org.opensourcephysics.numerics
Class Matrix3DTransformation

java.lang.Object
  org.opensourcephysics.numerics.Matrix3DTransformation

All Implemented Interfaces:

java.lang.Cloneable, MatrixTransformation, Transformation

public class Matrix3DTransformation
extends java.lang.Object
implements MatrixTransformation

Matrix3DTransformation implements 3D affine transformations using a matrix representation.

Nested Class Summary

protected static class

Matrix3DTransformation.Affine3DTransformationLoader

Constructor Summary

Matrix3DTransformation(double[][] matrix)
Constructs a 3D transformation using the given matrix.

Method Summary

java.lang.Object	clone() Provides a copy of this transformation.
static Matrix3DTransformation	createAlignmentTransformation(double[] v1, double[] v2) Instantiates a rotation that aligns the first vector with the second vector.
double[]	direct(double[] point) Transforms the given point+.
double[][]	direct(double[][] mat) Transforms the given matrix into the transformation's coordinate system.
double[]	getFlatMatrix(double[] mat) Gets the direct homogeneous affine transformation flattened into a 1-d array.
static XML.ObjectLoader	getLoader()
double[]	getTransposedFlatMatrix(double[] mat) Gets the direct homogeneous affine transformation flattened into a 1-d array, ordered left to right, top to bottom If the mat parameter is null a double[16] array is created; otherwise the given array is used.
double[]	inverse(double[] point) Transforms the given point using the inverse transformation (if it exists).
double[][]	inverse(double[][] mat) Transforms the given matrix from the transformation's coordinate system.
void	multiply(double[][] mat) Multiplies this rotation matrix by the given matrix.
void	multiply(Matrix3DTransformation trans) Multiplies (concatenates) this transformation matrix with the given transformation.
static Matrix3DTransformation	Quaternion(double[] quaternion) Creates an transformation representing a rotation about the origin by the given quaternion.
static Matrix3DTransformation	Quaternion(double q0, double q1, double q2, double q3) Creates an AffineMatrix representing a rotation about the origin by the given quaternion components.
static Matrix3DTransformation	rotation(double theta, double[] axis) Creates a 3D transforamtion representing a rotation about the origin by the given angle around the given axis.
static Matrix3DTransformation	rotationX(double theta) Creates a 3D transforamtion representing a rotation about the x axis by the given angle.
static Matrix3DTransformation	rotationY(double theta) Creates a 3D transforamtion representing a rotation about the y axis by the given angle.
static Matrix3DTransformation	rotationZ(double theta) Creates a 3D transforamtion representing a rotation about the z axis by the given angle.
double[]	setOrigin(double[] origin) Sets the origin for this rotation.
void	setOrigin(double ox, double oy, double oz) Sets the origin for this rotation.
double[]	toQuaternion(double[] q)

Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Matrix3DTransformation

public Matrix3DTransformation(double[][] matrix)

Constructs a 3D transformation using the given matrix. Affine transformations can be applied to 3D coordinates. A 3 by 3 matrix sets the rotation and shear. A null matrix sets the transformation to the identity transformation.

Parameters:

matrix - double[][]

Method Detail

rotationX

public static Matrix3DTransformation rotationX(double theta)

Creates a 3D transforamtion representing a rotation about the x axis by the given angle.

Parameters:

theta - double

Returns:

Affine3DTransformation

rotationY

public static Matrix3DTransformation rotationY(double theta)

Creates a 3D transforamtion representing a rotation about the y axis by the given angle.

Parameters:

theta - double

Returns:

Affine3DTransformation

rotationZ

public static Matrix3DTransformation rotationZ(double theta)

Creates a 3D transforamtion representing a rotation about the z axis by the given angle.

Parameters:

theta - double

Returns:

Affine3DTransformation

rotation

public static Matrix3DTransformation rotation(double theta,
                                              double[] axis)

Creates a 3D transforamtion representing a rotation about the origin by the given angle around the given axis.

Parameters:

theta - double

axis - double[]

Returns:

Affine3DTransformation

Quaternion

public static Matrix3DTransformation Quaternion(double[] quaternion)

Creates an transformation representing a rotation about the origin by the given quaternion.

Parameters:

quaternion - double[]

Returns:

Affine3DTransformation

Quaternion

public static Matrix3DTransformation Quaternion(double q0,
                                                double q1,
                                                double q2,
                                                double q3)

Creates an AffineMatrix representing a rotation about the origin by the given quaternion components.

Parameters:

q0 -

q1 -

q2 -

q3 -

Returns:

Affine3DTransformation

clone

public java.lang.Object clone()

Provides a copy of this transformation.

Specified by:

clone in interface Transformation

Overrides:

clone in class java.lang.Object

getFlatMatrix

public final double[] getFlatMatrix(double[] mat)

Gets the direct homogeneous affine transformation flattened into a 1-d array. If the mat parameter is null a double[16] array is created; otherwise the given array is used.

Specified by:

getFlatMatrix in interface MatrixTransformation

Parameters:

mat - double[] optional matrix

Returns:

double[] the matrix

getTransposedFlatMatrix

public final double[] getTransposedFlatMatrix(double[] mat)

Gets the direct homogeneous affine transformation flattened into a 1-d array, ordered left to right, top to bottom If the mat parameter is null a double[16] array is created; otherwise the given array is used.

Parameters:

mat - double[] optional matrix

Returns:

double[] the matrix

toQuaternion

public final double[] toQuaternion(double[] q)

createAlignmentTransformation

public static Matrix3DTransformation createAlignmentTransformation(double[] v1,
                                                                   double[] v2)

Instantiates a rotation that aligns the first vector with the second vector.

Parameters:

v1 - double[]

v2 - double[]

Returns:

Quaternion

setOrigin

public void setOrigin(double ox,
                      double oy,
                      double oz)

Sets the origin for this rotation.

Parameters:

ox - double

oy - double

oz - double

multiply

public final void multiply(Matrix3DTransformation trans)

Multiplies (concatenates) this transformation matrix with the given transformation.

Parameters:

trans - Matrix3DTransformation

multiply

public final void multiply(double[][] mat)

Multiplies this rotation matrix by the given matrix.

Parameters:

mat - double[][]

setOrigin

public double[] setOrigin(double[] origin)

Sets the origin for this rotation.

Parameters:

origin - double[] the new origin

Returns:

double[]

direct

public double[] direct(double[] point)

Transforms the given point+.

Specified by:

direct in interface Transformation

Parameters:

point - the coordinates to be transformed

Returns:

double[] the transformed vector (i.e. point)

direct

public double[][] direct(double[][] mat)

Transforms the given matrix into the transformation's coordinate system.

Parameters:

matrix - to be transformed

inverse

public double[] inverse(double[] point)
                 throws java.lang.UnsupportedOperationException

Transforms the given point using the inverse transformation (if it exists). If the transformation is not invertible, then a call to this method must throw a UnsupportedOperationException exception.

Specified by:

inverse in interface Transformation

Parameters:

point - the coordinates to be transformed

Returns:

double[] the transformed vector (i.e. point)

Throws:

java.lang.UnsupportedOperationException - If the transformation is not invertible

inverse

public double[][] inverse(double[][] mat)

Transforms the given matrix from the transformation's coordinate system.

Parameters:

matrix - to be transformed

getLoader

public static XML.ObjectLoader getLoader()