m_matrix.h File Reference

Detailed Description

Defines basic structures for matrix-handling.

Data Structures

struct GLmatrix

Matrix type to represent 4x4 transformation matrices. More...

Related functions that don't actually operate on GLmatrix structs

#define TRANSFORM_POINT(Q, M, P)

#define TRANSFORM_POINT3(Q, M, P)

#define TRANSFORM_NORMAL(TO, N, MAT)

#define TRANSFORM_DIRECTION(TO, DIR, MAT)

Transform a direction by a matrix.

void _math_transposef (GLfloat to[16], const GLfloat from[16])

Transpose a GLfloat matrix.

void _math_transposed (GLdouble to[16], const GLdouble from[16])

Transpose a GLdouble matrix.

void _math_transposefd (GLfloat to[16], const GLdouble from[16])

Transpose a GLdouble matrix and convert to GLfloat.

void _mesa_transform_vector (GLfloat u[4], const GLfloat v[4], const GLfloat m[16])

Transform a 4-element row vector (1x4 matrix) by a 4x4 matrix.

Defines

Symbolic names to some of the entries in the matrix

These are handy for the viewport mapping, which is expressed as a matrix.

#define MAT_SX   0

#define MAT_SY   5

#define MAT_SZ   10

#define MAT_TX   12

#define MAT_TY   13

#define MAT_TZ   14

Enumerations

enum GLmatrixtype {
  MATRIX_GENERAL, MATRIX_IDENTITY, MATRIX_3D_NO_ROT, MATRIX_PERSPECTIVE,
  MATRIX_2D, MATRIX_2D_NO_ROT, MATRIX_3D
}

Different kinds of 4x4 transformation matrices. More...

Functions

void _math_matrix_ctr (GLmatrix *m)

Matrix constructor.

void _math_matrix_dtr (GLmatrix *m)

Matrix destructor.

void _math_matrix_alloc_inv (GLmatrix *m)

Allocate a matrix inverse.

void _math_matrix_mul_matrix (GLmatrix *dest, const GLmatrix *a, const GLmatrix *b)

Matrix multiplication.

void _math_matrix_mul_floats (GLmatrix *dest, const GLfloat *b)

Matrix multiplication.

void _math_matrix_loadf (GLmatrix *mat, const GLfloat *m)

Loads a matrix array into GLmatrix.

void _math_matrix_translate (GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z)

Multiply a matrix with a translation matrix.

void _math_matrix_rotate (GLmatrix *m, GLfloat angle, GLfloat x, GLfloat y, GLfloat z)

Generate a 4x4 transformation matrix from glRotate parameters, and post-multiply the input matrix by it.

void _math_matrix_scale (GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z)

Multiply a matrix with a general scaling matrix.

void _math_matrix_ortho (GLmatrix *mat, GLfloat left, GLfloat right, GLfloat bottom, GLfloat top, GLfloat nearval, GLfloat farval)

Apply an orthographic projection matrix.

void _math_matrix_frustum (GLmatrix *mat, GLfloat left, GLfloat right, GLfloat bottom, GLfloat top, GLfloat nearval, GLfloat farval)

Apply a perspective projection matrix.

void _math_matrix_viewport (GLmatrix *m, GLint x, GLint y, GLint width, GLint height, GLfloat zNear, GLfloat zFar, GLfloat depthMax)

Set matrix to do viewport and depthrange mapping.

void _math_matrix_set_identity (GLmatrix *dest)

Set a matrix to the identity matrix.

void _math_matrix_copy (GLmatrix *to, const GLmatrix *from)

Copy a matrix.

void _math_matrix_analyse (GLmatrix *mat)

Analyze and update a matrix.

void _math_matrix_print (const GLmatrix *m)

Dumps the contents of a GLmatrix structure.

GLboolean _math_matrix_is_length_preserving (const GLmatrix *m)

Test if the given matrix preserves vector lengths.

GLboolean _math_matrix_has_rotation (const GLmatrix *m)

Test if the given matrix does any rotation.

GLboolean _math_matrix_is_general_scale (const GLmatrix *m)

GLboolean _math_matrix_is_dirty (const GLmatrix *m)

Define Documentation

#define MAT_SX 0

#define MAT_SY 5

#define MAT_SZ 10

#define MAT_TX 12

#define MAT_TY 13

#define MAT_TZ 14

#define TRANSFORM_DIRECTION	(	TO,
		DIR,
		MAT	)

Value:

do {                                                            \
   TO[0] = DIR[0] * MAT[0] + DIR[1] * MAT[4] + DIR[2] * MAT[8]; \
   TO[1] = DIR[0] * MAT[1] + DIR[1] * MAT[5] + DIR[2] * MAT[9]; \
   TO[2] = DIR[0] * MAT[2] + DIR[1] * MAT[6] + DIR[2] * MAT[10];\
} while (0)

Transform a direction by a matrix.

