no.geosoft.cc.geometry
Class Matrix4x4

Object
  |
  +--Matrix4x4

public class Matrix4x4

extends Object

Implementation of a 4x4 matrix suited for use in a 2D and 3D graphics rendering engine.

Author:

GeoSoft

Constructor Summary

Matrix4x4()
Construct a 4x4 identity matrix.

Matrix4x4(double[] m)
Construct a 4x4 matrix with the specified element values.

Matrix4x4(double m00, double m01, double m02, double m03, double m10, double m11, double m12, double m13, double m20, double m21, double m22, double m23, double m30, double m31, double m32, double m33)
Construct a 4x4 matrix with the specified values.

Matrix4x4(Matrix4x4 matrix)
Constrauct a 4x4 matrix as a copy of the specified matrix.

Method Summary

void	add(Matrix4x4 matrix) Add the specified 4x4 matrix to this matrix.
static Matrix4x4	add(Matrix4x4 m1, Matrix4x4 m2) Add two matrices and return the result matrix.
boolean	equals(Object object) Check if this 4x4 matrix equals the specified object.
double[]	get() Return the values of this 4x4 matrix.
double	getElement(int i, int j) Return matrix element [i,j].
static Matrix4x4	inverse(Matrix4x4 matrix) Return the inverse of the specified matrix.
void	invert() Invert this 4x4 matrix.
void	multiply(Matrix4x4 matrix) Multiply this 4x4 matrix with the specified matrix and store the result in this 4x4 matrix.
static Matrix4x4	multiply(Matrix4x4 m1, Matrix4x4 m2) Multiply two matrices and return the result matrix.
Vector4	multiply(Vector4 vector4) Multiply this 4x4 matrix with the specified vector.
void	rotate(double angle, double[] p0, double[] p1) Apply rotation around an arbitrary axis.
void	rotateX(double angle) Apply rotation around X axis to this matrix.
void	rotateY(double angle) Apply rotation around Y axis to this matrix.
void	rotateZ(double angle) Apply rotation around z axis to this matrix.
void	scale(double xScale, double yScale, double zScale) Apply scaling (relative to origo) to this 4x4 matrix.
void	scale(double xScale, double yScale, double zScale, double[] fixedPoint) Apply scaling relative to a fixed point to this 4x4 matrix.
void	set(double[] m) Set the values of this 4x4 matrix.
void	set(double m00, double m01, double m02, double m03, double m10, double m11, double m12, double m13, double m20, double m21, double m22, double m23, double m30, double m31, double m32, double m33) Set the values of this 4x4 matrix.
void	set(Matrix4x4 matrix) Set the value of this 4x4matrix according to the specified matrix
void	setElement(int i, int j, double value) Set specified matrix element.
void	setIdentity() Make an identity matrix out of this 4x4 matrix.
void	setWorld2DeviceTransform(double[] w0, double[] w1, double[] w2, int x0, int y0, int width, int height) Make this 4x4 matrix a world-2-device transformation matrix.
Vector4	solve(Vector4 vector) Solve the A x = b equation, where A is this 4x4 matrix, b is the specified result vector and the returned vector is the unknown x.
String	toString() Create a string representation of this matrix.
double[]	transformPoint(double[] point) Transform one coordinate using this 4x4 matrix.
void	transformPoints(double[] points) Transform a set of 3D coordinates using this 4x4 matrix.
void	transformPoints(int[] points) Transform a set of 3D coordinates using this 4x4 matrix.
void	transformXyPoints(double[] points) Transform a set of 2D (x,y) coordinates using this 4x4 matrix.
void	transformXyPoints(int[] points) Transform a set of 2D (x,y) coordinates using this 4x4 matrix.
void	translate(double dx, double dy) Apply specified XY translation to this 4x4 matrix.
void	translate(double dx, double dy, double dz) Apply specified translation to this 4x4 matrix.

Methods inherited from class Object

getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

Matrix4x4

public Matrix4x4()

Construct a 4x4 identity matrix.

Matrix4x4

public Matrix4x4(double[] m)

Construct a 4x4 matrix with the specified element values.

Parameters:

m - Array of 16 matrix elements, m00, m01, etc.

Matrix4x4

public Matrix4x4(Matrix4x4 matrix)

Constrauct a 4x4 matrix as a copy of the specified matrix.

Parameters:

matrix - Matrix to copy.

