cairo_matrix_t

cairo_matrix_t — Generic matrix operations

Synopsis

cairo_matrix_t;
void                cairo_matrix_init                   (cairo_matrix_t *matrix,
double xx,
double yx,
double xy,
double yy,
double x0,
double y0);
void                cairo_matrix_init_identity          (cairo_matrix_t *matrix);
void                cairo_matrix_init_translate         (cairo_matrix_t *matrix,
double tx,
double ty);
void                cairo_matrix_init_scale             (cairo_matrix_t *matrix,
double sx,
double sy);
void                cairo_matrix_init_rotate            (cairo_matrix_t *matrix,
void                cairo_matrix_translate              (cairo_matrix_t *matrix,
double tx,
double ty);
void                cairo_matrix_scale                  (cairo_matrix_t *matrix,
double sx,
double sy);
void                cairo_matrix_rotate                 (cairo_matrix_t *matrix,
cairo_status_t      cairo_matrix_invert                 (cairo_matrix_t *matrix);
void                cairo_matrix_multiply               (cairo_matrix_t *result,
const cairo_matrix_t *a,
const cairo_matrix_t *b);
void                cairo_matrix_transform_distance     (const cairo_matrix_t *matrix,
double *dx,
double *dy);
void                cairo_matrix_transform_point        (const cairo_matrix_t *matrix,
double *x,
double *y);

Description

cairo_matrix_t is used throughout cairo to convert between different coordinate spaces. A cairo_matrix_t holds an affine transformation, such as a scale, rotation, shear, or a combination of these. The transformation of a point (x,y) is given by:

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

The current transformation matrix of a cairo_t, represented as a cairo_matrix_t, defines the transformation from user-space coordinates to device-space coordinates. See cairo_get_matrix() and cairo_set_matrix().

Details

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;

 double xx; xx component of the affine transformation double yx; yx component of the affine transformation double xy; xy component of the affine transformation double yy; yy component of the affine transformation double x0; X translation component of the affine transformation double y0; Y translation component of the affine transformation

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;

 matrix : a cairo_matrix_t xx : xx component of the affine transformation yx : yx component of the affine transformation xy : xy component of the affine transformation yy : yy component of the affine transformation x0 : X translation component of the affine transformation y0 : Y translation component of the affine transformation

cairo_matrix_init_identity ()

void                cairo_matrix_init_identity          (cairo_matrix_t *matrix);

Modifies matrix to be an identity transformation.

 matrix : a cairo_matrix_t

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.

 matrix : a cairo_matrix_t tx : amount to translate in the X direction ty : amount to translate in the Y direction

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.

 matrix : a cairo_matrix_t sx : scale factor in the X direction sy : scale factor in the Y direction

cairo_matrix_init_rotate ()

void                cairo_matrix_init_rotate            (cairo_matrix_t *matrix,

Initialized matrix to a transformation that rotates by radians.

 matrix : a cairo_matrix_t radians : angle of rotation, in radians. The direction of rotation is defined such that positive angles rotate in the direction from the positive X axis toward the positive Y axis. With the default axis orientation of cairo, positive angles rotate in a clockwise direction.

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.

 matrix : a cairo_matrix_t tx : amount to translate in the X direction ty : amount to translate in the Y direction

cairo_matrix_scale ()

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

Applies scaling by sx, sy 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.

 matrix : a cairo_matrix_t sx : scale factor in the X direction sy : scale factor in the Y direction

cairo_matrix_rotate ()

void                cairo_matrix_rotate                 (cairo_matrix_t *matrix,

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.

 matrix : a cairo_matrix_t radians : angle of rotation, in radians. The direction of rotation is defined such that positive angles rotate in the direction from the positive X axis toward the positive Y axis. With the default axis orientation of cairo, positive angles rotate in a clockwise direction.

cairo_matrix_invert ()

cairo_status_t      cairo_matrix_invert                 (cairo_matrix_t *matrix);

Changes matrix to be the inverse of its 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.

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

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.

 result : a cairo_matrix_t in which to store the result a : a cairo_matrix_t b : a cairo_matrix_t

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.

 matrix : a cairo_matrix_t dx : X component of a distance vector. An in/out parameter dy : Y component of a distance vector. An in/out parameter

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.

 matrix : a cairo_matrix_t x : X position. An in/out parameter y : Y position. An in/out parameter