#define TRANSFORM_NORMAL	(	TO,
		N,
		MAT	)

Value:

do {                                                            \
   TO[0] = N[0] * MAT[0] + N[1] * MAT[1] + N[2] * MAT[2];       \
   TO[1] = N[0] * MAT[4] + N[1] * MAT[5] + N[2] * MAT[6];       \
   TO[2] = N[0] * MAT[8] + N[1] * MAT[9] + N[2] * MAT[10];      \
} while (0)

#define TRANSFORM_POINT	(	Q,
		M,
		P	)

Value:

Q[0] = M[0] * P[0] + M[4] * P[1] + M[8] *  P[2] + M[12] * P[3]; \
   Q[1] = M[1] * P[0] + M[5] * P[1] + M[9] *  P[2] + M[13] * P[3];      \
   Q[2] = M[2] * P[0] + M[6] * P[1] + M[10] * P[2] + M[14] * P[3];      \
   Q[3] = M[3] * P[0] + M[7] * P[1] + M[11] * P[2] + M[15] * P[3];

#define TRANSFORM_POINT3	(	Q,
		M,
		P	)

Value:

Q[0] = M[0] * P[0] + M[4] * P[1] + M[8] *  P[2] + M[12];        \
   Q[1] = M[1] * P[0] + M[5] * P[1] + M[9] *  P[2] + M[13];     \
   Q[2] = M[2] * P[0] + M[6] * P[1] + M[10] * P[2] + M[14];     \
   Q[3] = M[3] * P[0] + M[7] * P[1] + M[11] * P[2] + M[15];

Enumeration Type Documentation

enum GLmatrixtype

Different kinds of 4x4 transformation matrices.

We use these to select specific optimized vertex transformation routines.

Enumerator:

MATRIX_GENERAL	general 4x4 matrix
MATRIX_IDENTITY	identity matrix
MATRIX_3D_NO_ROT	orthogonal projection and others. ..
MATRIX_PERSPECTIVE	perspective projection matrix
MATRIX_2D	2-D transformation
MATRIX_2D_NO_ROT	2-D scale & translate only
MATRIX_3D	3-D transformation

Function Documentation

void _math_matrix_alloc_inv ( GLmatrix * m )

Allocate a matrix inverse.

Parameters:

matrix.

Allocates the matrix inverse, GLmatrix::inv, and sets it to Identity.

void _math_matrix_analyse ( GLmatrix * mat )

Analyze and update a matrix.

Parameters:

mat

matrix.

If the matrix type is dirty then calls either analyse_from_scratch() or analyse_from_flags() to determine its type, according to whether the flags are dirty or not, respectively. If the matrix has an inverse and it's dirty then calls matrix_invert(). Finally clears the dirty flags.

void _math_matrix_copy	(	GLmatrix *	to,
		const GLmatrix *	from
	)

Copy a matrix.

Parameters:

	to	destination matrix.
	from	source matrix.

Copies all fields in GLmatrix, creating an inverse array if necessary.

void _math_matrix_ctr ( GLmatrix * m )

Matrix constructor.

Parameters:

matrix.

Initialize the GLmatrix fields.

void _math_matrix_dtr ( GLmatrix * m )

Matrix destructor.

Parameters:

matrix.

Frees the data in a GLmatrix.

void _math_matrix_frustum	(	GLmatrix *	mat,
		GLfloat	left,
		GLfloat	right,
		GLfloat	bottom,
		GLfloat	top,
		GLfloat	nearval,
		GLfloat	farval
	)

Apply a perspective projection matrix.

Parameters:

	mat	matrix to apply the projection.
	left	left clipping plane coordinate.
	right	right clipping plane coordinate.
	bottom	bottom clipping plane coordinate.
	top	top clipping plane coordinate.
	nearval	distance to the near clipping plane.
	farval	distance to the far clipping plane.

Creates the projection matrix and multiplies it with mat, marking the MAT_FLAG_PERSPECTIVE flag.

GLboolean _math_matrix_has_rotation ( const GLmatrix * m )

Test if the given matrix does any rotation.

(or perhaps if the upper-left 3x3 is non-identity)

GLboolean _math_matrix_is_dirty ( const GLmatrix * m )

GLboolean _math_matrix_is_general_scale ( const GLmatrix * m )

GLboolean _math_matrix_is_length_preserving ( const GLmatrix * m )

Test if the given matrix preserves vector lengths.

void _math_matrix_loadf	(	GLmatrix *	mat,
		const GLfloat *	m
	)

Loads a matrix array into GLmatrix.

