Matrix Class Reference

Inherits ScriptObject.

Public Types
enum	EulerConvention {   EULER_XZX_S, EULER_YXY_S, EULER_ZYZ_S, EULER_XZX_R,   EULER_YXY_R, EULER_ZYZ_R, EULER_XZY_S, EULER_YXZ_S,   EULER_ZYX_S, EULER_YZX_R, EULER_ZXY_R, EULER_XYZ_R,   EULER_XYX_S, EULER_YZY_S, EULER_ZXZ_S, EULER_XYX_R,   EULER_YZY_R, EULER_ZXZ_R, EULER_XYZ_S, EULER_YZX_S,   EULER_ZXY_S, EULER_ZYX_R, EULER_XZY_R, EULER_YXZ_R }

Public Member Functions
	Matrix ()
	Matrix (Number scale)
	Matrix (Vector right, Vector up, Vector forward)
	Matrix (Number m[9])
	Matrix (Vector axis, Number angle)
	rotateX (Number angle)
	rotateY (Number angle)
	rotateZ (Number angle)
Number	getElement (Integer row, Integer column)
	setElement (Integer row, Integer column, Number value)
Vector	getRow (Integer row)
	setRow (Integer row, Vector value)
Vector	getColumn (Integer column)
	setColumn (Integer column, Vector value)
Vector	getForward ()
	setForward (Vector value)
Vector	getUp ()
	setUp (Vector value)
Vector	getRight ()
	setRight (Vector value)
Vector	getTiltAndTilt (Integer primary, Integer secondary)
Vector	getTurnAndTilt (Integer primary, Integer secondary)
Vector	getEuler (Integer convention)
Vector	getEuler2 (Integer convention)
Vector	getEulerZXZ ()
Vector	getEulerZYZ ()
Vector	getEulerXYZ ()
Vector	getEulerZYX ()
	clamp (Number epsilon)
Boolean	isZero ()
Boolean	isIdentity ()
Number	getN1 ()
Number	getN2 ()
	normalize ()
	add (Matrix right)
	subtract (Matrix right)
	negate ()
Matrix	getNegated ()
	transpose ()
Matrix	getTransposed ()
Matrix	multiply (Number right)
Matrix	multiply (Matrix right)
Vector	multiply (Vector right)
String	toString ()

Static Public Member Functions
static Matrix	getAxisRotation (Vector axis, Number angle)
static Matrix	getXRotation (Number angle)
static Matrix	getYRotation (Number angle)
static Matrix	getZRotation (Number angle)
static Matrix	getXYZRotation (Vector abc)
static Matrix	getEulerRotation (Integer convention, Vector angles)
static Matrix	getEulerXZXRotation (Vector angles)
static Matrix	getEulerYXYRotation (Vector angles)
static Matrix	getEulerZYZRotation (Vector angles)
static Matrix	getEulerXZYRotation (Vector angles)
static Matrix	getEulerYXZRotation (Vector angles)
static Matrix	getEulerZYXRotation (Vector angles)
static Matrix	getEulerXYXRotation (Vector angles)
static Matrix	getEulerYZYRotation (Vector angles)
static Matrix	getEulerZXZRotation (Vector angles)
static Matrix	getEulerXYZRotation (Vector angles)
static Matrix	getEulerYZXRotation (Vector angles)
static Matrix	getEulerZXYRotation (Vector angles)
static Matrix	sum (Matrix left, Matrix right)
static Matrix	diff (Matrix left, Matrix right)
static Matrix	getOrientationFromDirection (Vector forward)

