From 561d0f0155f4906d90eb7e73a3ff9cb28909126f Mon Sep 17 00:00:00 2001 From: Sébastien Dailly Date: Fri, 5 Feb 2021 09:08:39 +0100 Subject: Update project structure --- script.it/layer/canvaPrinter.ml | 42 +++ script.it/layer/canvaPrinter.mli | 2 + script.it/layer/ductusEngine.ml | 82 ++++++ script.it/layer/ductusEngine.mli | 2 + script.it/layer/dune | 8 + script.it/layer/fillEngine.ml | 89 ++++++ script.it/layer/fillEngine.mli | 2 + script.it/layer/lineEngine.ml | 68 +++++ script.it/layer/lineEngine.mli | 2 + script.it/layer/paths.ml | 244 ++++++++++++++++ script.it/layer/repr.ml | 49 ++++ script.it/layer/svg.ml | 64 +++++ script.it/layer/wireFramePrinter.ml | 80 ++++++ script.it/layer/wireFramePrinter.mli | 27 ++ script.it/path/builder.ml | 224 +++++++++++++++ script.it/path/builder.mli | 43 +++ script.it/path/dune | 7 + script.it/path/fixed.ml | 487 ++++++++++++++++++++++++++++++++ script.it/path/fixed.mli | 81 ++++++ script.it/path/path.ml | 7 + script.it/path/point.ml | 77 +++++ script.it/path/point.mli | 40 +++ script.it/path/repr.ml | 19 ++ script.it/shapes/bezier.ml | 228 +++++++++++++++ script.it/shapes/bezier.mli | 40 +++ script.it/shapes/bspline.ml | 149 ++++++++++ script.it/shapes/bspline.mli | 24 ++ script.it/shapes/dd_splines.pdf | Bin 0 -> 184248 bytes script.it/shapes/dune | 7 + script.it/shapes/matrix/EltsI.ml | 28 ++ script.it/shapes/matrix/Helpers.ml | 16 ++ script.it/shapes/matrix/Matrix.ml | 529 +++++++++++++++++++++++++++++++++++ script.it/shapes/matrix/MatrixI.ml | 105 +++++++ script.it/shapes/matrix/Order.ml | 2 + script.it/shapes/matrix/dune | 3 + script.it/shapes/tools/dune | 6 + script.it/shapes/tools/utils.ml | 63 +++++ script.it/shapes/tools/utils.mli | 21 ++ 38 files changed, 2967 insertions(+) create mode 100755 script.it/layer/canvaPrinter.ml create mode 100755 script.it/layer/canvaPrinter.mli create mode 100755 script.it/layer/ductusEngine.ml create mode 100755 script.it/layer/ductusEngine.mli create mode 100755 script.it/layer/dune create mode 100755 script.it/layer/fillEngine.ml create mode 100755 script.it/layer/fillEngine.mli create mode 100755 script.it/layer/lineEngine.ml create mode 100755 script.it/layer/lineEngine.mli create mode 100755 script.it/layer/paths.ml create mode 100755 script.it/layer/repr.ml create mode 100755 script.it/layer/svg.ml create mode 100755 script.it/layer/wireFramePrinter.ml create mode 100755 script.it/layer/wireFramePrinter.mli create mode 100755 script.it/path/builder.ml create mode 100755 script.it/path/builder.mli create mode 100755 script.it/path/dune create mode 100755 script.it/path/fixed.ml create mode 100755 script.it/path/fixed.mli create mode 100755 script.it/path/path.ml create mode 100755 script.it/path/point.ml create mode 100755 script.it/path/point.mli create mode 100755 script.it/path/repr.ml create mode 100755 script.it/shapes/bezier.ml create mode 100755 script.it/shapes/bezier.mli create mode 100755 script.it/shapes/bspline.ml create mode 100755 script.it/shapes/bspline.mli create mode 100755 script.it/shapes/dd_splines.pdf create