3x3 floating point matrices

---

Definition and operations for 3x3 matrices.

Functions
Eina_Matrix_Type	eina_matrix3_type_get (const Eina_Matrix3 *m)
	Returns the type of the given floating point matrix.
void	eina_matrix3_values_set (Eina_Matrix3 *m, double xx, double xy, double xz, double yx, double yy, double yz, double zx, double zy, double zz)
	Sets the values of the coefficients of the given floating point matrix.
void	eina_matrix3_values_get (const Eina_Matrix3 *m, double *xx, double *xy, double *xz, double *yx, double *yy, double *yz, double *zx, double *zy, double *zz)
	Gets the values of the coefficients of the given floating point matrix.
void	eina_matrix3_fixed_values_get (const Eina_Matrix3 *m, Eina_F16p16 *xx, Eina_F16p16 *xy, Eina_F16p16 *xz, Eina_F16p16 *yx, Eina_F16p16 *yy, Eina_F16p16 *yz, Eina_F16p16 *zx, Eina_F16p16 *zy, Eina_F16p16 *zz)
	Gets the values of the coefficients of the given fixed point matrix.
void	eina_matrix3_matrix3_f16p16_to (const Eina_Matrix3 *m, Eina_Matrix3_F16p16 *fm)
	Transforms the given floating point matrix to the given fixed point matrix.
Eina_Bool	eina_matrix3_equal (const Eina_Matrix3 *m1, const Eina_Matrix3 *m2)
	Checks whether the two matrices are equivalent.
void	eina_matrix3_compose (const Eina_Matrix3 *m1, const Eina_Matrix3 *m2, Eina_Matrix3 *dst)
	Sets dst as the matrix multiplication (composition) of two matrices.
void	eina_matrix3_translate (Eina_Matrix3 *t, double tx, double ty)
	Sets the matrix values for a translation operation.
void	eina_matrix3_scale (Eina_Matrix3 *t, double sx, double sy)
	Sets the matrix values for a scaling operation.
void	eina_matrix3_rotate (Eina_Matrix3 *t, double rad)
	Sets the matrix values for a rotation operation.
void	eina_matrix3_identity (Eina_Matrix3 *t)
	Sets the given floating point matrix to the identity matrix.
double	eina_matrix3_determinant (const Eina_Matrix3 *m)
	Calculates the determinant of the given matrix.
void	eina_matrix3_divide (Eina_Matrix3 *m, double scalar)
	Divides the given matrix by a scalar number.
void	eina_matrix3_inverse (const Eina_Matrix3 *m, Eina_Matrix3 *m2)
	Computes the inverse of the given matrix.
void	eina_matrix3_transpose (const Eina_Matrix3 *m, Eina_Matrix3 *a)
	Computes the transpose of the given matrix.
void	eina_matrix3_cofactor (const Eina_Matrix3 *m, Eina_Matrix3 *a)
	Computes the cofactor of the given matrix.
void	eina_matrix3_adjoint (const Eina_Matrix3 *m, Eina_Matrix3 *a)
	Computes the adjoint of the given matrix.
void	eina_matrix3_point_transform (const Eina_Matrix3 *m, double x, double y, double *xr, double *yr)
	Computes the transform of a 2D point using the given matrix.
void	eina_matrix3_rectangle_transform (const Eina_Matrix3 *m, const Eina_Rectangle *r, const Eina_Quad *q)
	Computes the transformation of a rectangle using the given matrix.
Eina_Bool	eina_matrix3_quad_quad_map (Eina_Matrix3 *m, const Eina_Quad *src, const Eina_Quad *dst)
	Creates a projective matrix that maps a quadrangle to a quadrangle.
Eina_Bool	eina_matrix3_square_quad_map (Eina_Matrix3 *m, const Eina_Quad *q)
	Creates a matrix for unit-square to quad mapping.
Eina_Bool	eina_matrix3_quad_square_map (Eina_Matrix3 *m, const Eina_Quad *q)
	Creates a matrix for mapping squares to match quad.
void	eina_matrix3_array_set (Eina_Matrix3 *m, const double *v)
	Sets matrix values using an array.
void	eina_matrix3_copy (Eina_Matrix3 *dst, const Eina_Matrix3 *src)
	Copies a matrix.
void	eina_matrix3_multiply (Eina_Matrix3 *out, const Eina_Matrix3 *mat_a, const Eina_Matrix3 *mat_b)
	Multiplies two matrices.
void	eina_matrix3_multiply_copy (Eina_Matrix3 *out, const Eina_Matrix3 *mat_a, const Eina_Matrix3 *mat_b)
	Multiplies two matrices without overwriting them.
void	eina_matrix3_scale_transform_set (Eina_Matrix3 *out, double s_x, double s_y)
	Sets the scale parameters (XX, YY) of a matrix.
void	eina_matrix3_position_transform_set (Eina_Matrix3 *out, const double p_x, const double p_y)
	Sets the positional parameters (XZ, YZ) of a matrix.
void	eina_normal3_matrix_get (Eina_Matrix3 *out, const Eina_Matrix4 *m)
	Sets normal of the given matrix.
void	eina_matrix3_matrix4_to (Eina_Matrix4 *m4, const Eina_Matrix3 *m3)
	Converts an Eina_Matrix3 into an Eina_Matrix4.
Typedefs
typedef struct _Eina_Matrix3	Eina_Matrix3
Defines
#define	EINA_MATRIX3_FORMAT   "g %g %g | %g %g %g | %g %g %g"
#define	EINA_MATRIX3_ARGS(m)

