DD::Image::Matrix3 Class Reference

A 3x3 transformation matrix. More...

Public Member Functions
float *	operator[] (int i)
const float *	operator[] (int i) const
const float *	array () const
	Matrix3 (float a, float b, float c, float d, float e, float f, float g, float h, float i)
void	set (float a, float b, float c, float d, float e, float f, float g, float h, float i)
Matrix3	operator* (const Matrix3 &) const
Matrix3 &	operator*= (const Matrix3 &)
Matrix3	operator+ (const Matrix3 &) const
Matrix3 &	operator+= (const Matrix3 &)
Matrix3	operator- (const Matrix3 &) const
Matrix3 &	operator-= (const Matrix3 &)
Matrix3	operator* (float) const
Matrix3 &	operator*= (float)
Matrix3	operator/ (float d) const
Matrix3 &	operator/= (float d)
Vector3	operator* (const Vector3 &v) const
Vector3	transform (const Vector3 &v) const
bool	operator!= (const Matrix3 &b) const
bool	operator== (const Matrix3 &b) const
float	determinant () const
Matrix3	inverse (float det) const
Matrix3	inverse () const
void	makeIdentity ()
void	scaling (float)
void	scaling (float, float, float)
void	scaling (const Vector3 &v)
void	rotationX (float)
void	rotationY (float)
void	rotationZ (float)
void	rotation (float a)
void	rotation (float a, float x, float y, float z)
void	rotation (float a, const Vector3 &v)
void	scale (float)
void	scale (float, float, float=1)
void	scale (const Vector3 &v)
void	rotateX (float)
void	rotateY (float)
void	rotateZ (float)
void	rotate (float a)
void	rotate (float a, float x, float y, float z)
void	rotate (float a, const Vector3 &v)
void	skew (float a)
void	append (Hash &) const

Static Public Member Functions
static const Matrix3 &	identity ()

Public Attributes
float	a00
float	a10
float	a20
float	a01
float	a11
float	a21
float	a02
float	a12
float	a22

Static Public Attributes
static const Matrix3	_identity

Friends
std::ostream &	operator<< (std::ostream &o, const Matrix3 &matrix)

Detailed Description

A 3x3 transformation matrix.

You multiply a Vector3 by one of these to go from one 3D space to another. This cannot represent 3D translations or perspective, use a Matrix4 for that. This is also often used to transform color spaces.

The data is stored packed together in OpenGL order, which is transposed from the way used in most modern graphics literature. This affects how the array() and [] operator work, these are all equal:

• matrix.a12
• matrix[2][1]
• matrix.array()[1+3*2]

Constructor & Destructor Documentation

DD::Image::Matrix3::Matrix3 ( float  a, float  b, float  c, float  d, float  e, float  f, float  g, float  h, float  i  )

inline

Initialize with a00=a, a01=b, a02=c, etc, ie the arguments are given as rows.

Member Function Documentation

float * DD::Image::Matrix3::operator[] ( int  i )

inline

Return a pointer to the column number i.

const float * DD::Image::Matrix3::operator[] ( int  i ) const

inline

Return a pointer to the column number i.

const float * DD::Image::Matrix3::array ( ) const

inline

Return a pointer to a00. This array is in the correct order to send it to OpenGL.

Matrix3 Matrix3::operator*

(

const Matrix3 &

B

)

const

Does matrix multiplication.

Matrix3 & Matrix3::operator*=

(

const Matrix3 &

B

)

Does matrix multiplication.

Matrix3 Matrix3::operator+

(

const Matrix3 &

B

)

const

Add each matching locations.

Matrix3 & Matrix3::operator+=

(

const Matrix3 &

B

)

Add each matching locations.

Matrix3 Matrix3::operator-

(

const Matrix3 &

B

)

const

Subtract each matching locations.

Matrix3 & Matrix3::operator-=

(

const Matrix3 &

B

)

Subtract each matching locations.

Matrix3 Matrix3::operator*

(

float

f

)

const

Multiplies every location by f.

Matrix3 & Matrix3::operator*=

(

float

f

)

Multiplies every location by f.

