org.apache.commons.math3.geometry.euclidean.threed
Class Plane

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

All Implemented Interfaces:

InfiniteShape, Shape, Embedding<Euclidean3D,Euclidean2D>, Hyperplane<Euclidean3D>

public class Plane
extends Object
implements Hyperplane<Euclidean3D>, Embedding<Euclidean3D,Euclidean2D>, InfiniteShape

The class represent planes in a three dimensional space.

Since:

3.0

Version:

$Id: Plane.java 7721 2013-02-14 14:07:13Z CardosoP $

Constructor Summary

Plane(Line line, Vector3D vector)
Build a plane from a line and a vector.

Plane(Plane plane)
Copy constructor.

Plane(Vector3D normal)
Build a plane normal to a given direction and containing the origin.

Plane(Vector3D point, Line line)
Build a plane from a line and a point out of the line.

Plane(Vector3D p, Vector3D normal)
Build a plane from a point and a normal.

Plane(Vector3D p1, Vector3D p2, Vector3D p3)
Build a plane from three points.

Plane(Vector3D p, Vector3D v1, Vector3D v2, boolean isFrame)
Build a plane from a point and two vectors.

Method Summary

Vector3D[]	closestPointTo(Line line) Computes the points of the shape and the line realizing the shortest distance.
boolean	contains(Vector3D p) Check if the instance contains a point.
Plane	copySelf() Copy the instance.
double	distanceTo(Line line) Computes the distance between this plane and a line.
double	distanceTo(Vector3D point) Computes the distance between this plane and a point of space.
Vector3D[]	getIntersectionPoints(Line line) Compute the intersection points with a line.
Vector3D	getNormal() Get the normalized normal vector.
double	getOffset(Plane plane) Get the offset (oriented distance) of a parallel plane.
double	getOffset(Vector<Euclidean3D> point) Get the offset (oriented distance) of a point.
Vector3D	getOrigin() Get the origin point of the plane frame.
Vector3D	getPointAt(Vector2D inPlane, double offset) Get one point from the 3D-space.
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	intersects(Line line) Tests the intersection with a line.
boolean	isSimilarTo(Plane plane) Check if the instance is similar to another plane.
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(Vector<Euclidean2D> point) Transform an in-plane point into a 3D space point.
Vector2D	toSubSpace(Vector<Euclidean3D> point) Transform a 3D space point into an in-plane 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)
      throws MathArithmeticException

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

public Plane(Vector3D p,
             Vector3D normal)
      throws MathArithmeticException

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

public Plane(Vector3D p1,
             Vector3D p2,
             Vector3D p3)
      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

Throws:

MathArithmeticException - if the points do not constitute a plane

Plane

public Plane(Vector3D p,
             Vector3D v1,
             Vector3D v2,
             boolean isFrame)

Build a plane from a point and two vectors.

The plane is oriented in the direction of (v1) ^ (v2)

Parameters:

p - first point belonging to the plane

v1 - second point belonging to the plane

v2 - third point belonging to the plane

isFrame - boolean to choose if the given point and vectors constitute the local frame (they may be not orthogonal)

Throws:

IllegalArgumentException - if the point and vectors do not constitute a plane

Plane

public Plane(Line line,
             Vector3D vector)

Build a plane from a line and a vector.

The plane is created to contain the line and be directed by the vector

Parameters:

line - a line belonging to the plane

vector - a vector belonging to the plane

Throws:

IllegalArgumentException - if the line and vector do not constitute a plane

Plane

public Plane(Vector3D point,
             Line line)

Build a plane from a line and a point out of the line.

The plane is created to contain the line and the point

Parameters:

point - a point belonging to the plane

line - a line belonging to the plane

Throws:

IllegalArgumentException - if the line and point 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()

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> 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)

toSpace

public Vector3D toSpace(Vector<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)

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> 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

distanceTo

public double distanceTo(Vector3D point)

Computes the distance between this plane and a point of space.

Parameters:

point - any point of space

Returns:

the distance between this and the given point

intersects

public boolean intersects(Line line)

Tests the intersection with a line.

Specified by:

intersects in interface Shape

Parameters:

line - the line

Returns:

true if the line intersects the shape

getIntersectionPoints

public Vector3D[] getIntersectionPoints(Line line)

Compute the intersection points with a line.

Specified by:

getIntersectionPoints in interface Shape

Parameters:

line - the line

Returns:

the intersection points if they exist. If no intersection is found, the dimension is zero

distanceTo

public double distanceTo(Line line)

Computes the distance between this plane and a line.

Specified by:

distanceTo in interface Shape

Parameters:

line - a line of space

Returns:

the distance between this plane and the line : zero if the line intersects this plane

closestPointTo

public final Vector3D[] closestPointTo(Line line)

Computes the points of the shape and the line realizing the shortest distance. If the line intersects the shape, the returned points are identical : this point is the first common point found.

Specified by:

closestPointTo in interface Shape

Parameters:

line - the line

Returns:

the two points : first the one from the line, and the one from the shape.