
  - reset
```
public void reset(Vector3D p,
         Vector3D normal)
           throws MathArithmeticException
```
    Reset the instance as if built from a point and a normal.
    
    Parameters:
    p - point belonging to the plane
    normal - normal direction to the plane
    
    Throws:
    
    MathArithmeticException - if the normal norm is too small
  - reset
```
public void reset(Plane original)
```
    Reset the instance from another one.
    The updated instance is completely independant of the original one. A deep reset is used none of the underlying object is shared.
    
    Parameters:
    original - plane to reset from
  - getOrigin
```
public Vector3D getOrigin()
```
    Get the origin point of the plane frame.
    The point returned is the orthogonal projection of the 3D-space origin in the plane.
    
    Returns:
    the origin point of the plane frame (point closest to the 3D-space origin)
  - getNormal
```
public Vector3D getNormal()
```
    Get the normalized normal vector.
    The frame defined by (getU, getV, getNormal) is a rigth-handed orthonormalized frame).
    
    Returns:
    normalized normal vector
    See Also:
    getU(), getV()
  - getU
```
public Vector3D getU()
```
    Get the plane first canonical vector.
    The frame defined by (getU, getV, getNormal) is a rigth-handed orthonormalized frame).
    
    Returns:
    normalized first canonical vector
    See Also:
    getV(), getNormal()
  - getV
```
public Vector3D getV()
```
    Get the plane second canonical vector.
    The frame defined by (getU, getV, getNormal) is a rigth-handed orthonormalized frame).
    
    Returns:
    normalized second canonical vector
    See Also:
    getU(), getNormal()
  - project
```
public Point<Euclidean3D> project(Point<Euclidean3D> point)
```
    Project a point to the hyperplane.
    
    Specified by:
    
    project in interface Hyperplane<Euclidean3D>
    
    Parameters:
    point - point to project
    
    Returns:
    projected point
    Since:
    
    3.3
  - getTolerance
```
public double getTolerance()
```
    Get the tolerance below which points are considered to belong to the hyperplane.
    
    Specified by:
    
    getTolerance in interface Hyperplane<Euclidean3D>
    
    Returns:
    tolerance below which points are considered to belong to the hyperplane
    Since:
    
    3.3
  - revertSelf
```
public void revertSelf()
```
    Revert the plane.
    Replace the instance by a similar plane with opposite orientation.
    
    The new plane frame is chosen in such a way that a 3D point that had (x, y) in-plane coordinates and z offset with respect to the plane and is unaffected by the change will have (y, x) in-plane coordinates and -z offset with respect to the new plane. This means that the u and v vectors returned by the getU() and getV() methods are exchanged, and the w vector returned by the getNormal() method is reversed.
  - toSubSpace
```
public Vector2D toSubSpace(Vector<Euclidean3D> vector)
```
    Transform a space point into a sub-space point.
    
    Parameters:
    vector - n-dimension point of the space
    
    Returns:
    (n-1)-dimension point of the sub-space corresponding to the specified space point
  - toSpace
```
public Vector3D toSpace(Vector<Euclidean2D> vector)
```
    Transform a sub-space point into a space point.
    
    Parameters:
    vector - (n-1)-dimension point of the sub-space
    
    Returns:
    n-dimension point of the space corresponding to the specified sub-space point
  - toSubSpace
```
public Vector2D toSubSpace(Point<Euclidean3D> point)
```
    Transform a 3D space point into an in-plane point.
    
    Specified by:
    
    toSubSpace in interface Embedding<Euclidean3D,Euclidean2D>
    
    Parameters:
    point - point of the space (must be a Vector3D instance)
    
    Returns:
    in-plane point (really a Vector2D instance)
    See Also:
    toSpace(org.apache.commons.math3.geometry.Vector<org.apache.commons.math3.geometry.euclidean.twod.Euclidean2D>)
  - toSpace
```
public Vector3D toSpace(Point<Euclidean2D> point)
```
    Transform an in-plane point into a 3D space point.
    
    Specified by:
    
    toSpace in interface Embedding<Euclidean3D,Euclidean2D>
    
    Parameters:
    point - in-plane point (must be a Vector2D instance)
    
    Returns:
    3D space point (really a Vector3D instance)
    See Also:
    toSubSpace(org.apache.commons.math3.geometry.Vector<org.apache.commons.math3.geometry.euclidean.threed.Euclidean3D>)
  - getPointAt
```
public Vector3D getPointAt(Vector2D inPlane,
                  double offset)
```
    Get one point from the 3D-space.
    
