Definition and operations for 3x3 matrices. More...
Data Structures | |
| struct | _Eina_Matrix3 |
| A 3x3 floating point matrix. More... | |
Macros | |
| #define | EINA_MATRIX3_FORMAT "g %g %g | %g %g %g | %g %g %g" |
| Helper macro for printf formatting. | |
| #define | EINA_MATRIX3_ARGS(m) |
| Helper macro for printf formatting arg. More... | |
Typedefs | |
| typedef struct _Eina_Matrix3 | Eina_Matrix3 |
| A 3x3 floating point matrix. | |
Functions | |
| EAPI Eina_Matrix_Type | eina_matrix3_type_get (const Eina_Matrix3 *m) |
| Returns the type of the given floating point matrix. More... | |
| EAPI 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. More... | |
| EAPI 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. More... | |
| EAPI 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. More... | |
| EAPI 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. More... | |
| EAPI Eina_Bool | eina_matrix3_equal (const Eina_Matrix3 *m1, const Eina_Matrix3 *m2) |
| Checks whether the two matrices are equivalent. More... | |
| EAPI 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. More... | |
| EAPI void | eina_matrix3_translate (Eina_Matrix3 *m, double tx, double ty) |
| Sets the matrix values for a translation operation. More... | |
| EAPI void | eina_matrix3_scale (Eina_Matrix3 *m, double sx, double sy) |
| Sets the matrix values for a scaling operation. More... | |
| EAPI void | eina_matrix3_rotate (Eina_Matrix3 *m, double rad) |
| Sets the matrix values for a rotation operation. More... | |
| EAPI void | eina_matrix3_identity (Eina_Matrix3 *m) |
| Sets the given floating point matrix to the identity matrix. More... | |
| EAPI double | eina_matrix3_determinant (const Eina_Matrix3 *m) |
| Calculates the determinant of the given matrix. More... | |
| EAPI void | eina_matrix3_divide (Eina_Matrix3 *m, double scalar) |
| Divides the given matrix by a scalar number. More... | |
| EAPI void | eina_matrix3_inverse (const Eina_Matrix3 *m, Eina_Matrix3 *m2) |
| Computes the inverse of the given matrix. More... | |
| EAPI void | eina_matrix3_transpose (const Eina_Matrix3 *m, Eina_Matrix3 *a) |
| Computes the transpose of the given matrix. More... | |
| EAPI void | eina_matrix3_cofactor (const Eina_Matrix3 *m, Eina_Matrix3 *a) |
| Computes the cofactor of the given matrix. More... | |
| EAPI void | eina_matrix3_adjoint (const Eina_Matrix3 *m, Eina_Matrix3 *a) |
| Computes the adjoint of the given matrix. More... | |
| EAPI 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. More... | |
| EAPI 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. More... | |
| EAPI 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. More... | |
| EAPI Eina_Bool | eina_matrix3_square_quad_map (Eina_Matrix3 *m, const Eina_Quad *q) |
| Creates a matrix for unit-square to quad mapping. More... | |
| EAPI Eina_Bool | eina_matrix3_quad_square_map (Eina_Matrix3 *m, const Eina_Quad *q) |
| Creates a matrix for mapping squares to match quad. More... | |
| EAPI void | eina_matrix3_array_set (Eina_Matrix3 *m, const double *v) |
| Sets matrix values using an array. More... | |
| EAPI void | eina_matrix3_copy (Eina_Matrix3 *dst, const Eina_Matrix3 *src) |
| Copies a matrix. More... | |
| EAPI void | eina_matrix3_multiply (Eina_Matrix3 *out, const Eina_Matrix3 *mat_a, const Eina_Matrix3 *mat_b) |
| Multiplies two matrices. More... | |
| EAPI void | eina_matrix3_multiply_copy (Eina_Matrix3 *out, const Eina_Matrix3 *mat_a, const Eina_Matrix3 *mat_b) |
| Multiplies two matrices without overwriting them. More... | |
| EAPI void | eina_matrix3_scale_transform_set (Eina_Matrix3 *out, double s_x, double s_y) |
| Sets the scale parameters (XX, YY) of a matrix. More... | |
| EAPI 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. More... | |
| EAPI void | eina_normal3_matrix_get (Eina_Matrix3 *out, const Eina_Matrix4 *m) |
| Sets normal of the given matrix. More... | |
| EAPI void | eina_matrix3_matrix4_to (Eina_Matrix4 *m4, const Eina_Matrix3 *m3) |
| Converts an Eina_Matrix3 into an Eina_Matrix4. More... | |
Definition and operations for 3x3 matrices.
| #define EINA_MATRIX3_ARGS | ( | m | ) |
Helper macro for printf formatting arg.
| EAPI Eina_Matrix_Type eina_matrix3_type_get | ( | const Eina_Matrix3 * | m | ) |
Returns the type of the given floating point matrix.
| [in] | m | The floating point matrix. |
This function returns the type of the matrix m. No check is done on m.
