org.sunflow.math
Class Matrix4

java.lang.Object
  org.sunflow.math.Matrix4

public final class Matrix4
extends java.lang.Object

This class is used to represent general affine transformations in 3D. The bottom row of the matrix is assumed to be [0,0,0,1]. Note that the rotation matrices assume a right-handed convention.

Field Summary

static Matrix4	IDENTITY
static Matrix4	ZERO

Constructor Summary

Matrix4(float[] m, boolean rowMajor)
Initialize a matrix from the specified 16 element array.

Matrix4(float m00, float m01, float m02, float m03, float m10, float m11, float m12, float m13, float m20, float m21, float m22, float m23)
Creates a matrix with the specified elements

Method Summary

float[]	asColMajor()
float[]	asRowMajor()
static Matrix4	blend(Matrix4 m0, Matrix4 m1, float t)
float	determinant() Compute the matrix determinant.
boolean	equals(Matrix4 m)
static Matrix4	fromBasis(OrthoNormalBasis basis) Creates a rotation matrix from an OrthonormalBasis.
Matrix4	inverse() Compute the inverse of this matrix and return it as a new object.
boolean	isIndentity()
static Matrix4	lookAt(Point3 eye, Point3 target, Vector3 up) Creates a camera positioning matrix from the given eye and target points and up vector.
Matrix4	multiply(Matrix4 m) Computes this*m and return the result as a new Matrix4
static Matrix4	rotate(float x, float y, float z, float theta) Creates a rotation matrix about the specified axis.
static Matrix4	rotateX(float theta) Creates a rotation matrix about the X axis.
static Matrix4	rotateY(float theta) Creates a rotation matrix about the Y axis.
static Matrix4	rotateZ(float theta) Creates a rotation matrix about the Z axis.
static Matrix4	scale(float s) Create a uniform scaling matrix.
static Matrix4	scale(float sx, float sy, float sz) Creates a non-uniform scaling matrix.
BoundingBox	transform(BoundingBox b) Transforms each corner of the specified axis-aligned bounding box and returns a new bounding box which incloses the transformed corners.
Point3	transformP(Point3 p) Computes this*p and returns the result as a new Point3 object.
float	transformPX(float x, float y, float z) Computes the x component of this*(x,y,z,1).
float	transformPY(float x, float y, float z) Computes the y component of this*(x,y,z,1).
float	transformPZ(float x, float y, float z) Computes the z component of this*(x,y,z,1).
Vector3	transformTransposeV(Vector3 v) Computes (this^T)*v and returns the result as a new Vector3 object.
float	transformTransposeVX(float x, float y, float z) Computes the x component of (this^T)*(x,y,z,0).
float	transformTransposeVY(float x, float y, float z) Computes the y component of (this^T)*(x,y,z,0).
float	transformTransposeVZ(float x, float y, float z) Computes the z component of (this^T)*(x,y,z,0).
Vector3	transformV(Vector3 v) Computes this*v and returns the result as a new Vector3 object.
float	transformVX(float x, float y, float z) Computes the x component of this*(x,y,z,0).
float	transformVY(float x, float y, float z) Computes the y component of this*(x,y,z,0).
float	transformVZ(float x, float y, float z) Computes the z component of this*(x,y,z,0).
static Matrix4	translation(float x, float y, float z) Create a translation matrix for the specified vector.

Methods inherited from class java.lang.Object

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

Field Detail

ZERO

public static final Matrix4 ZERO

IDENTITY

public static final Matrix4 IDENTITY

Constructor Detail

Matrix4

public Matrix4(float m00,
               float m01,
               float m02,
               float m03,
               float m10,
               float m11,
               float m12,
               float m13,
               float m20,
               float m21,
               float m22,
               float m23)

Creates a matrix with the specified elements

Parameters:

m00 - value at row 0, col 0

m01 - value at row 0, col 1

m02 - value at row 0, col 2

m03 - value at row 0, col 3

m10 - value at row 1, col 0

m11 - value at row 1, col 1

m12 - value at row 1, col 2

m13 - value at row 1, col 3

m20 - value at row 2, col 0

m21 - value at row 2, col 1

m22 - value at row 2, col 2

m23 - value at row 2, col 3

Matrix4

public Matrix4(float[] m,
               boolean rowMajor)

Initialize a matrix from the specified 16 element array. The matrix may be given in row or column major form.

Parameters:

m - a 16 element array in row or column major form

rowMajor - true if the array is in row major form, falseif it is in column major form

Method Detail

isIndentity

public final boolean isIndentity()

equals

public final boolean equals(Matrix4 m)

asRowMajor

public final float[] asRowMajor()

asColMajor

public final float[] asColMajor()

determinant

public final float determinant()

Compute the matrix determinant.

Returns:

determinant of this matrix

inverse

public final Matrix4 inverse()

Compute the inverse of this matrix and return it as a new object. If the matrix is not invertible, null is returned.

Returns:

the inverse of this matrix, or null if not invertible

multiply

public final Matrix4 multiply(Matrix4 m)

Computes this*m and return the result as a new Matrix4

Parameters:

m - right hand side of the multiplication

Returns:

a new Matrix4 object equal to this*m

transform

public final BoundingBox transform(BoundingBox b)

Transforms each corner of the specified axis-aligned bounding box and returns a new bounding box which incloses the transformed corners.

Parameters:

b - original bounding box

Returns:

a new BoundingBox object which encloses the transform version of b

transformV

public final Vector3 transformV(Vector3 v)

Computes this*v and returns the result as a new Vector3 object. This method assumes the bottom row of the matrix is [0,0,0,1].

