cairo_matrix_t

typedef struct {
    double xx; double yx;
    double xy; double yy;
    double x0; double y0;
} cairo_matrix_t;

A cairo_matrix_t holds an affine transformation, such as a scale, rotation, shear, or a combination of those. The transformation of a point (x, y) is given by:

    x_new = xx * x + xy * y + x0;
    y_new = yx * x + yy * y + y0;

cairo_matrix_init ()

void        cairo_matrix_init               (cairo_matrix_t *matrix,
                                             double xx,
                                             double yx,
                                             double xy,
                                             double yy,
                                             double x0,
                                             double y0);

Sets matrix to be the affine transformation given by xx, yx, xy, yy, x0, y0. The transformation is given by:

 x_new = xx * x + xy * y + x0;
 y_new = yx * x + yy * y + y0;

cairo_matrix_init_identity ()

void        cairo_matrix_init_identity      (cairo_matrix_t *matrix);

Modifies matrix to be an identity transformation.

cairo_matrix_init_translate ()

void        cairo_matrix_init_translate     (cairo_matrix_t *matrix,
                                             double tx,
                                             double ty);

Initializes matrix to a transformation that translates by tx and ty in the X and Y dimensions, respectively.

cairo_matrix_init_scale ()

void        cairo_matrix_init_scale         (cairo_matrix_t *matrix,
                                             double sx,
                                             double sy);

Initializes matrix to a transformation that scales by sx and sy in the X and Y dimensions, respectively.

cairo_matrix_init_rotate ()

void        cairo_matrix_init_rotate        (cairo_matrix_t *matrix,
                                             double radians);

Initialized matrix to a transformation that rotates by radians.

cairo_matrix_translate ()

void        cairo_matrix_translate          (cairo_matrix_t *matrix,
                                             double tx,
                                             double ty);

Applies a translation by tx, ty to the transformation in matrix. The effect of the new transformation is to first translate the coordinates by tx and ty, then apply the original transformation to the coordinates.

cairo_matrix_scale ()

void        cairo_matrix_scale              (cairo_matrix_t *matrix,
                                             double sx,
                                             double sy);

Applies scaling by tx, ty to the transformation in matrix. The effect of the new transformation is to first scale the coordinates by sx and sy, then apply the original transformation to the coordinates.

cairo_matrix_rotate ()

void        cairo_matrix_rotate             (cairo_matrix_t *matrix,
                                             double radians);

Applies rotation by radians to the transformation in matrix. The effect of the new transformation is to first rotate the coordinates by radians, then apply the original transformation to the coordinates.

cairo_matrix_invert ()

cairo_status_t cairo_matrix_invert          (cairo_matrix_t *matrix);

Changes matrix to be the inverse of it's original value. Not all transformation matrices have inverses; if the matrix collapses points together (it is degenerate), then it has no inverse and this function will fail.

Returns: If matrix has an inverse, modifies matrix to be the inverse matrix and returns CAIRO_STATUS_SUCCESS. Otherwise,

cairo_matrix_multiply ()

void        cairo_matrix_multiply           (cairo_matrix_t *result,
                                             const cairo_matrix_t *a,
                                             const cairo_matrix_t *b);

Multiplies the affine transformations in a and b together and stores the result in result. The effect of the resulting transformation is to first apply the transformation in a to the coordinates and then apply the transformation in b to the coordinates.

It is allowable for result to be identical to either a or b.

cairo_matrix_transform_distance ()

void        cairo_matrix_transform_distance (const cairo_matrix_t *matrix,
                                             double *dx,
                                             double *dy);

Transforms the distance vector (dx,dy) by matrix. This is similar to cairo_matrix_transform_point() except that the translation components of the transformation are ignored. The calculation of the returned vector is as follows:

dx2 = dx1 * a + dy1 * c;
dy2 = dx1 * b + dy1 * d;

Affine transformations are position invariant, so the same vector always transforms to the same vector. If (x1,y1) transforms to (x2,y2) then (x1+dx1,y1+dy1) will transform to (x1+dx2,y1+dy2) for all values of x1 and x2.

cairo_matrix_transform_point ()

void        cairo_matrix_transform_point    (const cairo_matrix_t *matrix,
                                             double *x,
                                             double *y);

Transforms the point (x, y) by matrix.