---

Define Documentation

#define EINA_MATRIX3_ARGS

(

m

)

Value:

(m)->xx, (m)->xy, (m)->xz, \
    (m)->yx, (m)->yy, (m)->yz,                          \
    (m)->zx, (m)->zy, (m)->zz

Helper macro for printf formatting arg

#define EINA_MATRIX3_FORMAT   "g %g %g | %g %g %g | %g %g %g"

Helper macro for printf formatting

---

Typedef Documentation

Eina_Matrix3

A 3x3 floating point matrix.

---

Function Documentation

void eina_matrix3_adjoint	(	const Eina_Matrix3 *	m,
		Eina_Matrix3 *	a
	)

Computes the adjoint of the given matrix.

Parameters:

[in]	m	The matrix to be adjointed.
[out]	a	The adjoint matrix.

This function finds the adjoint of the matrix m and stores the result in a. No check is done on m or a. The adjoint of a matrix3 is effectively the transpose of its cofactor.

Since (EFL) :

1.14

Since :

3.0f(2.3.1)

void eina_matrix3_array_set	(	Eina_Matrix3 *	m,
		const double *	v
	)

Sets matrix values using an array.

Parameters:

[out]	m	The result matrix.
[in]	v	The array[9] of values.

Uses the first 9 elements in the given C array v to set the values in the matrix m. The values will be set in the order of the elements in the Eina_Matrix3 structure.

Since (EFL) :

1.17

Since :

3.0f(2.3.1)

void eina_matrix3_cofactor	(	const Eina_Matrix3 *	m,
		Eina_Matrix3 *	a
	)

Computes the cofactor of the given matrix.

Parameters:

[in]	m	The source matrix.
[out]	a	The cofactored matrix.

This function cofactors the matrix m and stores the result in a. No check is done on m or a. The cofactor of a matrix3 at row i, column j is computed by taking the determinant of the submatrix formed by deleting the i-th row and j-th column, and then multiplying by (-1)^(i+j).

Since (EFL) :

1.14

Since :

3.0f(2.3.1)

void eina_matrix3_compose	(	const Eina_Matrix3 *	m1,
		const Eina_Matrix3 *	m2,
		Eina_Matrix3 *	dst
	)

Sets dst as the matrix multiplication (composition) of two matrices.

Parameters:

[in]	m1	The first matrix. Must be non-NULL.
[in]	m2	The second matrix. Must be non-NULL.
[out]	dst	The results matrix.

In matrix multiplication, AB, the resultant matrix is created from the rows of A multiplied against the columns of B and summed. This is not commutative; i.e. AB != BA, so the ordering of arguments m1 and m2 matters.

Since (EFL) :

1.14

Since :

3.0f(2.3.1)

void eina_matrix3_copy	(	Eina_Matrix3 *	dst,
		const Eina_Matrix3 *	src
	)

Copies a matrix.

Parameters:

[out]	dst	Copy of the matrix.
[in]	src	The matrix to copy.

Since (EFL) :

1.16

Since :

3.0f(2.3.1)

double eina_matrix3_determinant

(

const Eina_Matrix3 *

m

)

Calculates the determinant of the given matrix.

Parameters:

[in]

m

The matrix.

Returns:

The determinant.