Public Attributes
Number	n1
	The 1-norm.
Number	n2
	The 2-norm.
Matrix	negated
	The negated matrix.
Matrix	transposed
	The transposed matrix (equal to the inverse for rotations).
Vector	up
	The up vector.
Vector	right
	The right vector.
Vector	forward
	The forward vector.
Vector	eulerXZX
	Euler angles in radians for XZX static/world convention.
Vector	eulerYXY
	Euler angles in radians for YXY static/world convention.
Vector	eulerZYZ
	Euler angles in radians for ZYZ static/world convention.
Vector	eulerXZX_R
	Euler angles in radians for XZX body convention.
Vector	eulerYXY_R
	Euler angles in radians for YXY body convention.
Vector	eulerZYZ_R
	Euler angles in radians for ZYZ body convention.
Vector	eulerXZY
	Euler angles in radians for XZY static/world convention.
Vector	eulerYXZ
	Euler angles in radians for YXZ static/world convention.
Vector	eulerZYX
	Euler angles in radians for ZYX static/world convention.
Vector	eulerYZX_R
	Euler angles in radians for YZX body convention.
Vector	eulerZXY_R
	Euler angles in radians for ZXY body convention.
Vector	eulerXYZ_R
	Euler angles in radians for XYZ body convention.
Vector	eulerXYX
	Euler angles in radians for XYX static/world convention.
Vector	eulerYZY
	Euler angles in radians for YZY static/world convention.
Vector	eulerZXZ
	Euler angles in radians for ZXZ static/world convention.
Vector	eulerXYX_R
	Euler angles in radians for XYX body convention.
Vector	eulerYZY_R
	Euler angles in radians for YZY body convention.
Vector	eulerZXZ_R
	Euler angles in radians for ZXZ body convention.
Vector	eulerXYZ
	Euler angles in radians for XYZ static/world convention.
Vector	eulerYZX
	Euler angles in radians for YZX static/world convention.
Vector	eulerZXY
	Euler angles in radians for ZXY static/world convention.
Vector	eulerZYX_R
	Euler angles in radians for ZYX body convention.
Vector	eulerXZY_R
	Euler angles in radians for XZY body convention.
Vector	eulerYXZ_R
	Euler angles in radians for YXZ body convention.

Detailed Description

A 3 by 3 matrix.

Member Enumeration Documentation

EulerConvention

enum EulerConvention

Euler conventions.

Enumerator
EULER_XZX_S	Euler XZX static/world convention.
EULER_YXY_S	Euler YXY static/world convention.
EULER_ZYZ_S	Euler ZYZ static/world convention.
EULER_XZX_R	Euler XZX body convention.
EULER_YXY_R	Euler YXY body convention.
EULER_ZYZ_R	Euler ZYZ body convention.
EULER_XZY_S	Euler XZY static/world convention.
EULER_YXZ_S	Euler YXZ static/world convention.
EULER_ZYX_S	Euler ZYX static/world convention.
EULER_YZX_R	Euler YZX body convention.
EULER_ZXY_R	Euler ZXY body convention.
EULER_XYZ_R	Euler XYZ body convention.
EULER_XYX_S	Euler XYX static/world convention.
EULER_YZY_S	Euler YZY static/world convention.
EULER_ZXZ_S	Euler ZXZ static/world convention.
EULER_XYX_R	Euler XYX body convention.
EULER_YZY_R	Euler YZY body convention.
EULER_ZXZ_R	Euler ZXZ body convention.
EULER_XYZ_S	Euler XYZ static/world convention.
EULER_YZX_S	Euler YZX static/world convention.
EULER_ZXY_S	Euler ZXY static/world convention.
EULER_ZYX_R	Euler ZYX body convention.
EULER_XZY_R	Euler XZY body convention.
EULER_YXZ_R	Euler YXZ body convention.

Constructor & Destructor Documentation

Matrix() [1/5]

Matrix

(

)

Construct a matrix as the identity matrix.

Matrix() [2/5]

Matrix

(

Number

scale

)

Construct a matrix as a scaling matrix.

Matrix() [3/5]

Matrix	(	Vector	right,
		Vector	up,
		Vector	forward
	)

Constructs the matrix with the specified right, up, and forward directions.

Matrix() [4/5]

Matrix

(

Number

m[9]

)

Constructs the matrix with the specified elements.

Matrix() [5/5]

Matrix	(	Vector	axis,
		Number	angle
	)

Constructs the matrix as the specified axis rotation.

Parameters

axis	The axis of rotation.
angle	The angle of rotation (radians).

Precondition

axis.getLength() == 1

Member Function Documentation

add()

add

(

Matrix

right

)

Adds the specified matrix to this matrix.

clamp()

clamp

(

Number

epsilon

)

Clamps the matrix elements to -1, 0, and -1 with the specified epsilon value.

diff()

static Matrix diff ( Matrix  left, Matrix  right  )

static

Returns the difference between the specified matrices.

getAxisRotation()

static Matrix getAxisRotation ( Vector  axis, Number  angle  )

static

Returns the rotation matrix for the specified axis rotation.

Parameters

axis	The axis of rotation.
angle	The angle (in radians).

