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Cairo: A Vector Graphics Library | ![]() |
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cairo_matrix_tcairo_matrix_t — Transformation matrices |
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, double radians); 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, double radians); 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);
cairo_matrix_t is used throughout Cairo to represents between different coordinates spaces. A cairo_matrix holds an affine transformation, such as a scale, rotation, or shear, or a combination of those. Mathematically, the effect of an affine transformation on a point (x,y) is given by:
x_new = x * a + y * c + tx; y_new = x * b + y * d + ty;
The parameters a, b, c, d, tx, ty can be retrieved with cairo_matrix_get_affine() and set with cairo_matrix_get_affine().
The primary use of transformation matrices in Cairo is as the current transformation matrix in a cairo_t. The current transformation matrix gives the transformation from user space coordinates to device coordinates. See cairo_set_matrix(), cairo_current_matrix().
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, or shear, or a combination of those. The transformation 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 |
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 |
void cairo_matrix_init_identity (cairo_matrix_t *matrix);
Modifies matrix to be an identity transformation.
matrix : | a cairo_matrix_t |
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 |
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 |
void cairo_matrix_init_rotate (cairo_matrix_t *matrix, double radians);
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. |
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 |
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.
matrix : | a cairo_matrix_t |
sx : | scale factor in the X direction |
sy : | scale factor in the Y direction |
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.
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_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,
matrix : | a cairo_matrix_t |
Returns : | CAIRO_STATUS_INVALID_MATRIX. |
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 |
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() 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 |
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 |
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