caml2geom / caml2geom.mli

(*
  Copyright (c) 2011 Barry Schwartz

  Permission is hereby granted, free of charge, to any person
  obtaining a copy of this software and associated documentation
  files (the "Software"), to deal in the Software without
  restriction, including without limitation the rights to use,
  copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the
  Software is furnished to do so, subject to the following
  conditions:

  The above copyright notice and this permission notice shall be
  included in all copies or substantial portions of the Software.

  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
  EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
  OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
  NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
  HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
  WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
  FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
  OTHER DEALINGS IN THE SOFTWARE.
*)

module type Fragment =
sig
  type t
  type output_type
  val default : unit -> t
  val is_zero : t -> bool
  val is_constant : t -> bool
  val is_finite : t -> bool
  val at0 : t -> output_type
  val at1 : t -> output_type
  val value_at : t -> float -> output_type
end

module D2 :
sig
  module type S =
  sig
    type elt
    type t
    val make : elt -> elt -> t
    val coord : t -> int -> elt
    val fst : t -> elt
    val snd : t -> elt
    val is_zero : t -> bool
    val is_constant : t -> bool
    val is_finite : t -> bool
  end

  module Make(Elt : Fragment) : S with type elt = Elt.t
end

module Coord :
sig
  type t = float
  type dim2 = X | Y
  val epsilon : t
  external infinity : unit -> t = "infinity_wrapper"
  external are_near : t -> t -> bool = "are_near_wrapper"
  external are_near_eps : t -> t -> t -> bool = "are_near_eps_wrapper"
  external rel_error_bound : t -> t -> bool = "rel_error_bound_wrapper"
  external rel_error_bound_eps : t -> t -> t -> bool = "rel_error_bound_eps_wrapper"
end

module Int_coord :
sig
  type t = int
end

module Point :
sig
  type t
  external default : unit -> t = "new_default_point_wrapper"
  external make : Coord.t -> Coord.t -> t = "new_point_wrapper"
  external copy : t -> t = "copy_point_wrapper"
  external coord : t -> int -> Coord.t = "point_coord_wrapper"
  external set_coord : t -> int -> Coord.t -> unit = "set_point_coord_wrapper"
  external length : t -> Coord.t = "point_length_wrapper"
  external normalize : t -> unit = "point_normalize_wrapper"
  external ccw : t -> t = "point_ccw_wrapper"
  external cw : t -> t = "point_cw_wrapper"
  external neg : t -> t = "point_neg_wrapper"
  external set : t -> t -> unit = "point_set_wrapper"
  external add_to : t -> t -> unit = "point_add_to_wrapper"
  external sub_from : t -> t -> unit = "point_sub_from_wrapper"
  external mul_by : t -> Coord.t -> unit = "point_mul_by_wrapper"
  external div_by : t -> Coord.t -> unit = "point_div_by_wrapper"

  val of_tuple : Coord.t * Coord.t -> t
  val to_tuple : t -> Coord.t * Coord.t
  val of_complex : Complex.t -> t
  val to_complex : t -> Complex.t
end

module Interval :
sig
  type t
  external default : unit -> t = "new_default_interval_wrapper"
end

module Rect :
sig
  type t
  external default : unit -> t = "new_default_rect_wrapper"
  external min : t -> Point.t = "rect_min_wrapper"
  external max : t -> Point.t = "rect_max_wrapper"
  external corner : t -> int -> Point.t = "rect_corner_wrapper"
end

module Crossing :
sig
  type t = {
    dir : bool;                (* True: along a, a becomes outside. *)
    ta : float;                (* Time of crossing on a. *)
    tb : float;                (* Time of crossing on b. *)
    a : int;                   (* Storage of indices. *)
    b : int;                   (* Storage of indices. *)
  }
  val get_other : t -> int -> int
  val get_time : t -> int -> float
  val get_other_time : t -> int -> float
  val on_ix : t -> int -> bool
end