Precondition

axis.getLength() == 1

getColumn()

Vector getColumn

(

Integer

column

)

Returns the specified column.

Parameters

column

The column [0; 2].

getElement()

Number getElement	(	Integer	row,
		Integer	column
	)

Returns the value of the specified element.

Parameters

row	The row [0; 2].
column	The column [0; 2].

getEuler()

Vector getEuler

(

Integer

convention

)

Returns the Euler angle for the specified convention in radians. Use getEuler2() instead to get the standard Euler conventions.

Deprecated:

getEuler2()

Vector getEuler2

(

Integer

convention

)

Returns the Euler angle for the specified convention in radians.

Since

r41257

getEulerRotation()

static Matrix getEulerRotation ( Integer  convention, Vector  angles  )

static

Returns the rotation for the specified Euler angles and convention.

getEulerXYXRotation()

static Matrix getEulerXYXRotation ( Vector  angles )

static

Returns the rotation matrix for the specified Euler rotation (XYX static convention). Angles are in radians.

getEulerXYZ()

Vector getEulerXYZ

(

)

Returns the Euler angles (XYZ convention) in radians. Use Matrix.getEuler2() instead.

Deprecated:

getEulerXYZRotation()

static Matrix getEulerXYZRotation ( Vector  angles )

static

Returns the rotation matrix for the specified Euler rotation (XYZ static convention). Angles are in radians.

getEulerXZXRotation()

static Matrix getEulerXZXRotation ( Vector  angles )

static

Returns the rotation matrix for the specified Euler rotation (XZX static convention). Angles are in radians.

getEulerXZYRotation()

static Matrix getEulerXZYRotation ( Vector  angles )

static

Returns the rotation matrix for the specified Euler rotation (XZY static convention). Angles are in radians.

getEulerYXYRotation()

static Matrix getEulerYXYRotation ( Vector  angles )

static

Returns the rotation matrix for the specified Euler rotation (YXY static convention). Angles are in radians.

getEulerYXZRotation()

static Matrix getEulerYXZRotation ( Vector  angles )

static

Returns the rotation matrix for the specified Euler rotation (YXZ static convention). Angles are in radians.

getEulerYZXRotation()

static Matrix getEulerYZXRotation ( Vector  angles )

static

Returns the rotation matrix for the specified Euler rotation (YZX static convention). Angles are in radians.

getEulerYZYRotation()

static Matrix getEulerYZYRotation ( Vector  angles )

static

Returns the rotation matrix for the specified Euler rotation (YZY static convention). Angles are in radians.

getEulerZXYRotation()

static Matrix getEulerZXYRotation ( Vector  angles )

static

Returns the rotation matrix for the specified Euler rotation (ZXY static convention). Angles are in radians.

getEulerZXZ()

Vector getEulerZXZ

(

)

Returns the Euler angles (ZXZ convention) in radians. Use Matrix.getEuler2() instead.

Deprecated:

getEulerZXZRotation()

static Matrix getEulerZXZRotation ( Vector  angles )

static

Returns the rotation matrix for the specified Euler rotation (ZXZ static convention). Angles are in radians.

getEulerZYX()

Vector getEulerZYX

(

)

Returns the Euler angles (ZYX convention) in radians. Use Matrix.getEuler2() instead.

Deprecated:

getEulerZYXRotation()

static Matrix getEulerZYXRotation ( Vector  angles )

static

Returns the rotation matrix for the specified Euler rotation (ZYX static convention). Angles are in radians.

getEulerZYZ()

Vector getEulerZYZ

(

)

Returns the Euler angles (ZYZ convention) in radians. Use Matrix.getEuler2() instead.

Deprecated:

getEulerZYZRotation()

static Matrix getEulerZYZRotation ( Vector  angles )

static

Returns the rotation matrix for the specified Euler rotation (ZYZ static convention). Angles are in radians.

getForward()

Vector getForward

(

)

Returns the forward vector.

getN1()

Number getN1

(

)

Return N1 of this matrix.

getN2()

Number getN2

(

)

Return N2 of this matrix.

getNegated()

Matrix getNegated

(

)

Returns the negated matrix.

getOrientationFromDirection()

static Matrix getOrientationFromDirection ( Vector  forward )

static

Returns a matrix that satisfies the supplied forward vector. Since only a single vector is supplied the resultant matrix can be rotated at any angle around the forward vector.

getRight()

Vector getRight

(

)

Returns the right vector.

getRow()

Vector getRow

(

Integer

row

)

Returns the specified row.