mode 100755 script.it/shapes/dune create mode 100755 script.it/shapes/matrix/EltsI.ml create mode 100755 script.it/shapes/matrix/Helpers.ml create mode 100755 script.it/shapes/matrix/Matrix.ml create mode 100755 script.it/shapes/matrix/MatrixI.ml create mode 100755 script.it/shapes/matrix/Order.ml create mode 100755 script.it/shapes/matrix/dune create mode 100755 script.it/shapes/tools/dune create mode 100755 script.it/shapes/tools/utils.ml create mode 100755 script.it/shapes/tools/utils.mli (limited to 'script.it') diff --git a/script.it/layer/canvaPrinter.ml b/script.it/layer/canvaPrinter.ml new file mode 100755 index 0000000..23cf842 --- /dev/null +++ b/script.it/layer/canvaPrinter.ml @@ -0,0 +1,42 @@ +module Path = Brr_canvas.C2d.Path +module V2 = Gg.V2 + +type t = Path.t + +let create + : unit -> t + = Path.create + +(* Start a new path. *) +let move_to + : Gg.v2 -> t -> t + = fun point path -> + let x, y = V2.to_tuple point in + Path.move_to ~x ~y path; + path + +let line_to + : Gg.v2 -> t -> t + = fun point path -> + let x, y = V2.to_tuple point in + Path.line_to ~x ~y path; + path + +let quadratic_to + : Gg.v2 -> Gg.v2 -> Gg.v2 -> t -> t + = fun ctrl0 ctrl1 p1 path -> + let cx, cy = V2.to_tuple ctrl0 + and cx', cy' = V2.to_tuple ctrl1 + and x, y = V2.to_tuple p1 in + Path.ccurve_to + ~cx ~cy + ~cx' ~cy' + ~x ~y + path; + path + +let close + : t -> t + = fun path -> + Path.close path; + path diff --git a/script.it/layer/canvaPrinter.mli b/script.it/layer/canvaPrinter.mli new file mode 100755 index 0000000..0c46448 --- /dev/null +++ b/script.it/layer/canvaPrinter.mli @@ -0,0 +1,2 @@ +include Repr.PRINTER + with type t = Brr_canvas.C2d.Path.t diff --git a/script.it/layer/ductusEngine.ml b/script.it/layer/ductusEngine.ml new file mode 100755 index 0000000..b943467 --- /dev/null +++ b/script.it/layer/ductusEngine.ml @@ -0,0 +1,82 @@ +module Make(Layer: Repr.PRINTER) = struct + + type point = Path.Point.t + + type t = + { path: (Layer.t) + } + + type repr = Layer.t + + let create_path + : 'b -> t + = fun _ -> + { path = Layer.create () + } + + let start + : point -> point -> t -> t + = fun p1 p2 { path } -> + let path = + Layer.move_to (Path.Point.get_coord p1) path + |> Layer.line_to (Path.Point.get_coord p2) in + { path + } + + let line_to + : (point * point) -> (point * point) -> t -> t + = fun (_, p1) (_, p1') {path} -> + let path = Layer.move_to (Path.Point.get_coord p1) path in + let path = Layer.line_to (Path.Point.get_coord p1') path in + { path + } + + let quadratic_to + : (point * Gg.v2 * Gg.v2 * point) -> (point * Gg.v2 * Gg.v2 * point) -> t -> t + = fun (p0, ctrl0, ctrl1, p1) (p0', ctrl0', ctrl1', p1') {path} -> + + let bezier = + { Shapes.Bezier.p0 = Path.Point.get_coord p0 + ; ctrl0 + ; ctrl1 + ; p1 = Path.Point.get_coord p1 + } + + and bezier' = + { Shapes.Bezier.p0 = Path.Point.get_coord p0' + ; ctrl0 = ctrl0' + ; ctrl1 = ctrl1' + ; p1 = Path.Point.get_coord p1' + } in + + (* Mark each point on the bezier curve. The first point is the most + recent point *) + let delay = + ((Path.Point.get_stamp p0) -. (Path.Point.get_stamp p1)) + *. 