(** Immutable 2d transform module. 
    @author Victor Nicollet *)

(** Transform type. Transforms are represented as complex plane transforms
    f(z) = za + b. Therefore, a represents the the rotation/scaling and b 
    represents the translation. *)
type transform = 
    { 
      ar : float; ai : float;
      br : float; bi : float;
    }

(** Identity transform. *)
val identity : transform

(** Rotate a transform by a certain angle. *)
val rotate : transform -> float -> transform

(** Scale a transform by a certain angle. *)
val scale : transform -> float -> transform

(** Translate a transform by a vector. *)
val translate : transform -> Vector.vector -> transform

(** A description of a transform in less compressed terms. *)
type transform_description =
    { 
      angle : float;
      scale : float;
      position : Vector.vector
    }
  
(** Construct a transform from a description *)
val make : transform_description -> transform

(** Describe a transform in simpler terms *)
val describe : transform -> transform_description

(** Transform a vector by a transform. *)
val apply : transform -> Vector.vector -> Vector.vector

(** Compose a transform by applying it after another. 
    That is, [apply a (apply b v)] is equivalent to [apply (compose a b) v] *)
val compose : transform -> transform -> transform