This function returns the determinant of the matrix m. No check is done on m.

Since (EFL) :

1.14

Since :

3.0f(2.3.1)

void eina_matrix3_divide	(	Eina_Matrix3 *	m,
		double	scalar
	)

Divides the given matrix by a scalar number.

Parameters:

[in,out]	m	The matrix.
[in]	scalar	The scalar number.

This function divides the matrix m by scalar. No check is done on m.

Since (EFL) :

1.14

Since :

3.0f(2.3.1)

Eina_Bool eina_matrix3_equal	(	const Eina_Matrix3 *	m1,
		const Eina_Matrix3 *	m2
	)

Checks whether the two matrices are equivalent.

Parameters:

[in]	m1	The first matrix.
[in]	m2	The second matrix.

Returns:

EINA_TRUE if the two matrices are equal, EINA_FALSE otherwise.

This function returns EINA_TRUE if the matrices m1 and m2 are equal, EINA_FALSE otherwise. No check is done on the matrices.

Since (EFL) :

1.14

Since :

3.0f(2.3.1)

void eina_matrix3_fixed_values_get	(	const Eina_Matrix3 *	m,
		Eina_F16p16 *	xx,
		Eina_F16p16 *	xy,
		Eina_F16p16 *	xz,
		Eina_F16p16 *	yx,
		Eina_F16p16 *	yy,
		Eina_F16p16 *	yz,
		Eina_F16p16 *	zx,
		Eina_F16p16 *	zy,
		Eina_F16p16 *	zz
	)

Gets the values of the coefficients of the given fixed point matrix.

Parameters:

[in]	m	The fixed point matrix.
[out]	xx	The first coefficient value.
[out]	xy	The second coefficient value.
[out]	xz	The third coefficient value.
[out]	yx	The fourth coefficient value.
[out]	yy	The fifth coefficient value.
[out]	yz	The sixth coefficient value.
[out]	zx	The seventh coefficient value.
[out]	zy	The eighth coefficient value.
[out]	zz	The nine-th coefficient value.

This function gets the values of the coefficients of the matrix m. No check is done on m.

See also:

eina_matrix3_values_set()

Since (EFL) :

1.14

Since :

3.0f(2.3.1)

void eina_matrix3_identity

(

Eina_Matrix3 *

t

)

Sets the given floating point matrix to the identity matrix.

Parameters:

[out]

m

The matrix to set to identity.

This function sets m to the identity matrix. No check is done on m.

Since (EFL) :

1.14

Since :

3.0f(2.3.1)

void eina_matrix3_inverse	(	const Eina_Matrix3 *	m,
		Eina_Matrix3 *	m2
	)

Computes the inverse of the given matrix.

Parameters:

[in]	m	The source matrix.
[out]	m2	The inverse matrix.

This function inverts the matrix m and stores the result in m2. No check is done on m or m2. If m cannot be inverted, then m2 is set to the identity matrix.

Since (EFL) :

1.14

Since :

3.0f(2.3.1)

void eina_matrix3_matrix3_f16p16_to	(	const Eina_Matrix3 *	m,
		Eina_Matrix3_F16p16 *	fm
	)

Transforms the given floating point matrix to the given fixed point matrix.

Parameters:

[in]	m	The floating point matrix.
[out]	fm	The fixed point matrix.

This function transforms the floating point matrix m to a fixed point matrix and stores the coefficients into the fixed point matrix fm.

Since (EFL) :

1.14

Since :

3.0f(2.3.1)

void eina_matrix3_matrix4_to	(	Eina_Matrix4 *	m4,
		const Eina_Matrix3 *	m3
	)

Converts an Eina_Matrix3 into an Eina_Matrix4.

Parameters:

[out]	m3	The destination Eina_Matrix3.
[in]	m4	The source Eina_Matrix4.

Since (EFL) :

1.15

Since :

3.0f(2.3.1)

void eina_matrix3_multiply	(	Eina_Matrix3 *	out,
		const Eina_Matrix3 *	mat_a,
		const Eina_Matrix3 *	mat_b
	)

Multiplies two matrices.

Parameters:

[out]	out	The resulting matrix.
[in]	mat_a	The first member of the multiplication.
[in]	mat_b	The second member of the multiplication.

out must not point to the same structure as mat_a or mat_b, else the calculation results will be incorrect. Use eina_matrix3_multiply_copy() instead in this case.