module Bezier :
sig
  type t
  type output_type = Coord.t
  external default : unit -> t = "new_default_bezier_wrapper"
  external make_order0 : Coord.t -> t = "new_bezier_order0_wrapper"
  external make_order1 : Coord.t -> Coord.t -> t = "new_bezier_order1_wrapper"
  external make_order2 : Coord.t -> Coord.t -> Coord.t -> t = "new_bezier_order2_wrapper"
  external make_order3 : Coord.t -> Coord.t -> Coord.t -> Coord.t -> t = "new_bezier_order3_wrapper"
  external is_zero : t -> bool = "bezier_is_zero_wrapper"
  external is_constant : t -> bool = "bezier_is_constant_wrapper"
  external is_finite : t -> bool = "bezier_is_finite_wrapper"
  external at0 : t -> Coord.t = "bezier_at0_wrapper"
  external at1 : t -> Coord.t = "bezier_at1_wrapper"
  external value_at : t -> float -> Coord.t = "bezier_value_at_wrapper"

  val of_2tuple : Coord.t * Coord.t -> t
  val of_3tuple : Coord.t * Coord.t * Coord.t -> t
  val of_4tuple : Coord.t * Coord.t * Coord.t * Coord.t -> t
end

module Curve :
sig
  type t
  external initial_point : t -> Point.t = "curve_initial_point_wrapper"
  external final_point : t -> Point.t = "curve_final_point_wrapper"
  external is_degenerate : t -> bool = "curve_is_degenerate_wrapper"
  external point_at : t -> Coord.t -> Point.t = "curve_point_at_wrapper"
  external value_at : t -> Coord.t -> Coord.dim2 -> Coord.t = "curve_value_at_wrapper"
  external point_and_derivatives : t -> Coord.t -> int -> Point.t array = "curve_point_and_derivatives_wrapper"
  external set_initial : t -> Point.t -> unit = "curve_set_initial_wrapper"
  external set_final : t -> Point.t -> unit = "curve_set_final_wrapper"
  external bounds_fast : t -> Rect.t = "curve_bounds_fast_wrapper"
  external bounds_exact : t -> Rect.t = "curve_bounds_exact_wrapper"
  external portion : t -> Coord.t -> Coord.t -> t = "curve_portion_wrapper"
  external reverse : t -> t = "curve_reverse_wrapper"
  external derivative : t -> t = "curve_derivative_wrapper"
  external length : t -> Coord.t -> Coord.t = "curve_length_wrapper"
  external nearest_point : t -> ?t1:Coord.t -> ?t2:Coord.t -> Point.t -> Coord.t  = "curve_nearest_point_wrapper"
  external roots : t -> Coord.t -> Coord.dim2 -> Coord.t array = "curve_roots_wrapper"
  external winding : t -> Point.t -> int = "curve_winding_wrapper"
  external unit_tangent_at : ?num_derivs:int -> t -> Coord.t -> Point.t = "curve_unit_tangent_at_wrapper"
  external degrees_of_freedom : t -> int = "curve_degrees_of_freedom_wrapper"
  external crossings : t -> t -> Crossing.t array = "curve_crossings_wrapper"
end

module Bezier_curve :
sig
  type t
  external to_curve : t -> Curve.t = "%identity"
  external of_two_beziers : Bezier.t -> Bezier.t -> t = "bezier_curve_of_two_beziers_wrapper"
  external of_two_points : Point.t -> Point.t -> t = "bezier_curve_of_two_points_wrapper"
  external of_three_points : Point.t -> Point.t -> Point.t -> t = "bezier_curve_of_three_points_wrapper"
  external of_four_points : Point.t -> Point.t -> Point.t -> Point.t -> t = "bezier_curve_of_four_points_wrapper"
  external order : t -> int = "bezier_curve_order_wrapper"
  external subdivide : t -> float -> t * t = "bezier_curve_subdivide_wrapper"
  external optimize : t -> t = "bezier_curve_optimize_wrapper"
  external initial_point : t -> Point.t = "bezier_curve_initial_point_wrapper"
  external final_point : t -> Point.t = "bezier_curve_final_point_wrapper"
  external is_degenerate : t -> bool = "bezier_curve_is_degenerate_wrapper"
  external point_at : t -> Coord.t -> Point.t = "bezier_curve_point_at_wrapper"
  external value_at : t -> Coord.t -> Coord.dim2 -> Coord.t = "bezier_curve_value_at_wrapper"
  external point_and_derivatives : t -> Coord.t -> int -> Point.t array = "bezier_curve_point_and_derivatives_wrapper"
  external set_initial : t -> Point.t -> unit = "bezier_curve_set_initial_wrapper"
  external set_final : t -> Point.t -> unit = "bezier_curve_set_final_wrapper"
  external bounds_fast : t -> Rect.t = "bezier_curve_bounds_fast_wrapper"
  external bounds_exact : t -> Rect.t = "bezier_curve_bounds_exact_wrapper"
  external portion : t -> Coord.t -> Coord.t -> t = "bezier_curve_portion_wrapper"
  external reverse : t -> t = "bezier_curve_reverse_wrapper"
  external derivative : t -> t = "bezier_curve_derivative_wrapper"
  external length : t -> Coord.t -> Coord.t = "bezier_curve_length_wrapper"
  external nearest_point : t -> ?t1:Coord.t -> ?t2:Coord.t -> Point.t -> Coord.t  = "bezier_curve_nearest_point_wrapper"
  external roots : t -> Coord.t -> Coord.dim2 -> Coord.t array = "bezier_curve_roots_wrapper"
  external winding : t -> Point.t -> int = "bezier_curve_winding_wrapper"
  external unit_tangent_at : ?num_derivs:int -> t -> Coord.t -> Point.t = "bezier_curve_unit_tangent_at_wrapper"
  external degrees_of_freedom : t -> int = "bezier_curve_degrees_of_freedom_wrapper"
  external crossings : t -> t -> Crossing.t array = "bezier_curve_crossings_wrapper"