Vector3 DD::Image::Matrix3::operator* ( const Vector3 &  v ) const

inline

Returns the transformation of v by this matrix.

Vector3 DD::Image::Matrix3::transform ( const Vector3 &  v ) const

inline

Same as this*v

bool DD::Image::Matrix3::operator!= ( const Matrix3 &  b ) const

inline

Returns true if any of all 9 locations are different.

bool DD::Image::Matrix3::operator== ( const Matrix3 &  b ) const

inline

Returns true if all 9 locations are equal.

float DD::Image::Matrix3::determinant ( void  ) const

inline

Return the determinant. Non-zero means the transformation can be inverted.

Matrix3 Matrix3::inverse

(

float

det

)

const

Returns the inverse of this matrix where det is the precomputed determinant. This is useful if you already computed the determinant in order to see if you can invert the matrix.

Matrix3 DD::Image::Matrix3::inverse ( ) const

inline

Returns the inverse of this matrix. If determinant() is zero this will replace all the items with +/- infinity or zero.

References inverse().

Referenced by inverse().

void DD::Image::Matrix3::makeIdentity ( )

inline

Replace the contents with the identity.

void Matrix3::scaling

(

float

x

)

Replace the contents with a uniform scale by x.

void Matrix3::scaling	(	float	x,
		float	y,
		float	z
	)

Replace the contents with a scale by x,y,z.

void DD::Image::Matrix3::scaling ( const Vector3 &  v )

inline

Replace the contents with a scale by the x,y,z of the vector.

References scaling().

Referenced by scaling().

void Matrix3::rotationX

(

float

angle

)

Replace the contents with a rotation by angle (in radians) around the X axis.

Referenced by rotateX().

void Matrix3::rotationY

(

float

angle

)

Replace the contents with a rotation by angle (in radians) around the Y axis.

Referenced by rotateY().

void Matrix3::rotationZ

(

float

angle

)

Replace the contents with a rotation by angle (in radians) around the Z axis.

Referenced by rotateZ().

void DD::Image::Matrix3::rotation ( float  angle )

inline

Same as rotationZ(angle).

Referenced by rotate().

void Matrix3::rotation	(	float	a,
		float	x,
		float	y,
		float	z
	)

Replace the contents with a rotation by angle (in radians) around the vector x,y,z.

void DD::Image::Matrix3::rotation ( float  angle, const Vector3 &  v  )

inline

Replace the contents with a rotation by angle (in radians) around the vector.

References rotation().

Referenced by rotation().

void Matrix3::scale

(

float

s

)

Scale the transformation by s.

void Matrix3::scale	(	float	x,
		float	y,
		float	z = 1
	)

Scale the transformation by x,y,z.

void DD::Image::Matrix3::scale ( const Vector3 &  v )

inline

Scale the transformation by the x,y,z of the vector.

References scale().

Referenced by scale().

void Matrix3::rotateX

(

float

a

)

Rotate the transformation by a radians about the X axis.

References rotationX().

void Matrix3::rotateY

(

float

a

)

Rotate the transformation by a radians about the Y axis.

References rotationY().

void Matrix3::rotateZ

(

float

a

)

Rotate the transformation by a radians about the Z axis.

References rotationZ().

void DD::Image::Matrix3::rotate ( float  a )

inline

Same as rotateZ(a).

void Matrix3::rotate	(	float	a,
		float	x,
		float	y,
		float	z
	)

Rotate the transformation by a radians about the vector x,y,z.

References rotation().

void DD::Image::Matrix3::rotate ( float  a, const Vector3 &  v  )

inline

Rotate the transformation by a radians about the vector.

References rotate().

Referenced by rotate().

void Matrix3::skew

(

float

a

)

Skew the transformation by a (X positions have a*Y added to them).

void Matrix3::append

(

Hash &

hash

)

const

Add this to the Hash object.

Friends And Related Function Documentation

std::ostream& operator<< ( std::ostream &  o, const Matrix3 &  matrix  )

friend

Writes it in nuke/tcl notation, with nested curly braces