Since (EFL) :

1.17

Since :

3.0f(2.3.1)

void eina_matrix3_multiply_copy	(	Eina_Matrix3 *	out,
		const Eina_Matrix3 *	mat_a,
		const Eina_Matrix3 *	mat_b
	)

Multiplies two matrices without overwriting them.

Parameters:

[out]	out	The resulting matrix.
[in]	mat_a	The first member of the multiplication.
[in]	mat_b	The second member of the multiplication.

Safely multiplies mat_a and mat_b by checking if the out parameter points to either of them, and if so uses a temporary matrix for the intermediary calculations.

Since (EFL) :

1.17

Since :

3.0f(2.3.1)

void eina_matrix3_point_transform	(	const Eina_Matrix3 *	m,
		double	x,
		double	y,
		double *	xr,
		double *	yr
	)

Computes the transform of a 2D point using the given matrix.

Parameters:

[in]	m	The transformation matrix to apply.
[in]	x	The x point to be transformed.
[in]	y	The y point to be transformed.
[out]	xr	The transformed x point.
[out]	yr	The transformed y point.

Applies the transformation matrix m to the point (x,y), and stores the result in (*xr,*yr). No check is done on m; xr and yr must point to valid memory. A fast-path is included for if the zx and zy components of the matrix are zero.

Since (EFL) :

1.14

Since :

3.0f(2.3.1)

void eina_matrix3_position_transform_set	(	Eina_Matrix3 *	out,
		const double	p_x,
		const double	p_y
	)

Sets the positional parameters (XZ, YZ) of a matrix.

Parameters:

[out]	out	The resulting matrix.
[in]	p_x	The position value for x.
[in]	p_y	The position value for y.

Sets only the XZ and YZ components of the matrix, leaving the rest of the matrix as it was.

Since (EFL) :

1.17

Since :

3.0f(2.3.1)

Eina_Bool eina_matrix3_quad_quad_map	(	Eina_Matrix3 *	m,
		const Eina_Quad *	src,
		const Eina_Quad *	dst
	)

Creates a projective matrix that maps a quadrangle to a quadrangle.

Parameters:

[out]	m	The transformation matrix to create.
[in]	src	The source quadrangle.
[in]	dst	The destination quadrangle.

Returns:

EINA_TRUE if matrix could be successfully created, EINA_FALSE otherwise.

Calculates a matrix m that can be used to transform from an arbitrary source quadrangle src to another arbitrary quadrangle dst.

Since :

3.0f(2.3.1)

Eina_Bool eina_matrix3_quad_square_map	(	Eina_Matrix3 *	m,
		const Eina_Quad *	q
	)

Creates a matrix for mapping squares to match quad.

Parameters:

[out]	m	The transformation matrix to create.
[in]	q	The source quadrangle.

Returns:

EINA_FALSE on successful transform creation, EINA_FALSE otherwise.

Calculates a matrix m that can be used to transform a square to fit a given quadrangle. The created matrix will always have its zz element equal to 1.0. The m matrix and q quad must be valid memory.

Since (EFL) :

1.14

Since :

3.0f(2.3.1)

void eina_matrix3_rectangle_transform	(	const Eina_Matrix3 *	m,
		const Eina_Rectangle *	r,
		const Eina_Quad *	q
	)

Computes the transformation of a rectangle using the given matrix.

Parameters:

[in]	m	The transformation matrix to apply.
[in]	r	The rectangle to be transformed.
[out]	q	The resultant transformed points.

Performs a point transformation of each corner of the rectangle r, and stores the result in the quadrangle q. No checks are done on the inputs, and q must point to valid memory.

Since (EFL) :

1.14

Since :

3.0f(2.3.1)

void eina_matrix3_rotate	(	Eina_Matrix3 *	t,
		double	rad
	)

Sets the matrix values for a rotation operation.

Parameters:

[out]	t	The matrix.
[in]	rad	The number of radians to rotate.

Since (EFL) :

1.14

Since :

3.0f(2.3.1)

void eina_matrix3_scale	(	Eina_Matrix3 *	t,
		double	sx,
		double	sy
	)

Sets the matrix values for a scaling operation.

Parameters:

[out]	m	The matrix.
[in]	sx	The X coordinate scaling factor.
[in]	sy	The Y coordinate scaling factor.

Since (EFL) :

1.14

Since :

3.0f(2.3.1)

void eina_matrix3_scale_transform_set	(	Eina_Matrix3 *	out,
		double	s_x,
		double	s_y
	)

Sets the scale parameters (XX, YY) of a matrix.