References EINA_DBL_EQ, EINA_MATRIX_TYPE_AFFINE, EINA_MATRIX_TYPE_IDENTITY, and EINA_MATRIX_TYPE_PROJECTIVE.
Referenced by eina_matrix3_multiply().
| EAPI 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.
| [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.
| EAPI 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.
| [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.
| EAPI 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.
| [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.
References eina_f16p16_double_from().
Referenced by eina_matrix3_matrix3_f16p16_to().
| EAPI 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.
| [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.
References eina_matrix3_fixed_values_get().
| EAPI Eina_Bool eina_matrix3_equal | ( | const Eina_Matrix3 * | m1, |
| const Eina_Matrix3 * | m2 | ||
| ) |
Checks whether the two matrices are equivalent.
| [in] | m1 | The first matrix. |
| [in] | m2 | The second matrix. |
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.
References EINA_DBL_EQ, EINA_FALSE, EINA_TRUE, _Eina_Matrix3::xx, _Eina_Matrix3::xy, _Eina_Matrix3::xz, _Eina_Matrix3::yx, _Eina_Matrix3::yy, _Eina_Matrix3::yz, _Eina_Matrix3::zx, _Eina_Matrix3::zy, and _Eina_Matrix3::zz.
| EAPI 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.
| [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.
Referenced by eina_matrix3_multiply(), eina_matrix3_quad_quad_map(), eina_matrix3_rotate(), eina_matrix3_scale(), and eina_matrix3_translate().
| EAPI void eina_matrix3_translate | ( | Eina_Matrix3 * | m, |
| double | tx, | ||
| double | ty | ||
| ) |
Sets the matrix values for a translation operation.
| [out] | m | The matrix. |
| [in] | tx | The X coordinate translation. |
| [in] | ty | The Y coordinate translation. |
References eina_matrix3_compose().
| EAPI void eina_matrix3_scale | ( | Eina_Matrix3 * | m, |
| double | sx, | ||
| double | sy | ||
| ) |
Sets the matrix values for a scaling operation.
| [out] | m | The matrix. |
| [in] | sx | The X coordinate scaling factor. |
| [in] | sy | The Y coordinate scaling factor. |
References eina_matrix3_compose().
| EAPI void eina_matrix3_rotate | ( | Eina_Matrix3 * | m, |
| double | rad | ||
| ) |
Sets the matrix values for a rotation operation.
| [out] | m | The matrix. |
| [in] | rad | The number of radians to rotate. |
References eina_matrix3_compose().
| EAPI void eina_matrix3_identity | ( | Eina_Matrix3 * | m | ) |
Sets the given floating point matrix to the identity matrix.
| [out] | m | The matrix to set to identity. |
This function sets m to the identity matrix. No check is done on m.
Referenced by eina_matrix3_inverse(), eina_matrix3_position_transform_set(), and eina_matrix3_scale_transform_set().
| EAPI double eina_matrix3_determinant | ( | const Eina_Matrix3 * | m | ) |
Calculates the determinant of the given matrix.
| [in] | m | The matrix. |
This function returns the determinant of the matrix m. No check is done on m.
Referenced by eina_matrix3_inverse().
| EAPI void eina_matrix3_divide | ( | Eina_Matrix3 * | m, |
| double | scalar | ||
| ) |
Divides the given matrix by a scalar number.
| [in,out] | m | The matrix. |
| [in] | scalar | The scalar number. |
This function divides the matrix m by scalar. No check is done on m.
Referenced by eina_matrix3_inverse(), and eina_matrix3_quad_square_map().
| EAPI void eina_matrix3_inverse | ( | const Eina_Matrix3 * | m, |
| Eina_Matrix3 * | m2 | ||
| ) |
Computes the inverse of the given matrix.
| [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.
References EINA_DBL_EQ, eina_matrix3_adjoint(), eina_matrix3_determinant(), eina_matrix3_divide(), and eina_matrix3_identity().
Referenced by eina_matrix3_quad_square_map().
| EAPI void eina_matrix3_transpose | ( | const Eina_Matrix3 * | m, |
| Eina_Matrix3 * | a | ||
| ) |
Computes the transpose of the given matrix.
| [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.