Matrix4x4

public Matrix4x4(double m00,
                 double m01,
                 double m02,
                 double m03,
                 double m10,
                 double m11,
                 double m12,
                 double m13,
                 double m20,
                 double m21,
                 double m22,
                 double m23,
                 double m30,
                 double m31,
                 double m32,
                 double m33)

Construct a 4x4 matrix with the specified values.

Parameters:

m00 - Value of element m[0,0].

m01 - Value of element m[0,1].

m02 - Value of element m[0,2].

m03 - Value of element m[0,3].

m10 - Value of element m[1,0].

m11 - Value of element m[1,1].

m12 - Value of element m[1,2].

m13 - Value of element m[1,3].

m20 - Value of element m[2,0].

m21 - Value of element m[2,1].

m22 - Value of element m[2,2].

m23 - Value of element m[2,3].

m30 - Value of element m[3,0].

m31 - Value of element m[3,1].

m32 - Value of element m[3,2].

m33 - Value of element m[3,3].

Method Detail

setIdentity

public void setIdentity()

Make an identity matrix out of this 4x4 matrix.

set

public void set(Matrix4x4 matrix)

Set the value of this 4x4matrix according to the specified matrix

Parameters:

matrix - Matrix to copy.

set

public void set(double[] m)

Set the values of this 4x4 matrix.

Parameters:

m - Array of 16 matrix elements, m00, m01, etc.

set

public void set(double m00,
                double m01,
                double m02,
                double m03,
                double m10,
                double m11,
                double m12,
                double m13,
                double m20,
                double m21,
                double m22,
                double m23,
                double m30,
                double m31,
                double m32,
                double m33)

Set the values of this 4x4 matrix.

Parameters:

m00 - Value of element m[0,0].

m01 - Value of element m[0,1].

m02 - Value of element m[0,2].

m03 - Value of element m[0,3].

m10 - Value of element m[1,0].

m11 - Value of element m[1,1].

m12 - Value of element m[1,2].

m13 - Value of element m[1,3].

m20 - Value of element m[2,0].

m21 - Value of element m[2,1].

m22 - Value of element m[2,2].

m23 - Value of element m[2,3].

m30 - Value of element m[3,0].

m31 - Value of element m[3,1].

m32 - Value of element m[3,2].

m33 - Value of element m[3,3].

get

public double[] get()

Return the values of this 4x4 matrix.

Returns:

Array ov values: m00, m01, etc.

equals

public boolean equals(Object object)

Check if this 4x4 matrix equals the specified object.

Overrides:

equals in class Object

Parameters:

object - Object to check.

Returns:

True if the two are equal, false otherwise.

Throws:

ClassCastException - if object is not of type Matrix4x4.

getElement

public double getElement(int i,
                         int j)

Return matrix element [i,j].

Parameters:

i - Row of element to get (first row is 0).

j - Column of element to get (first column is 0).

Returns:

Element at specified position.

Throws:

ArrayOutOfBoundsException

setElement

public void setElement(int i,
                       int j,
                       double value)

Set specified matrix element.

Parameters:

i - Row of element to set (first row is 0).

j - Column of element to set (first column is 0).

value - New element value.

Throws:

ArrayOutOfBoundsException

add

public void add(Matrix4x4 matrix)

Add the specified 4x4 matrix to this matrix.

Parameters:

matrix - Matrix to add.

add

public static Matrix4x4 add(Matrix4x4 m1,
                            Matrix4x4 m2)

Add two matrices and return the result matrix.

Parameters:

m1 - First matrix to add.

m2 - Second matrix to add.

Returns:

Sum m1 + m2.

multiply

public void multiply(Matrix4x4 matrix)

Multiply this 4x4 matrix with the specified matrix and store the result in this 4x4 matrix.

Parameters:

matrix - Matrix to multiply with.

multiply

public static Matrix4x4 multiply(Matrix4x4 m1,
                                 Matrix4x4 m2)

Multiply two matrices and return the result matrix.

Parameters:

m1 - First matrix to multiply.

m2 - Second matrix to multiply.

Returns:

Product m1 * m2.

multiply

public Vector4 multiply(Vector4 vector4)

Multiply this 4x4 matrix with the specified vector.

Parameters:

vector4 - Vector to multiply with.

Returns:

Result of operation.

transformPoint

public double[] transformPoint(double[] point)

Transform one coordinate using this 4x4 matrix.