  val of_array : Point.t array -> t
  external to_array : t -> Point.t array = "bezier_curve_points_wrapper"
  val of_tuple_array : (Coord.t * Coord.t) array -> t
  val to_tuple_array : t -> (Coord.t * Coord.t) array
  val of_complex_array : Complex.t array -> t
  val to_complex_array : t -> Complex.t array
end

module Line_segment :
sig
  type t
  external to_curve : t -> Curve.t = "%identity"
  external to_bezier_curve : t -> Bezier_curve.t = "%identity"
  external of_two_points : Point.t -> Point.t -> t = "line_segment_of_two_points_wrapper"
  external order : t -> int = "line_segment_order_wrapper"
  external subdivide : t -> float -> Bezier_curve.t * Bezier_curve.t = "line_segment_subdivide_wrapper"
  external optimize : t -> t = "line_segment_optimize_wrapper"
  external initial_point : t -> Point.t = "line_segment_initial_point_wrapper"
  external final_point : t -> Point.t = "line_segment_final_point_wrapper"
  external is_degenerate : t -> bool = "line_segment_is_degenerate_wrapper"
  external point_at : t -> Coord.t -> Point.t = "line_segment_point_at_wrapper"
  external value_at : t -> Coord.t -> Coord.dim2 -> Coord.t = "line_segment_value_at_wrapper"
  external point_and_derivatives : t -> Coord.t -> int -> Point.t array = "line_segment_point_and_derivatives_wrapper"
  external set_initial : t -> Point.t -> unit = "line_segment_set_initial_wrapper"
  external set_final : t -> Point.t -> unit = "line_segment_set_final_wrapper"
  external bounds_fast : t -> Rect.t = "line_segment_bounds_fast_wrapper"
  external bounds_exact : t -> Rect.t = "line_segment_bounds_exact_wrapper"
  external portion : t -> Coord.t -> Coord.t -> t = "line_segment_portion_wrapper"
  external reverse : t -> t = "line_segment_reverse_wrapper"
  external derivative : t -> Bezier_curve.t = "line_segment_derivative_wrapper"
  external length : t -> Coord.t -> Coord.t = "line_segment_length_wrapper"
  external nearest_point : t -> ?t1:Coord.t -> ?t2:Coord.t -> Point.t -> Coord.t  = "line_segment_nearest_point_wrapper"
  external roots : t -> Coord.t -> Coord.dim2 -> Coord.t array = "line_segment_roots_wrapper"
  external winding : t -> Point.t -> int = "line_segment_winding_wrapper"
  val unit_tangent_at : ?num_derivs:int -> t -> Coord.t -> Point.t
  external degrees_of_freedom : t -> int = "line_segment_degrees_of_freedom_wrapper"
  external crossings : t -> t -> Crossing.t array = "line_segment_crossings_wrapper"

  val of_array : Point.t array -> t
  external to_array : t -> Point.t array = "line_segment_points_wrapper"
  val of_tuple_array : (Coord.t * Coord.t) array -> t
  val to_tuple_array : t -> (Coord.t * Coord.t) array
  val of_complex_array : Complex.t array -> t
  val to_complex_array : t -> Complex.t array
end