Referenced by eina_matrix3_adjoint().
| EAPI void eina_matrix3_cofactor | ( | const Eina_Matrix3 * | m, |
| Eina_Matrix3 * | a | ||
| ) |
Computes the cofactor of the given matrix.
| [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).
Referenced by eina_matrix3_adjoint().
| EAPI void eina_matrix3_adjoint | ( | const Eina_Matrix3 * | m, |
| Eina_Matrix3 * | a | ||
| ) |
Computes the adjoint of the given matrix.
| [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.
References eina_matrix3_cofactor(), and eina_matrix3_transpose().
Referenced by eina_matrix3_inverse().
| EAPI 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.
| [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.
References EINA_DBL_EQ.
Referenced by eina_matrix3_rectangle_transform().
| EAPI 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.
| [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.
References eina_matrix3_point_transform().
| EAPI 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.
| [out] | m | The transformation matrix to create. |
| [in] | src | The source quadrangle. |
| [in] | dst | The destination quadrangle. |
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.
References EINA_FALSE, eina_matrix3_compose(), eina_matrix3_quad_square_map(), eina_matrix3_square_quad_map(), and EINA_TRUE.
| EAPI Eina_Bool eina_matrix3_square_quad_map | ( | Eina_Matrix3 * | m, |
| const Eina_Quad * | q | ||
| ) |
Creates a matrix for unit-square to quad mapping.
| [out] | m | The transformation matrix to create. |
| [in] | q | The source quadrangle. |
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.
References EINA_DBL_EQ, EINA_FALSE, and EINA_TRUE.
Referenced by eina_matrix3_quad_quad_map(), and eina_matrix3_quad_square_map().
| EAPI Eina_Bool eina_matrix3_quad_square_map | ( | Eina_Matrix3 * | m, |
| const Eina_Quad * | q | ||
| ) |
Creates a matrix for mapping squares to match quad.
| [out] | m | The transformation matrix to create. |
| [in] | q | The source quadrangle. |
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.
References EINA_DBL_EQ, EINA_FALSE, eina_matrix3_divide(), eina_matrix3_inverse(), eina_matrix3_square_quad_map(), and EINA_TRUE.
Referenced by eina_matrix3_quad_quad_map().
| EAPI void eina_matrix3_array_set | ( | Eina_Matrix3 * | m, |
| const double * | v | ||
| ) |
Sets matrix values using an array.
| [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.
| EAPI void eina_matrix3_copy | ( | Eina_Matrix3 * | dst, |
| const Eina_Matrix3 * | src | ||
| ) |
Copies a matrix.
| [out] | dst | Copy of the matrix. |
| [in] | src | The matrix to copy. |
Referenced by eina_matrix3_multiply(), and eina_matrix3_multiply_copy().
| EAPI void eina_matrix3_multiply | ( | Eina_Matrix3 * | out, |
| const Eina_Matrix3 * | mat_a, | ||
| const Eina_Matrix3 * | mat_b | ||
| ) |
Multiplies two matrices.
| [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.
References eina_matrix3_compose(), eina_matrix3_copy(), eina_matrix3_type_get(), and EINA_MATRIX_TYPE_IDENTITY.
Referenced by eina_matrix3_multiply_copy().
| EAPI void eina_matrix3_multiply_copy | ( | Eina_Matrix3 * | out, |
| const Eina_Matrix3 * | mat_a, | ||
| const Eina_Matrix3 * | mat_b | ||
| ) |
Multiplies two matrices without overwriting them.
| [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.
References eina_matrix3_copy(), and eina_matrix3_multiply().
| EAPI void eina_matrix3_scale_transform_set | ( | Eina_Matrix3 * | out, |
| double | s_x, | ||
| double | s_y | ||
| ) |
Sets the scale parameters (XX, YY) of a matrix.
| [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.
References eina_matrix3_identity().
| EAPI 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.
| [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.
References eina_matrix3_identity().
| EAPI void eina_normal3_matrix_get | ( | Eina_Matrix3 * | out, |
| const Eina_Matrix4 * | m | ||
| ) |
Sets normal of the given matrix.
| [out] | out | The resulting matrix. |
| [in] | m | The matrix. |
| EAPI void eina_matrix3_matrix4_to | ( | Eina_Matrix4 * | m4, |
| const Eina_Matrix3 * | m3 | ||
| ) |
Converts an Eina_Matrix3 into an Eina_Matrix4.
| [out] | m3 | The destination Eina_Matrix3. |
| [in] | m4 | The source Eina_Matrix4. |