    Parameters:
    inPlane - desired in-plane coordinates for the point in the plane
    offset - desired offset for the point
    
    Returns:
    one point in the 3D-space, with given coordinates and offset relative to the plane
  - isSimilarTo
```
public boolean isSimilarTo(Plane plane)
```
    Check if the instance is similar to another plane.
    Planes are considered similar if they contain the same points. This does not mean they are equal since they can have opposite normals.
    
    Parameters:
    plane - plane to which the instance is compared
    
    Returns:
    true if the planes are similar
  - rotate
```
public Plane rotate(Vector3D center,
           Rotation rotation)
```
    Rotate the plane around the specified point.
    The instance is not modified, a new instance is created.
    
    Parameters:
    center - rotation center
    rotation - vectorial rotation operator
    
    Returns:
    a new plane
  - translate
```
public Plane translate(Vector3D translation)
```
    Translate the plane by the specified amount.
    The instance is not modified, a new instance is created.
    
    Parameters:
    translation - translation to apply
    
    Returns:
    a new plane
  - intersection
```
public Vector3D intersection(Line line)
```
    Get the intersection of a line with the instance.
    
    Parameters:
    line - line intersecting the instance
    
    Returns:
    intersection point between between the line and the instance (null if the line is parallel to the instance)
  - intersection
```
public Line intersection(Plane other)
```
    Build the line shared by the instance and another plane.
    
    Parameters:
    other - other plane
    
    Returns:
    line at the intersection of the instance and the other plane (really a Line instance)
  - intersection
```
public static Vector3D intersection(Plane plane1,
                    Plane plane2,
                    Plane plane3)
```
    Get the intersection point of three planes.
    
    Parameters:
    plane1 - first plane1
    plane2 - second plane2
    plane3 - third plane2
    
    Returns:
    intersection point of three planes, null if some planes are parallel
  - wholeHyperplane
```
public SubPlane wholeHyperplane()
```
    Build a region covering the whole hyperplane.
    
    Specified by:
    
    wholeHyperplane in interface Hyperplane<Euclidean3D>
    
    Returns:
    a region covering the whole hyperplane
  - wholeSpace
```
public PolyhedronsSet wholeSpace()
```
    Build a region covering the whole space.
    
    Specified by:
    
    wholeSpace in interface Hyperplane<Euclidean3D>
    
    Returns:
    a region containing the instance (really a PolyhedronsSet instance)
  - contains
```
public boolean contains(Vector3D p)
```
    Check if the instance contains a point.
    
    Parameters:
    p - point to check
    
    Returns:
    true if p belongs to the plane
  - getOffset
```
public double getOffset(Plane plane)
```
    Get the offset (oriented distance) of a parallel plane.
    This method should be called only for parallel planes otherwise the result is not meaningful.
    
    The offset is 0 if both planes are the same, it is positive if the plane is on the plus side of the instance and negative if it is on the minus side, according to its natural orientation.
    
    Parameters:
    plane - plane to check
    
    Returns:
    offset of the plane
  - getOffset
```
public double getOffset(Vector<Euclidean3D> vector)
```
    Get the offset (oriented distance) of a vector.
    
    Parameters:
    vector - vector to check
    
    Returns:
    offset of the vector
  - getOffset
```
public double getOffset(Point<Euclidean3D> 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.
    
    Specified by:
    
    getOffset in interface Hyperplane<Euclidean3D>
    
    Parameters:
    point - point to check
    
    Returns:
    offset of the point
  - sameOrientationAs
```
public boolean sameOrientationAs(Hyperplane<Euclidean3D> other)
```
    Check if the instance has the same orientation as another hyperplane.
    
    Specified by:
    
    sameOrientationAs in interface Hyperplane<Euclidean3D>
    
    Parameters:
    other - other hyperplane to check against the instance
    
    Returns:
    true if the instance and the other hyperplane have the same orientation

Class Plane

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

Plane

Plane

Plane

Plane

Plane

Plane

Plane

Method Detail

copySelf

reset

reset

getOrigin

getNormal

getU

getV

project

getTolerance

revertSelf

toSubSpace

toSpace

toSubSpace

toSpace

getPointAt

isSimilarTo

rotate

translate

intersection

intersection

intersection

wholeHyperplane

wholeSpace

contains

getOffset

getOffset

getOffset

sameOrientationAs