module Quadratic_bezier :
sig
  type t
  external to_curve : t -> Curve.t = "%identity"
  external to_bezier_curve : t -> Bezier_curve.t = "%identity"
  external of_three_points : Point.t -> Point.t -> Point.t -> t = "quadratic_bezier_of_three_points_wrapper"
  external order : t -> int = "quadratic_bezier_order_wrapper"
  external subdivide : t -> float -> Bezier_curve.t * Bezier_curve.t = "quadratic_bezier_subdivide_wrapper"
  external optimize : t -> t = "quadratic_bezier_optimize_wrapper"
  external initial_point : t -> Point.t = "quadratic_bezier_initial_point_wrapper"
  external final_point : t -> Point.t = "quadratic_bezier_final_point_wrapper"
  external is_degenerate : t -> bool = "quadratic_bezier_is_degenerate_wrapper"
  external point_at : t -> Coord.t -> Point.t = "quadratic_bezier_point_at_wrapper"
  external value_at : t -> Coord.t -> Coord.dim2 -> Coord.t = "quadratic_bezier_value_at_wrapper"
  external point_and_derivatives : t -> Coord.t -> int -> Point.t array = "quadratic_bezier_point_and_derivatives_wrapper"
  external set_initial : t -> Point.t -> unit = "quadratic_bezier_set_initial_wrapper"
  external set_final : t -> Point.t -> unit = "quadratic_bezier_set_final_wrapper"
  external bounds_fast : t -> Rect.t = "quadratic_bezier_bounds_fast_wrapper"
  external bounds_exact : t -> Rect.t = "quadratic_bezier_bounds_exact_wrapper"
  external portion : t -> Coord.t -> Coord.t -> t = "quadratic_bezier_portion_wrapper"
  external reverse : t -> t = "quadratic_bezier_reverse_wrapper"
  external derivative : t -> Bezier_curve.t = "quadratic_bezier_derivative_wrapper"
  external length : t -> Coord.t -> Coord.t = "quadratic_bezier_length_wrapper"
  external nearest_point : t -> ?t1:Coord.t -> ?t2:Coord.t -> Point.t -> Coord.t  = "quadratic_bezier_nearest_point_wrapper"
  external roots : t -> Coord.t -> Coord.dim2 -> Coord.t array = "quadratic_bezier_roots_wrapper"
  external winding : t -> Point.t -> int = "quadratic_bezier_winding_wrapper"
  val unit_tangent_at : ?num_derivs:int -> t -> Coord.t -> Point.t
  external degrees_of_freedom : t -> int = "quadratic_bezier_degrees_of_freedom_wrapper"
  external crossings : t -> t -> Crossing.t array = "quadratic_bezier_crossings_wrapper"

  val of_array : Point.t array -> t
  external to_array : t -> Point.t array = "quadratic_bezier_points_wrapper"
  val of_tuple_array : (Coord.t * Coord.t) array -> t
  val to_tuple_array : t -> (Coord.t * Coord.t) array
  val of_complex_array : Complex.t array -> t
  val to_complex_array : t -> Complex.t array
end

module Cubic_bezier :
sig
  type t
  external to_curve : t -> Curve.t = "%identity"
  external to_bezier_curve : t -> Bezier_curve.t = "%identity"
  external of_four_points : Point.t -> Point.t -> Point.t -> Point.t -> t = "cubic_bezier_of_four_points_wrapper"
  external order : t -> int = "cubic_bezier_order_wrapper"
  external subdivide : t -> float -> Bezier_curve.t * Bezier_curve.t = "cubic_bezier_subdivide_wrapper"
  external optimize : t -> t = "cubic_bezier_optimize_wrapper"
  external initial_point : t -> Point.t = "cubic_bezier_initial_point_wrapper"
  external final_point : t -> Point.t = "cubic_bezier_final_point_wrapper"
  external is_degenerate : t -> bool = "cubic_bezier_is_degenerate_wrapper"
  external point_at : t -> Coord.t -> Point.t = "cubic_bezier_point_at_wrapper"
  external value_at : t -> Coord.t -> Coord.dim2 -> Coord.t = "cubic_bezier_value_at_wrapper"
  external point_and_derivatives : t -> Coord.t -> int -> Point.t array = "cubic_bezier_point_and_derivatives_wrapper"
  external set_initial : t -> Point.t -> unit = "cubic_bezier_set_initial_wrapper"
  external set_final : t -> Point.t -> unit = "cubic_bezier_set_final_wrapper"
  external bounds_fast : t -> Rect.t = "cubic_bezier_bounds_fast_wrapper"
  external bounds_exact : t -> Rect.t = "cubic_bezier_bounds_exact_wrapper"
  external portion : t -> Coord.t -> Coord.t -> t = "cubic_bezier_portion_wrapper"
  external reverse : t -> t = "cubic_bezier_reverse_wrapper"
  external derivative : t -> Bezier_curve.t = "cubic_bezier_derivative_wrapper"
  external length : t -> Coord.t -> Coord.t = "cubic_bezier_length_wrapper"
  external nearest_point : t -> ?t1:Coord.t -> ?t2:Coord.t -> Point.t -> Coord.t = "cubic_bezier_nearest_point_wrapper"
  external roots : t -> Coord.t -> Coord.dim2 -> Coord.t array = "cubic_bezier_roots_wrapper"
  external winding : t -> Point.t -> int = "cubic_bezier_winding_wrapper"
  val unit_tangent_at : ?num_derivs:int -> t -> Coord.t -> Point.t
  external degrees_of_freedom : t -> int = "cubic_bezier_degrees_of_freedom_wrapper"
  external crossings : t -> t -> Crossing.t array = "cubic_bezier_crossings_wrapper"