Parameters:

	m	matrix array.
	mat	matrix.

Copies m into GLmatrix::m and marks the MAT_FLAG_GENERAL and MAT_DIRTY flags.

void _math_matrix_mul_floats	(	GLmatrix *	dest,
		const GLfloat *	m
	)

Matrix multiplication.

Parameters:

	dest	left and destination matrix.
	m	right matrix array.

Marks the matrix flags with general flag, and type and inverse dirty flags. Calls matmul4() for the multiplication.

void _math_matrix_mul_matrix	(	GLmatrix *	dest,
		const GLmatrix *	a,
		const GLmatrix *	b
	)

Matrix multiplication.

Parameters:

	dest	destination matrix.
	a	left matrix.
	b	right matrix.

Joins both flags and marks the type and inverse as dirty. Calls matmul34() if both matrices are 3D, or matmul4() otherwise.

void _math_matrix_ortho	(	GLmatrix *	mat,
		GLfloat	left,
		GLfloat	right,
		GLfloat	bottom,
		GLfloat	top,
		GLfloat	nearval,
		GLfloat	farval
	)

Apply an orthographic projection matrix.

Parameters:

	mat	matrix to apply the projection.
	left	left clipping plane coordinate.
	right	right clipping plane coordinate.
	bottom	bottom clipping plane coordinate.
	top	top clipping plane coordinate.
	nearval	distance to the near clipping plane.
	farval	distance to the far clipping plane.

Creates the projection matrix and multiplies it with mat, marking the MAT_FLAG_GENERAL_SCALE and MAT_FLAG_TRANSLATION flags.

void _math_matrix_print ( const GLmatrix * m )

Dumps the contents of a GLmatrix structure.

Parameters:

pointer to the GLmatrix structure.

void _math_matrix_rotate	(	GLmatrix *	mat,
		GLfloat	angle,
		GLfloat	x,
		GLfloat	y,
		GLfloat	z
	)

Generate a 4x4 transformation matrix from glRotate parameters, and post-multiply the input matrix by it.

Author:: This function was contributed by Erich Boleyn (erich@uruk.org). Optimizations contributed by Rudolf Opalla (rudi@khm.de).

void _math_matrix_scale	(	GLmatrix *	mat,
		GLfloat	x,
		GLfloat	y,
		GLfloat	z
	)

Multiply a matrix with a general scaling matrix.

Parameters:

	mat	matrix.
	x	x axis scale factor.
	y	y axis scale factor.
	z	z axis scale factor.

Multiplies in-place the elements of mat by the scale factors. Checks if the scales factors are roughly the same, marking the MAT_FLAG_UNIFORM_SCALE flag, or MAT_FLAG_GENERAL_SCALE. Marks the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE dirty flags.

void _math_matrix_set_identity ( GLmatrix * mat )

Set a matrix to the identity matrix.

Parameters:

mat

matrix.

Copies Identity into GLmatrix::m, and into GLmatrix::inv if not NULL. Sets the matrix type to identity, and clear the dirty flags.

void _math_matrix_translate	(	GLmatrix *	mat,
		GLfloat	x,
		GLfloat	y,
		GLfloat	z
	)

Multiply a matrix with a translation matrix.

Parameters:

	mat	matrix.
	x	translation vector x coordinate.
	y	translation vector y coordinate.
	z	translation vector z coordinate.

Adds the translation coordinates to the elements of mat in-place. Marks the MAT_FLAG_TRANSLATION flag, and the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE dirty flags.

void _math_matrix_viewport	(	GLmatrix *	m,
		GLint	x,
		GLint	y,
		GLint	width,
		GLint	height,
		GLfloat	zNear,
		GLfloat	zFar,
		GLfloat	depthMax
	)

Set matrix to do viewport and depthrange mapping.

Transforms Normalized Device Coords to window/Z values.

void _math_transposed	(	GLdouble	to[16],
		const GLdouble	from[16]
	)

Transpose a GLdouble matrix.

Parameters:

	to	destination array.
	from	source array.

void _math_transposef	(	GLfloat	to[16],
		const GLfloat	from[16]
	)

Transpose a GLfloat matrix.

Parameters:

	to	destination array.
	from	source array.

void _math_transposefd	(	GLfloat	to[16],
		const GLdouble	from[16]
	)

Transpose a GLdouble matrix and convert to GLfloat.