Parameters:

point - [x0,y0,z0]

Returns:

Result of operation: [x0',y0',z0']

transformPoints

public void transformPoints(double[] points)

Transform a set of 3D coordinates using this 4x4 matrix. The result of the operation is put back in the original array.

transformXyPoints

public void transformXyPoints(double[] points)

Transform a set of 2D (x,y) coordinates using this 4x4 matrix. The result of the operation is put back in the original array rounded to the nearest integer.

Parameters:

points - Points to transform [x0,y0,x1,y1,...].

transformPoints

public void transformPoints(int[] points)

Transform a set of 3D coordinates using this 4x4 matrix. The result of the operation is put back in the original array.

Parameters:

points - Points to transform [x0,y0,z0,x1,y1,z1,...].

transformXyPoints

public void transformXyPoints(int[] points)

Transform a set of 2D (x,y) coordinates using this 4x4 matrix. The result of the operation is put back in the original array rounded to the nearest integer.

Parameters:

points - Points to transform [x0,y0,x1,y1,...].

translate

public void translate(double dx,
                      double dy,
                      double dz)

Apply specified translation to this 4x4 matrix.

Parameters:

dx - x translation.

dy - y translation.

dz - z translation.

translate

public void translate(double dx,
                      double dy)

Apply specified XY translation to this 4x4 matrix.

Parameters:

dx - x translation.

dy - y translation.

rotateX

public void rotateX(double angle)

Apply rotation around X axis to this matrix.

Parameters:

angle - Angle to rotate [radians].

rotateY

public void rotateY(double angle)

Apply rotation around Y axis to this matrix.

Parameters:

angle - Angle to rotate [radians].

rotateZ

public void rotateZ(double angle)

Apply rotation around z axis to this matrix.

Parameters:

angle - Angle to rotate [radians].

rotate

public void rotate(double angle,
                   double[] p0,
                   double[] p1)

Apply rotation around an arbitrary axis. Ref: http://www.swin.edu.au/astronomy/pbourke/geometry/rotate/ (but be aware of errors, corrected here)

Parameters:

angle - Angle to rotate [radians]

p0 - First point defining the axis (x,y,z)

p1 - Second point defining the axis (x,y,z)

scale

public void scale(double xScale,
                  double yScale,
                  double zScale)

Apply scaling (relative to origo) to this 4x4 matrix.

Parameters:

xScale - Scaling in x direction.

yScale - Scaling in y direction.

zScale - Scaling in z direction.

scale

public void scale(double xScale,
                  double yScale,
                  double zScale,
                  double[] fixedPoint)

Apply scaling relative to a fixed point to this 4x4 matrix.

Parameters:

xScale - Scaling in x direction.

yScale - Scaling in y direction.

zScale - Scaling in z direction.

fixedPoint - Scaling origo.

invert

public void invert()

Invert this 4x4 matrix.

inverse

public static Matrix4x4 inverse(Matrix4x4 matrix)

Return the inverse of the specified matrix.

Parameters:

matrix - Matrix to finr the inverse of.

Returns:

Inverse of the specified matrix.

solve

public Vector4 solve(Vector4 vector)

Solve the A x = b equation, where A is this 4x4 matrix, b is the specified result vector and the returned vector is the unknown x.

Parameters:

vector - Result vector

Returns:

Unknown vector.

setWorld2DeviceTransform

public void setWorld2DeviceTransform(double[] w0,
                                     double[] w1,
                                     double[] w2,
                                     int x0,
                                     int y0,
                                     int width,
                                     int height)

Make this 4x4 matrix a world-2-device transformation matrix.

The world system is defined as follows:

        w2 o 
           |
           |
           |
        w0 o-------o w1
 
 

 Each point is defined with x,y,z so this system may in effect be
 arbitrary oriented in space, and may include sharing.
 

 The device system is defined as follows:

 
             width
     x0,y0 o-------o
           |
    height |
           |
           o
 
 

 The matrix maps w2 to (x0,y0), w0 to the lower left corner of the
 device rectangle, and w1 to the lower right corner of the device
 rectangle.


Parameters:
w0 - x,y,z coordinate of first world position.
w1 - x,y,z coordinate of second world position.
w2 - x,y,z coordinate of third world position.
x0 - X coordinate of upper left corner of device.
y0 - Y coordinate of upper left corner of device.
width - Width of device
height - Height of device.

toString

public String toString()

Create a string representation of this matrix.

Overrides:

toString in class Object

Returns:

String representing this matrix.