  val of_array : Point.t array -> t
  external to_array : t -> Point.t array = "cubic_bezier_points_wrapper"
  val of_tuple_array : (Coord.t * Coord.t) array -> t
  val to_tuple_array : t -> (Coord.t * Coord.t) array
  val of_complex_array : Complex.t array -> t
  val to_complex_array : t -> Complex.t array
end

module Path :
sig
  type t
  type stitching = NO_STITCHING | STITCH_DISCONTINUOUS
  external default : unit -> t = "new_default_path_wrapper"
  external make : Point.t -> t = "new_path_wrapper"
  external point_at : t -> float -> Point.t = "path_point_at_wrapper"
  external value_at : t -> float -> Coord.dim2 -> float = "path_value_at_wrapper"
  external roots : t -> Coord.t -> Coord.dim2 -> Coord.t array = "path_roots_wrapper"
  external portion : t -> float -> float -> t = "path_portion_wrapper"
  external reverse : t -> t = "path_reverse_wrapper"
  external append_curve : ?stitch:stitching -> t -> Curve.t -> unit = "path_append_curve_wrapper"
  external append : ?stitch:stitching -> t -> t -> unit = "path_append_wrapper"
  external nearest_point : ?from_t:float -> ?to_t:float -> t -> Point.t -> float * float = "path_nearest_point_wrapper"
  external size_open : t -> int = "path_size_open_wrapper"
  external size_closed : t -> int = "path_size_closed_wrapper"
  external size_default : t -> int = "path_size_default_wrapper"
  external size : t -> int = "path_size_wrapper"
  external max_size : t -> int = "path_max_size_wrapper"
  external empty : t -> bool = "path_empty_wrapper"
  external closed : t -> bool = "path_closed_wrapper"
  external close : t -> bool -> unit = "path_close_wrapper"
  external bounds_fast : t -> Rect.t option = "path_bounds_fast_wrapper"
  external bounds_exact : t -> Rect.t option = "path_bounds_exact_wrapper"
  external to_cubic_beziers_open : t -> float -> Bezier_curve.t list = "path_to_cubic_bezier_curves_open_wrapper"
  external to_cubic_beziers_closed : t -> float -> Bezier_curve.t list = "path_to_cubic_bezier_curves_closed_wrapper"
  external to_cubic_beziers_default : t -> float -> Bezier_curve.t list = "path_to_cubic_bezier_curves_default_wrapper"
  external winding : t -> Point.t -> int = "path_winding_wrapper"
  external direction : t -> bool = "path_direction_wrapper"
  external contains : ?evenodd:bool -> t -> Point.t -> bool = "path_contains_wrapper"
  external mono_splits : t -> float array = "path_mono_splits_wrapper"
  external crossings_among : t array -> Crossing.t array array = "path_crossings_among_wrapper"
  external self_crossings : t -> Crossing.t array = "path_self_crossings_wrapper"
  external crossings : t -> t -> Crossing.t array = "path_crossings_wrapper"
  external crossings_between : t array -> t array -> Crossing.t array array = "path_crossings_between_wrapper"
end
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