Parameters:

	to	destination array.
	from	source array.

void _mesa_transform_vector	(	GLfloat	u[4],
		const GLfloat	v[4],
		const GLfloat	m[16]
	)

Transform a 4-element row vector (1x4 matrix) by a 4x4 matrix.

This function is used for transforming clipping plane equations and spotlight directions. Mathematically, u = v * m. Input: v - input vector m - transformation matrix Output: u - transformed vector

Generated on Sun Sep 27 06:47:50 2009 for Mesa math module by

1.5.4


Data Structures
struct	GLmatrix
	Matrix type to represent 4x4 transformation matrices. More...
Related functions that don't actually operate on GLmatrix structs
#define	TRANSFORM_POINT(Q, M, P)
#define	TRANSFORM_POINT3(Q, M, P)
#define	TRANSFORM_NORMAL(TO, N, MAT)
#define	TRANSFORM_DIRECTION(TO, DIR, MAT)
	Transform a direction by a matrix.
void	_math_transposef (GLfloat to[16], const GLfloat from[16])
	Transpose a GLfloat matrix.
void	_math_transposed (GLdouble to[16], const GLdouble from[16])
	Transpose a GLdouble matrix.
void	_math_transposefd (GLfloat to[16], const GLdouble from[16])
	Transpose a GLdouble matrix and convert to GLfloat.
void	_mesa_transform_vector (GLfloat u[4], const GLfloat v[4], const GLfloat m[16])
	Transform a 4-element row vector (1x4 matrix) by a 4x4 matrix.
Defines
Symbolic names to some of the entries in the matrix
These are handy for the viewport mapping, which is expressed as a matrix.
#define	MAT_SX 0
#define	MAT_SY 5
#define	MAT_SZ 10
#define	MAT_TX 12
#define	MAT_TY 13
#define	MAT_TZ 14
Enumerations
enum	GLmatrixtype { MATRIX_GENERAL, MATRIX_IDENTITY, MATRIX_3D_NO_ROT, MATRIX_PERSPECTIVE, MATRIX_2D, MATRIX_2D_NO_ROT, MATRIX_3D }
	Different kinds of 4x4 transformation matrices. More...
Functions
void	_math_matrix_ctr (GLmatrix *m)
	Matrix constructor.
void	_math_matrix_dtr (GLmatrix *m)
	Matrix destructor.
void	_math_matrix_alloc_inv (GLmatrix *m)
	Allocate a matrix inverse.
void	_math_matrix_mul_matrix (GLmatrix dest, const GLmatrix a, const GLmatrix *b)
	Matrix multiplication.
void	_math_matrix_mul_floats (GLmatrix dest, const GLfloat b)
	Matrix multiplication.
void	_math_matrix_loadf (GLmatrix mat, const GLfloat m)
	Loads a matrix array into GLmatrix.
void	_math_matrix_translate (GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z)
	Multiply a matrix with a translation matrix.
void	_math_matrix_rotate (GLmatrix *m, GLfloat angle, GLfloat x, GLfloat y, GLfloat z)
	Generate a 4x4 transformation matrix from glRotate parameters, and post-multiply the input matrix by it.
void	_math_matrix_scale (GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z)
	Multiply a matrix with a general scaling matrix.
void	_math_matrix_ortho (GLmatrix *mat, GLfloat left, GLfloat right, GLfloat bottom, GLfloat top, GLfloat nearval, GLfloat farval)
	Apply an orthographic projection matrix.
void	_math_matrix_frustum (GLmatrix *mat, GLfloat left, GLfloat right, GLfloat bottom, GLfloat top, GLfloat nearval, GLfloat farval)
	Apply a perspective projection matrix.
void	_math_matrix_viewport (GLmatrix *m, GLint x, GLint y, GLint width, GLint height, GLfloat zNear, GLfloat zFar, GLfloat depthMax)
	Set matrix to do viewport and depthrange mapping.
void	_math_matrix_set_identity (GLmatrix *dest)
	Set a matrix to the identity matrix.
void	_math_matrix_copy (GLmatrix to, const GLmatrix from)
	Copy a matrix.
void	_math_matrix_analyse (GLmatrix *mat)
	Analyze and update a matrix.
void	_math_matrix_print (const GLmatrix *m)
	Dumps the contents of a GLmatrix structure.
GLboolean	_math_matrix_is_length_preserving (const GLmatrix *m)
	Test if the given matrix preserves vector lengths.
GLboolean	_math_matrix_has_rotation (const GLmatrix *m)
	Test if the given matrix does any rotation.
GLboolean	_math_matrix_is_general_scale (const GLmatrix *m)
GLboolean	_math_matrix_is_dirty (const GLmatrix *m)