## GimpMatrix

GimpMatrix — Utilities to set up and manipulate 3x3 transformation matrices.

## Synopsis

                GimpMatrix2;
                GimpMatrix3;
                GimpMatrix4;
    void        gimp_matrix2_identity           (GimpMatrix2 *matrix);
    void        gimp_matrix2_mult               (const GimpMatrix2 *matrix1,
                                                 GimpMatrix2 *matrix2);
    void        gimp_matrix3_identity           (GimpMatrix3 *matrix);
    void        gimp_matrix3_mult               (const GimpMatrix3 *matrix1,
                                                 GimpMatrix3 *matrix2);
    void        gimp_matrix3_translate          (GimpMatrix3 *matrix,
                                                 gdouble x,
                                                 gdouble y);
    void        gimp_matrix3_scale              (GimpMatrix3 *matrix,
                                                 gdouble x,
                                                 gdouble y);
    void        gimp_matrix3_rotate             (GimpMatrix3 *matrix,
                                                 gdouble theta);
    void        gimp_matrix3_xshear             (GimpMatrix3 *matrix,
                                                 gdouble amount);
    void        gimp_matrix3_yshear             (GimpMatrix3 *matrix,
                                                 gdouble amount);
    void        gimp_matrix3_affine             (GimpMatrix3 *matrix,
                                                 gdouble a,
                                                 gdouble b,
                                                 gdouble c,
                                                 gdouble d,
                                                 gdouble e,
                                                 gdouble f);
    void        gimp_matrix3_transform_point    (const GimpMatrix3 *matrix,
                                                 gdouble x,
                                                 gdouble y,
                                                 gdouble *newx,
                                                 gdouble *newy);
    gdouble     gimp_matrix3_determinant        (const GimpMatrix3 *matrix);
    void        gimp_matrix3_invert             (GimpMatrix3 *matrix);
    gboolean    gimp_matrix3_is_diagonal        (const GimpMatrix3 *matrix);
    gboolean    gimp_matrix3_is_identity        (const GimpMatrix3 *matrix);
    gboolean    gimp_matrix3_is_simple          (const GimpMatrix3 *matrix);
    void        gimp_matrix4_to_deg             (const GimpMatrix4 *matrix,
                                                 gdouble *a,
                                                 gdouble *b,
                                                 gdouble *c);

## Description

When doing image manipulation you will often need 3x3 transformation matrices that define translation, rotation, scaling, shearing and arbitrary perspective transformations using a 3x3 matrix. Here you'll find a set of utility functions to set up those matrices and to perform basic matrix manipulations and tests.

## Details

### GimpMatrix2

    typedef struct {
      gdouble coeff[2][2];
    } GimpMatrix2;

A two by two matrix.

### GimpMatrix3

    typedef struct {
      gdouble coeff[3][3];
    } GimpMatrix3;

A three by three matrix.

### GimpMatrix4

    typedef struct {
      gdouble coeff[4][4];
    } GimpMatrix4;

A four by four matrix.

### gimp_matrix2_identity ()

    void        gimp_matrix2_identity           (GimpMatrix2 *matrix);

Sets the matrix to the identity matrix.

`matrix` : | A matrix.

### gimp_matrix2_mult ()

    void        gimp_matrix2_mult               (const GimpMatrix2 *matrix1,
                                                 GimpMatrix2 *matrix2);

Multiplies two matrices and puts the result into the second one.

`matrix1` : | The first input matrix.
`matrix2` : | The second input matrix which will be overwritten by the result.

### gimp_matrix3_identity ()

    void        gimp_matrix3_identity           (GimpMatrix3 *matrix);

Sets the matrix to the identity matrix.

`matrix` : | A matrix.

### gimp_matrix3_mult ()

    void        gimp_matrix3_mult               (const GimpMatrix3 *matrix1,
                                                 GimpMatrix3 *matrix2);

Multiplies two matrices and puts the result into the second one.

`matrix1` : | The first input matrix.
`matrix2` : | The second input matrix which will be overwritten by the result.

### gimp_matrix3_translate ()

    void        gimp_matrix3_translate          (GimpMatrix3 *matrix,
                                                 gdouble x,
                                                 gdouble y);

Translates the matrix by x and y.