Parameters:

[out]	out	The resulting matrix.
[in]	s_x	The scale value for x.
[in]	s_y	The scale value for y.

Sets only the XX and YY components of the matrix, leaving the rest of the matrix as it was.

Since (EFL) :

1.17

Since :

3.0f(2.3.1)

Eina_Bool eina_matrix3_square_quad_map	(	Eina_Matrix3 *	m,
		const Eina_Quad *	q
	)

Creates a matrix for unit-square to quad mapping.

Parameters:

[out]	m	The transformation matrix to create.
[in]	q	The source quadrangle.

Returns:

EINA_TRUE if matrix could be successfully created, EINA_FALSE otherwise.

Calculates a matrix m that can be used to transform an arbitrary quadrangle q into a square. If q is a parallelogram, then a fast path affine transformation is used, otherwise it computes the matrix using a full projective transformation operation. No other checks are done on m or q.

Since (EFL) :

1.14

Since :

3.0f(2.3.1)

void eina_matrix3_translate	(	Eina_Matrix3 *	t,
		double	tx,
		double	ty
	)

Sets the matrix values for a translation operation.

Parameters:

[out]	m	The matrix.
[in]	tx	The X coordinate translation.
[in]	ty	The Y coordinate translation.

Since (EFL) :

1.14

Since :

3.0f(2.3.1)

void eina_matrix3_transpose	(	const Eina_Matrix3 *	m,
		Eina_Matrix3 *	a
	)

Computes the transpose of the given matrix.

Parameters:

[in]	m	The source matrix.
[out]	a	The transposed matrix.

This function transposes the matrix m and stores the result in a. No check is done on m or a. The transpose of a matrix essentially flips a matrix over its diagonal.

Since (EFL) :

1.14

Since :

3.0f(2.3.1)

Eina_Matrix_Type eina_matrix3_type_get

(

const Eina_Matrix3 *

m

)

Returns the type of the given floating point matrix.

Parameters:

[in]

m

The floating point matrix.

Returns:

The type of the matrix.

This function returns the type of the matrix m. No check is done on m.

Since (EFL) :

1.14

Since :

3.0f(2.3.1)

void eina_matrix3_values_get	(	const Eina_Matrix3 *	m,
		double *	xx,
		double *	xy,
		double *	xz,
		double *	yx,
		double *	yy,
		double *	yz,
		double *	zx,
		double *	zy,
		double *	zz
	)

Gets the values of the coefficients of the given floating point matrix.

Parameters:

[in]	m	The floating point matrix.
[out]	xx	The first coefficient value.
[out]	xy	The second coefficient value.
[out]	xz	The third coefficient value.
[out]	yx	The fourth coefficient value.
[out]	yy	The fifth coefficient value.
[out]	yz	The sixth coefficient value.
[out]	zx	The seventh coefficient value.
[out]	zy	The eighth coefficient value.
[out]	zz	The ninth coefficient value.

This function gets the values of the coefficients of the matrix m. No check is done on m.

See also:

eina_matrix3_values_set()

Since (EFL) :

1.14

Since :

3.0f(2.3.1)

void eina_matrix3_values_set	(	Eina_Matrix3 *	m,
		double	xx,
		double	xy,
		double	xz,
		double	yx,
		double	yy,
		double	yz,
		double	zx,
		double	zy,
		double	zz
	)

Sets the values of the coefficients of the given floating point matrix.

Parameters:

[out]	m	The floating point matrix.
[in]	xx	The first coefficient value.
[in]	xy	The second coefficient value.
[in]	xz	The third coefficient value.
[in]	yx	The fourth coefficient value.
[in]	yy	The fifth coefficient value.
[in]	yz	The sixth coefficient value.
[in]	zx	The seventh coefficient value.
[in]	zy	The eighth coefficient value.
[in]	zz	The ninth coefficient value.

This function sets the values of the coefficients of the matrix m. No check is done on m.

See also:

eina_matrix3_values_get()

Since (EFL) :

1.14

Since :

3.0f(2.3.1)

void eina_normal3_matrix_get	(	Eina_Matrix3 *	out,
		const Eina_Matrix4 *	m
	)

Sets normal of the given matrix.

Parameters:

[out]	out	The resulting matrix.
[in]	m	The matrix.

Since (EFL) :

1.17

Since :

3.0f(2.3.1)