org.apache.commons.math4.geometry.euclidean.threed

Class 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, double tolerance)
Build a plane normal to a given direction and containing the origin.
Plane(Vector3D p, Vector3D normal, double tolerance)
Build a plane from a point and a normal.
Plane(Vector3D p1, Vector3D p2, Vector3D p3, double tolerance)
Build a plane from three points.
• Method Summary

All 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

public Plane(Plane plane)
Copy constructor.

The instance created is completely independent 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)
• 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
• 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