Module Cairo.Matrix

This is used throughout cairo to convert between different coordinate spaces.

type t = matrix
val init_identity : unit -> t

init_identity() returns the identity transformation.

val init_translate : float -> float -> t

init_translate tx ty return a transformation that translates by tx and ty in the X and Y dimensions, respectively.

val init_scale : float -> float -> t

init_scale sx sy return a transformation that scales by sx and sy in the X and Y dimensions, respectively.

val init_rotate : float -> t

init_rotate radians returns a a transformation that rotates by radians.

val translate : t -> float -> float -> unit

translate matrix tx 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.

val scale : t -> float -> float -> unit

scale matrix sx 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.

val rotate : t -> float -> unit

rotate matrix 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.

val invert : t -> unit

invert 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 raise Error INVALID_MATRIX.

val multiply : t -> t -> t

multiply a b multiplies the affine transformations in a and b together and return the 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.

val transform_distance : t -> dx:float -> dy:float -> float * float

transform_distance matrix dx 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.

val transform_point : t -> float -> float -> float * float

transform_point matrix x y transforms the point (x, y) by matrix.