Parameters:

v - vector to multiply

Returns:

a new Vector3 object equal to this*v

transformTransposeV

public final Vector3 transformTransposeV(Vector3 v)

Computes (this^T)*v and returns the result as a new Vector3 object. This method assumes the bottom row of the matrix is [0,0,0,1].

Parameters:

v - vector to multiply

Returns:

a new Vector3 object equal to (this^T)*v

transformP

public final Point3 transformP(Point3 p)

Computes this*p and returns the result as a new Point3 object. This method assumes the bottom row of the matrix is [0,0,0,1].

Parameters:

p - point to multiply

Returns:

a new Point3 object equal to this*v

transformVX

public final float transformVX(float x,
                               float y,
                               float z)

Computes the x component of this*(x,y,z,0).

Parameters:

x - x coordinate of the vector to multiply

y - y coordinate of the vector to multiply

z - z coordinate of the vector to multiply

Returns:

x coordinate transformation result

transformVY

public final float transformVY(float x,
                               float y,
                               float z)

Computes the y component of this*(x,y,z,0).

Parameters:

x - x coordinate of the vector to multiply

y - y coordinate of the vector to multiply

z - z coordinate of the vector to multiply

Returns:

y coordinate transformation result

transformVZ

public final float transformVZ(float x,
                               float y,
                               float z)

Computes the z component of this*(x,y,z,0).

Parameters:

x - x coordinate of the vector to multiply

y - y coordinate of the vector to multiply

z - z coordinate of the vector to multiply

Returns:

z coordinate transformation result

transformTransposeVX

public final float transformTransposeVX(float x,
                                        float y,
                                        float z)

Computes the x component of (this^T)*(x,y,z,0).

Parameters:

x - x coordinate of the vector to multiply

y - y coordinate of the vector to multiply

z - z coordinate of the vector to multiply

Returns:

x coordinate transformation result

transformTransposeVY

public final float transformTransposeVY(float x,
                                        float y,
                                        float z)

Computes the y component of (this^T)*(x,y,z,0).

Parameters:

x - x coordinate of the vector to multiply

y - y coordinate of the vector to multiply

z - z coordinate of the vector to multiply

Returns:

y coordinate transformation result

transformTransposeVZ

public final float transformTransposeVZ(float x,
                                        float y,
                                        float z)

Computes the z component of (this^T)*(x,y,z,0).

Parameters:

x - x coordinate of the vector to multiply

y - y coordinate of the vector to multiply

z - z coordinate of the vector to multiply

Returns:

zcoordinate transformation result

transformPX

public final float transformPX(float x,
                               float y,
                               float z)

Computes the x component of this*(x,y,z,1).

Parameters:

x - x coordinate of the vector to multiply

y - y coordinate of the vector to multiply

z - z coordinate of the vector to multiply

Returns:

x coordinate transformation result

transformPY

public final float transformPY(float x,
                               float y,
                               float z)

Computes the y component of this*(x,y,z,1).

Parameters:

x - x coordinate of the vector to multiply

y - y coordinate of the vector to multiply

z - z coordinate of the vector to multiply

Returns:

y coordinate transformation result

transformPZ

public final float transformPZ(float x,
                               float y,
                               float z)

Computes the z component of this*(x,y,z,1).

Parameters:

x - x coordinate of the vector to multiply

y - y coordinate of the vector to multiply

z - z coordinate of the vector to multiply

Returns:

z coordinate transformation result

translation

public static final Matrix4 translation(float x,
                                        float y,
                                        float z)

Create a translation matrix for the specified vector.

Parameters:

x - x component of translation

y - y component of translation

z - z component of translation

Returns:

a new Matrix4 object representing the translation

rotateX

public static final Matrix4 rotateX(float theta)

Creates a rotation matrix about the X axis.

Parameters:

theta - angle to rotate about the X axis in radians

Returns:

a new Matrix4 object representing the rotation

rotateY

public static final Matrix4 rotateY(float theta)

Creates a rotation matrix about the Y axis.

Parameters:

theta - angle to rotate about the Y axis in radians

Returns:

a new Matrix4 object representing the rotation

rotateZ

public static final Matrix4 rotateZ(float theta)

Creates a rotation matrix about the Z axis.

Parameters:

theta - angle to rotate about the Z axis in radians

Returns:

a new Matrix4 object representing the rotation

rotate

public static final Matrix4 rotate(float x,
                                   float y,
                                   float z,
                                   float theta)

Creates a rotation matrix about the specified axis. The axis vector need not be normalized.

Parameters:

x - x component of the axis vector

y - y component of the axis vector

z - z component of the axis vector

theta - angle to rotate about the axis in radians

Returns:

a new Matrix4 object representing the rotation

scale

public static final Matrix4 scale(float s)

Create a uniform scaling matrix.

Parameters:

s - scale factor for all three axes

Returns:

a new Matrix4 object representing the uniform scale

scale

public static final Matrix4 scale(float sx,
                                  float sy,
                                  float sz)

Creates a non-uniform scaling matrix.

Parameters:

sx - scale factor in the x dimension

sy - scale factor in the y dimension

sz - scale factor in the z dimension

Returns:

a new Matrix4 object representing the non-uniform scale

fromBasis

public static final Matrix4 fromBasis(OrthoNormalBasis basis)

Creates a rotation matrix from an OrthonormalBasis.

Parameters:

basis -

lookAt

public static final Matrix4 lookAt(Point3 eye,
                                   Point3 target,
                                   Vector3 up)

Creates a camera positioning matrix from the given eye and target points and up vector.

Parameters:

eye - location of the eye

target - location of the target

up - vector pointing upwards

Returns:

blend

public static final Matrix4 blend(Matrix4 m0,
                                  Matrix4 m1,
                                  float t)