Parameters

row	The row [0; 2].

getTiltAndTilt()

Vector getTiltAndTilt	(	Integer	primary,
		Integer	secondary
	)

Returns the X and Y rotations around the fixed frame to match the forward direction. Primary and secondary specifies the preferred rotations and must be different.

Parameters

primary	The primary coordinate (0, or 1).
secondary	The secondary coordinate (0 or 1).

getTransposed()

Matrix getTransposed

(

)

Returns the transposed matrix.

getTurnAndTilt()

Vector getTurnAndTilt	(	Integer	primary,
		Integer	secondary
	)

Returns the X, Y, Z rotations around the fixed frame to match the forward direction. Primary and secondary specifies the preferred rotations and must be different.

Parameters

primary	The primary coordinate (0, 1, or 2).
secondary	The secondary coordinate (0, 1, or 2).

getUp()

Vector getUp

(

)

Returns the up vector.

getXRotation()

static Matrix getXRotation ( Number  angle )

static

Returns the matrix for the specified X-axis rotation. The matrix will rotate the vector and not the frame.

Parameters

angle

The rotation angle in radians.

getXYZRotation()

static Matrix getXYZRotation ( Vector  abc )

static

Returns the matrix for the specified X, Y, and Z rotations. The matrix will rotate the vector and not the frame. The order of the rotations are X, Y, and then Z.

Parameters

abc	The rotation XYZ angles in radians.

getYRotation()

static Matrix getYRotation ( Number  angle )

static

Returns the matrix for the specified Y-axis rotation. The matrix will rotate the vector and not the frame.

Parameters

angle

The rotation angle in radians.

getZRotation()

static Matrix getZRotation ( Number  angle )

static

Returns the matrix for the specified Z-axis rotation. The matrix will rotate the vector and not the frame.

Parameters

angle

The rotation angle in radians.

isIdentity()

Boolean isIdentity

(

)

Returns true if the matrix is the identity matrix.

isZero()

Boolean isZero

(

)

Returns true if the matrix is the zero matrix (i.e. all elements are set to 0).

multiply() [1/3]

Matrix multiply

(

Number

right

)

Returns the multiple of this matrix (left) and the specified value (right).

multiply() [2/3]

Matrix multiply

(

Matrix

right

)

Returns the multiple of this matrix (left) and the specified matrix (right).

multiply() [3/3]

Vector multiply

(

Vector

right

)

Returns the multiple of this matrix (left) and the specified vector (right).

negate()

negate

(

)

Negates this matrix.

normalize()

normalize

(

)

Normalizes the orientation.

rotateX()

rotateX

(

Number

angle

)

Rotates this matrix around the X-axis by the specified angle.

Parameters

angle

The rotation angle in radians.

rotateY()

rotateY

(

Number

angle

)

Rotates this matrix around the Y-axis by the specified angle.

Parameters

angle

The rotation angle in radians.

rotateZ()

rotateZ

(

Number

angle

)

Rotates this matrix around the Z-axis by the specified angle.

Parameters

angle

The rotation angle in radians.

setColumn()

setColumn	(	Integer	column,
		Vector	value
	)

Sets the specified column.

Parameters

column	The column [0; 2].
value	The desired column vector.

setElement()

setElement	(	Integer	row,
		Integer	column,
		Number	value
	)

Sets the value of the specified element.

Parameters

row	The row [0; 2].
column	The column [0; 2].
value	The desired value of the element.

setForward()

setForward

(

Vector

value

)

Sets the forward vector.

Parameters

value

The forward vector.

setRight()

setRight

(

Vector

value

)

Sets the right vector.

Parameters

value

The right vector.

setRow()

setRow	(	Integer	row,
		Vector	value
	)

Sets the specified row.

Parameters

row	The row [0; 2].
value	The desired row vector.

setUp()

setUp

(

Vector

value

)

Sets the up vector.

Parameters

value

The up vector.

subtract()

subtract

(

Matrix

right

)

Subtracts the specified matrix from this matrix.

sum()

static Matrix sum ( Matrix  left, Matrix  right  )

static

Returns the difference between the specified matrices.

toString()

String toString

(

)

Converts the matrix to a string (e.g. [[1, 2, 3], [4, 5, 6], [7, 8, 9]]).

transpose()

transpose

(

)

Transposed this matrix.