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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 | (** Affine Transformations in Two Dimensions *)
(** {2 Types} *)
(** A single transformation operation. *)
type transform_op =
| Scale of (float * float) * float * float
| Rotate of (float * float) * float
| Translate of float * float
| ShearX of (float * float) * float
| ShearY of (float * float) * float
(** A list of transformations, the first at the end of the list (thus, to append
another transformation, just cons to the beginning.) *)
type transform = transform_op list
(** A transformation matrix (first row [a c e], second row [b d f], third row [0 0 1]) *)
type transform_matrix =
{a : float; b : float; c : float; d : float; e : float; f : float}
(** The identity transform *)
val i : transform
(** Make a string of a transform for debug purposes. *)
val string_of_transform : transform -> string
(** {2 Making transformation matrices} *)
(** The identity matrix *)
val i_matrix : transform_matrix
(** String of a transformation matrix. *)
val string_of_matrix : transform_matrix -> string
(** Make a transformation matrix from x and y translation. *)
val mktranslate : float -> float -> transform_matrix
(** Make a transformation matrix from an x and y scale and a point to scale about. *)
val mkscale : (float * float) -> float -> float -> transform_matrix
(** Make a rotation matrix to rotate by a number of radians around a point. *)
val mkrotate : (float * float) -> float -> transform_matrix
(** Matrix to shear in x by a given factor about a point. *)
val mkshearx : (float * float) -> float -> transform_matrix
(** Matrix to shear in y by a given factor about a point. *)
val mksheary : (float * float) -> float -> transform_matrix
(** {2 Composing and manipulating transforms} *)
(** [compose t ts] adds operation [t] to the transform [ts]. *)
val compose : transform_op -> transform -> transform
(** [append a b] is a transform with the same effect as performing b then a *)
val append : (transform -> transform -> transform)
(** [compose a b] produces a matrix equivalent to performing [b] then [a]. *)
val matrix_compose : transform_matrix -> transform_matrix -> transform_matrix
(** Make a matrix from a single transformation operation *)
val matrix_of_op : transform_op -> transform_matrix
(** Make a matrix from a transform *)
val matrix_of_transform : transform -> transform_matrix
(** {2 Inverting transforms} *)
(** Exception raised if a matrix is non-invertable *)
exception NonInvertable
(** Matrix inversion. May raise [NonInvertable] *)
val matrix_invert : transform_matrix -> transform_matrix
(** Transform a coordinate by a given transform. *)
val transform : transform -> float * float -> float * float
(** Transform a coordinate by a given transformation matrix. *)
val transform_matrix : transform_matrix -> float * float -> float * float
(** {2 Decomposing and recomposing matrices} *)
(** Decompose a transformation matrix to scale, aspect, rotation, shear,
translation in x, translation in y. Always succeeds, but results are not
guaranteed to mean anything. *)
val decompose :
transform_matrix -> float * float * float * float * float * float
(** Recompose from the above information. It is not guaranteed that recompose
(decompose t) = t *)
val recompose :
float -> float -> float -> float -> float -> float -> transform_matrix
|