`matrix` : | The matrix that is to be translated.
`x` : | Translation in X direction.
`y` : | Translation in Y direction.

### gimp_matrix3_scale ()

    void        gimp_matrix3_scale              (GimpMatrix3 *matrix,
                                                 gdouble x,
                                                 gdouble y);

Scales the matrix by x and y

`matrix` : | The matrix that is to be scaled.
`x` : | X scale factor.
`y` : | Y scale factor.

### gimp_matrix3_rotate ()

    void        gimp_matrix3_rotate             (GimpMatrix3 *matrix,
                                                 gdouble theta);

Rotates the matrix by theta degrees.

`matrix` : | The matrix that is to be rotated.
`theta` : | The angle of rotation (in radians).

### gimp_matrix3_xshear ()

    void        gimp_matrix3_xshear             (GimpMatrix3 *matrix,
                                                 gdouble amount);

Shears the matrix in the X direction.

`matrix` : | The matrix that is to be sheared.
`amount` : | X shear amount.

### gimp_matrix3_yshear ()

    void        gimp_matrix3_yshear             (GimpMatrix3 *matrix,
                                                 gdouble amount);

Shears the matrix in the Y direction.

`matrix` : | The matrix that is to be sheared.
`amount` : | Y shear amount.

### gimp_matrix3_affine ()

    void        gimp_matrix3_affine             (GimpMatrix3 *matrix,
                                                 gdouble a,
                                                 gdouble b,
                                                 gdouble c,
                                                 gdouble d,
                                                 gdouble e,
                                                 gdouble f);

Applies the affine transformation given by six values to `matrix`. The six values form define an affine transformation matrix as illustrated below:

( a c e ) ( b d f ) ( 0 0 1 )

`matrix` : | The input matrix.
`a` : |
`b` : |
`c` : |
`d` : |
`e` : |
`f` : |

### gimp_matrix3_transform_point ()

    void        gimp_matrix3_transform_point    (const GimpMatrix3 *matrix,
                                                 gdouble x,
                                                 gdouble y,
                                                 gdouble *newx,
                                                 gdouble *newy);

Transforms a point in 2D as specified by the transformation matrix.

`matrix` : | The transformation matrix.
`x` : | The source X coordinate.
`y` : | The source Y coordinate.
`newx` : | The transformed X coordinate.
`newy` : | The transformed Y coordinate.

### gimp_matrix3_determinant ()

    gdouble     gimp_matrix3_determinant        (const GimpMatrix3 *matrix);

Calculates the determinant of the given matrix.

`matrix` : | The input matrix.
Returns : | The determinant.

### gimp_matrix3_invert ()

    void        gimp_matrix3_invert             (GimpMatrix3 *matrix);

Inverts the given matrix.

`matrix` : | The matrix that is to be inverted.

### gimp_matrix3_is_diagonal ()

    gboolean    gimp_matrix3_is_diagonal        (const GimpMatrix3 *matrix);

Checks if the given matrix is diagonal.

`matrix` : | The matrix that is to be tested.
Returns : | TRUE if the matrix is diagonal.

### gimp_matrix3_is_identity ()

    gboolean    gimp_matrix3_is_identity        (const GimpMatrix3 *matrix);

Checks if the given matrix is the identity matrix.

`matrix` : | The matrix that is to be tested.
Returns : | TRUE if the matrix is the identity matrix.

### gimp_matrix3_is_simple ()

    gboolean    gimp_matrix3_is_simple          (const GimpMatrix3 *matrix);

Checks if we'll need to interpolate when applying this matrix as a transformation.

`matrix` : | The matrix that is to be tested.
Returns : | TRUE if all entries of the upper left 2x2 matrix are either 0 or 1

### gimp_matrix4_to_deg ()

    void        gimp_matrix4_to_deg             (const GimpMatrix4 *matrix,
                                                 gdouble *a,
                                                 gdouble *b,
                                                 gdouble *c);

`matrix` : |
`a` : |
`b` : |
`c` : |

## See Also

GimpVector2

GimpVector3

GimpVector4