## Transformations

Transformations — Manipulating the current transformation matrix

## Synopsis

    void                cairo_translate                     (cairo_t *cr,
                                                             double tx,
                                                             double ty);
    void                cairo_scale                         (cairo_t *cr,
                                                             double sx,
                                                             double sy);
    void                cairo_rotate                        (cairo_t *cr,
                                                             double angle);
    void                cairo_transform                     (cairo_t *cr,
                                                             const cairo_matrix_t *matrix);
    void                cairo_set_matrix                    (cairo_t *cr,
                                                             const cairo_matrix_t *matrix);
    void                cairo_get_matrix                    (cairo_t *cr,
                                                             cairo_matrix_t *matrix);
    void                cairo_identity_matrix               (cairo_t *cr);
    void                cairo_user_to_device                (cairo_t *cr,
                                                             double *x,
                                                             double *y);
    void                cairo_user_to_device_distance       (cairo_t *cr,
                                                             double *dx,
                                                             double *dy);
    void                cairo_device_to_user                (cairo_t *cr,
                                                             double *x,
                                                             double *y);
    void                cairo_device_to_user_distance       (cairo_t *cr,
                                                             double *dx,
                                                             double *dy);

## Description

The current transformation matrix, ctm, is a two-dimensional affine transformation that maps all coordinates and other drawing instruments from the user space into the surface's canonical coordinate system, also known as the device space.

## Details

### cairo_translate ()

    void                cairo_translate                     (cairo_t *cr,
                                                             double tx,
                                                             double ty);

Modifies the current transformation matrix (CTM) by translating the user-space origin by (`tx`, `ty`). This offset is interpreted as a user-space coordinate according to the CTM in place before the new call to `cairo_translate()`. In other words, the translation of the user-space origin takes place after any existing transformation.

`cr` : | a cairo context
`tx` : | amount to translate in the X direction
`ty` : | amount to translate in the Y direction

### cairo_scale ()

    void                cairo_scale                         (cairo_t *cr,
                                                             double sx,
                                                             double sy);

Modifies the current transformation matrix (CTM) by scaling the X and Y user-space axes by `sx` and `sy` respectively. The scaling of the axes takes place after any existing transformation of user space.

`cr` : | a cairo context
`sx` : | scale factor for the X dimension
`sy` : | scale factor for the Y dimension

### cairo_rotate ()

    void                cairo_rotate                        (cairo_t *cr,
                                                             double angle);

Modifies the current transformation matrix (CTM) by rotating the user-space axes by `angle` radians. The rotation of the axes takes places after any existing transformation of user space. The rotation direction for positive angles is from the positive X axis toward the positive Y axis.

`cr` : | a cairo context
`angle` : | angle (in radians) by which the user-space axes will be rotated

### cairo_transform ()

    void                cairo_transform                     (cairo_t *cr,
                                                             const cairo_matrix_t *matrix);

Modifies the current transformation matrix (CTM) by applying `matrix` as an additional transformation. The new transformation of user space takes place after any existing transformation.

`cr` : | a cairo context
`matrix` : | a transformation to be applied to the user-space axes

### cairo_set_matrix ()

    void                cairo_set_matrix                    (cairo_t *cr,
                                                             const cairo_matrix_t *matrix);

Modifies the current transformation matrix (CTM) by setting it equal to `matrix`.

`cr` : | a cairo context
`matrix` : | a transformation matrix from user space to device space

### cairo_get_matrix ()

    void                cairo_get_matrix                    (cairo_t *cr,
                                                             cairo_matrix_t *matrix);

Stores the current transformation matrix (CTM) into `matrix`.

`cr` : | a cairo context
`matrix` : | return value for the matrix

### cairo_identity_matrix ()

    void                cairo_identity_matrix               (cairo_t *cr);

Resets the current transformation matrix (CTM) by setting it equal to the identity matrix. That is, the user-space and device-space axes will be aligned and one user-space unit will transform to one device-space unit.

`cr` : | a cairo context

### cairo_user_to_device ()

    void                cairo_user_to_device                (cairo_t *cr,
                                                             double *x,
                                                             double *y);

Transform a coordinate from user space to device space by multiplying the given point by the current transformation matrix (CTM).

`cr` : | a cairo context
`x` : | X value of coordinate (in/out parameter)
`y` : | Y value of coordinate (in/out parameter)

### cairo_user_to_device_distance ()

    void                cairo_user_to_device_distance       (cairo_t *cr,
                                                             double *dx,
                                                             double *dy);

Transform a distance vector from user space to device space. This function is similar to `cairo_user_to_device()` except that the translation components of the CTM will be ignored when transforming (`dx`,`dy`).

`cr` : | a cairo context
`dx` : | X component of a distance vector (in/out parameter)
`dy` : | Y component of a distance vector (in/out parameter)

### cairo_device_to_user ()

    void                cairo_device_to_user                (cairo_t *cr,
                                                             double *x,
                                                             double *y);

Transform a coordinate from device space to user space by multiplying the given point by the inverse of the current transformation matrix (CTM).

`cr` : | a cairo
`x` : | X value of coordinate (in/out parameter)
`y` : | Y value of coordinate (in/out parameter)

### cairo_device_to_user_distance ()

    void                cairo_device_to_user_distance       (cairo_t *cr,
                                                             double *dx,
                                                             double *dy);

Transform a distance vector from device space to user space. This function is similar to `cairo_device_to_user()` except that the translation components of the inverse CTM will be ignored when transforming (`dx`,`dy`).

`cr` : | a cairo context
`dx` : | X component of a distance vector (in/out parameter)
`dy` : | Y component of a distance vector (in/out parameter)

## See Also

- cairo_matrix_t