30. + in + let path = ref path in + for i = 0 to ((Int.of_float delay) ) do + let ratio = (Float.of_int i) /. delay in + let bezier, _ = Shapes.Bezier.slice ratio bezier + and bezier', _ = Shapes.Bezier.slice ratio bezier' in + + let point = Path.Point.mix ratio bezier.Shapes.Bezier.p1 p0 p1 + and point' = Path.Point.mix ratio bezier'.Shapes.Bezier.p1 p0' p1' in + + path := Layer.move_to (Path.Point.get_coord point) !path; + path := Layer.line_to (Path.Point.get_coord point') !path; + done; + + { path = !path } + + let stop + : t -> t + = fun path -> path + + + let get + : t -> Layer.t + = fun {path; _} -> + path +end diff --git a/script.it/layer/ductusEngine.mli b/script.it/layer/ductusEngine.mli new file mode 100755 index 0000000..e1660f4 --- /dev/null +++ b/script.it/layer/ductusEngine.mli @@ -0,0 +1,2 @@ +module Make(R:Repr.PRINTER): + Repr.ENGINE with type repr = R.t diff --git a/script.it/layer/dune b/script.it/layer/dune new file mode 100755 index 0000000..3c617ad --- /dev/null +++ b/script.it/layer/dune @@ -0,0 +1,8 @@ +(library + (name layer) + (libraries + gg + brr + path + ) + ) diff --git a/script.it/layer/fillEngine.ml b/script.it/layer/fillEngine.ml new file mode 100755 index 0000000..9a3fe7e --- /dev/null +++ b/script.it/layer/fillEngine.ml @@ -0,0 +1,89 @@ +module Make(Layer: Repr.PRINTER) = struct + + type point = Path.Point.t + + type repr = Layer.t + + type t = + { path: Layer.t + ; close : Layer.t -> Layer.t + } + + let create_path + : (Layer.t -> Layer.t) -> t + = fun f -> + { close = f + ; path = Layer.create () + } + + (* Start a new path. *) + + let start + : point -> point -> t -> t + = fun p1 _ {close ; path } -> + let path = Layer.move_to (Path.Point.get_coord p1) path in + { close + ; path + } + + let line_to + : (point * point) -> (point * point) -> t -> t + = fun (p0, p1) (p0', p1') t -> + + let p0 = Path.Point.get_coord p0 + and p1 = Path.Point.get_coord p1 + and p0' = Path.Point.get_coord p0' + and p1' = Path.Point.get_coord p1' in + + let path = + Layer.move_to p1 t.path + |> Layer.line_to p1' + |> Layer.line_to p0' + |> Layer.line_to p0 + |> Layer.line_to p1 + |> Layer.close in + let path = t.close path in + { t with path} + + let quadratic_to + : (point * Gg.v2 * Gg.v2 * point) -> (point * Gg.v2 * Gg.v2 * point) -> t -> t + = fun (p0, ctrl0, ctrl1, p1) (p0', ctrl0', ctrl1', p1') t -> + + let p0 = Path.Point.get_coord p0 + and p1 = Path.Point.get_coord p1 + and p0' = Path.Point.get_coord p0' + and p1' = Path.Point.get_coord p1' + in + + let path = + Layer.move_to p1 t.path + |> Layer.line_to p1' + + (* Backward *) + |> Layer.quadratic_to + ctrl1' + ctrl0' + p0' + |> Layer.line_to p0 + + (* Forward *) + |> Layer.quadratic_to + ctrl0 + ctrl1 + p1 + |> Layer.close + |> t.close in + + + { t with path } + + let stop + : t -> t + = fun t -> + t + + let get + : t -> Layer.t + = fun t -> + t.path +end diff --git a/script.it/layer/fillEngine.mli b/script.it/layer/fillEngine.mli new file mode 100755 index 0000000..e1660f4 --- /dev/null +++ b/script.it/layer/fillEngine.mli @@ -0,0 +1,2 @@ +module Make(R:Repr.PRINTER): + Repr.ENGINE with type repr = R.t diff --git a/script.it/layer/lineEngine.ml b/script.it/layer/lineEngine.ml new file mode 100755 index 0000000..3d15d9c --- /dev/null +++ b/script.it/layer/lineEngine.ml @@ -0,0 +1,68 @@ +module Make(Layer: Repr.PRINTER) = struct + + type point = Path.Point.t + + let mark point path = + let open Gg.V2 in + let point = Path.Point.get_coord point in + + let dist = 5. + and dist' = -5. in + + let path = Layer.move_to (point - (of_tuple (dist, dist))) path + |> Layer.line_to ( point + (of_tuple (dist, dist))) + |> Layer.move_to (point + (of_tuple (dist', dist))) + |> Layer.line_to ( point + (of_tuple (dist, dist'))) + in + path + + + type t = + { path: (Layer.t) + } + + type repr = Layer.t + + let create_path + : 'b -> t + = fun _ -> + { path = Layer.create () + } + + let start + : point -> point -> t -> t + = fun p1 _ { path } -> + let path = mark p1 path in + { path + } + + let line_to + : (point * point) -> (point * point) -> t -> t + = fun (p0, p1) _ {path} -> + let path = Layer.move_to (Path.Point.get_coord p0) path + |> Layer.line_to (Path.Point.get_coord p1) + |> mark p1 in + { path + } + + let quadratic_to + : (point * Gg.v2 * Gg.v2 * point) -> (point * Gg.v2 * Gg.v2 * point) -> t -> t + = fun (p0, ctrl0, ctrl1, p1) _ {path} -> + + let path = Layer.move_to (Path.Point.get_coord p0) path + |> Layer.quadratic_to ctrl0 ctrl1 (Path.Point.get_coord p1) + |> mark p1 in + + { path = path } + + let stop + : t -> t + = fun path -> path + + + let get + : t -> Layer.t + = fun {path; _} -> + path + +end diff --git a/script.it/layer/lineEngine.mli b/script.it/layer/lineEngine.mli new file mode 100755 index 0000000..86ef5fb --- /dev/null +++ b/script.it/layer/lineEngine.mli @@ -0,0 +1,2 @@ +module Make(R:Repr.PRINTER): + Repr.ENGINE with type repr = R.t diff --git a/script.it/layer/paths.ml b/script.it/layer/paths.ml new file mode 100755 index 0000000..d3baf02 --- /dev/null +++ b/script.it/layer/paths.ml @@ -0,0 +1,244 @@ +open StdLabels +(** Common module for ensuring that the function is evaluated only once *) + +(** This represent a single path, which can be transformed throug a [repr] + function. *) +module type PATH = sig + type t + + (** Represent the path *) + val repr + : t -> (module Path.Repr.M + with type point = Path.Point.t + and type t = 's) -> 's -> 's +end + +type printer = + [ `Fill + | `Line + | `Ductus ] + + +module type P = sig + include Path.Repr.M + + type repr + + val create_path + : (repr -> repr) -> t + + val get + : t -> repr +end + + +module MakePrinter(M:Repr.ENGINE) : P + with type point = M.point + and type t = M.t + and type repr = M.repr = struct + + type t = M.t + + type point = M.point + + type repr = M.repr + + let get + : t -> repr + = M.get + + let create_path + : (repr -> repr) -> t + = M.create_path + + let start + : Path.Point.t -> t -> t + = fun pt t -> + M.start pt pt t + + let line_to + : Path.Point.t -> Path.Point.t -> t -> t + = fun p0 p1 t -> + + M.line_to + ( p0 + , p1 ) + ( Path.Point.copy p0 @@ Path.Point.get_coord' p0 + , Path.Point.copy p1 @@ Path.Point.get_coord' p1 ) + t + + let quadratic_to + : (Path.Point.t * Gg.v2 * Gg.v2 * Path.Point.t) -> t -> t + = fun (p0, ctrl0, ctrl1, p1) t -> + + + let ctrl0' = Path.Point.get_coord' @@ Path.Point.copy p0 ctrl0 + and ctrl1' = Path.Point.get_coord' @@ Path.Point.copy p1 ctrl1 in + M.quadratic_to + (p0, ctrl0, ctrl1, p1) + (Path.Point.copy p0 @@ Path.Point.get_coord' p0, ctrl0', ctrl1', Path.Point.copy p1 @@ Path.Point.get_coord' p1) + + t + + let stop = M.stop +end + +(** Transform the two path, into a single one. *) +module ReprSingle = struct + + type point = Path.Point.t + + type repr = + | Move of (point) + | Line_to of (point * point) + | Quadratic of (point * Gg.v2 * Gg.v2 * point) + + module R = struct + type t = repr list + + type point = Path.Point.t + + let start t actions = + (Move t)::actions + + let line_to p0 p1 actions = + Line_to (p0, p1)::actions + + let quadratic_to + : (point * Gg.v2 * Gg.v2 * point) -> t -> t + = fun q actions -> + (Quadratic q)::actions + + let stop + : t -> t + = fun v -> v + + end + + let repr + : (module PATH with type t = 't) -> 't -> 't -> repr list * repr list + = fun (type t) (module P:PATH with type t = t) path back -> + let path = P.repr path (module R) [] + and back = P.repr back (module R) [] in + path, back +end + +(* Canva representation *) + +module FillCanva = FillEngine.Make(CanvaPrinter) +module LineCanva = LineEngine.Make(CanvaPrinter) +module DuctusCanva = DuctusEngine.Make(CanvaPrinter) + +(* SVG representation *) + +module FillSVG = FillEngine.Make(Svg) +module DuctusSVG = DuctusEngine.Make(Svg) + + +(** Draw a path to a canva.contents + + The code may seems scary, but is very repetitive. Firt, all points (from the + main stroke, and the interior one) are evaluated. Then, they are both rendered + using the selected engine. +*) +let to_canva + : (module PATH with type t = 's) -> 's * 's -> Brr_canvas.C2d.t -> printer -> unit + = fun (type s) (module R:PATH with type t = s) (path, back) ctx engine -> + let f, b = ReprSingle.repr (module R) path back in + match engine with + | `Fill -> + let t = List.fold_left2 f b + ~init:(FillCanva.create_path (fun p -> Brr_canvas.C2d.fill ctx p; p)) + ~f:(fun ctx f b -> + match (f, b) with + | ReprSingle.Move p0, ReprSingle.Move p0' -> FillCanva.start p0 p0' ctx + | ReprSingle.Line_to l, ReprSingle.Line_to l' -> FillCanva.line_to l l' ctx + | ReprSingle.Quadratic q, ReprSingle.Quadratic q' -> FillCanva.quadratic_to q q' ctx + | _ -> ctx + ) in + FillCanva.get t + |> Brr_canvas.C2d.stroke ctx + | `Line -> + let t = List.fold_left2 f b + ~init:(LineCanva.create_path (fun p -> Brr_canvas.C2d.fill ctx p; p)) + ~f:(fun ctx f b -> + match (f, b) with + | ReprSingle.Move p0, ReprSingle.Move p0' -> LineCanva.start p0 p0' ctx + | ReprSingle.Line_to l, ReprSingle.Line_to l' -> LineCanva.line_to l l' ctx + | ReprSingle.Quadratic q, ReprSingle.Quadratic q' -> LineCanva.quadratic_to q q' ctx + | _ -> ctx + ) in + LineCanva.get t + |> Brr_canvas.C2d.stroke ctx + | `Ductus -> + let t = List.fold_left2 f b + ~init:(DuctusCanva.create_path (fun p -> Brr_canvas.C2d.fill ctx p; p)) + ~f:(fun ctx f b -> + match (f, b) with + | ReprSingle.Move p0, ReprSingle.Move p0' -> DuctusCanva.start p0 p0' ctx + | ReprSingle.Line_to l, ReprSingle.Line_to l' -> DuctusCanva.line_to l l' ctx + | ReprSingle.Quadratic q, ReprSingle.Quadratic q' -> DuctusCanva.quadratic_to q q' ctx + | _ -> ctx + ) in + DuctusCanva.get t + |> Brr_canvas.C2d.stroke ctx + + + +(** Draw a path and represent it as SVG *) +let to_svg + : (module PATH with type t = 's) -> color:Jstr.t -> 's * 's -> printer -> Brr.El.t + = fun (type s) (module R:PATH with type t = s) ~color (path, back) engine -> + let f, b = ReprSingle.repr (module R) path back in + match engine with + | `Fill -> + + (* In order to deal with over crossing path, I cut the path in as + many segment as there is curve, and fill them all. Then, all of theme + are grouped inside a single element *) + let paths = ref [] in + let init = (FillSVG.create_path + (fun p -> + let repr = Svg.path + ~at:Brr.At.[ v (Jstr.v "d") p ] + [] in + + paths := repr::!paths; + Jstr.empty)) in + let _ = List.fold_left2 f b + ~init + ~f:(fun ctx f b -> + match (f, b) with + | ReprSingle.Move p0, ReprSingle.Move p0' -> FillSVG.start p0 p0' ctx + | ReprSingle.Line_to l, ReprSingle.Line_to l' -> FillSVG.line_to l l' ctx + | ReprSingle.Quadratic q, ReprSingle.Quadratic q' -> FillSVG.quadratic_to q q' ctx + | _ -> ctx + ) in + + Brr.El.v (Jstr.v "g") + ~at:Brr.At.[ + v (Jstr.v "fill") color + ; v (Jstr.v "stroke") color] + !paths + + | `Ductus -> + let init = DuctusSVG.create_path (fun _ -> Jstr.empty) in + let svg_path = List.fold_left2 f b + ~init + ~f:(fun ctx f b -> + match (f, b) with + | ReprSingle.Move p0, ReprSingle.Move p0' -> DuctusSVG.start p0 p0' ctx + | ReprSingle.Line_to l, ReprSingle.Line_to l' -> DuctusSVG.line_to l l' ctx + | ReprSingle.Quadratic q, ReprSingle.Quadratic q' -> DuctusSVG.quadratic_to q q' ctx + | _ -> ctx + ) + |> DuctusSVG.get in + + Svg.path + ~at:Brr.At.[ + v (Jstr.v "fill") color + ; v (Jstr.v "stroke") color + ; v (Jstr.v "d") svg_path ] + [] + | `Line -> + raise Not_found diff --git a/script.it/layer/repr.ml b/script.it/layer/repr.ml new file mode 100755 index 0000000..552e2b7 --- /dev/null +++ b/script.it/layer/repr.ml @@ -0,0 +1,49 @@ +module type PRINTER = sig + + type t + + val create: unit -> t + + (* Start a new path. *) + val move_to: Gg.v2 -> t -> t + + val line_to: Gg.v2 -> t -> t + + (** [quadratic_to ctrl0 ctrl1 p1] create a quadratic curve from the current + point to [p1], with control points [ctrl0] and [ctrl1] *) + val quadratic_to: Gg.v2 -> Gg.v2 -> Gg.v2 -> t -> t + + (** Request for the path to be closed *) + val close: t -> t + +end + +module type ENGINE = sig + type t + + type point = Path.Point.t + + type repr + + val get + : t -> repr + + val create_path + : (repr -> repr) -> t + + val start + : point -> point -> t -> t + + val line_to + : (point * point) -> (point * point) -> t -> t + + val quadratic_to + : (point * Gg.v2 * Gg.v2 * point) + -> (point * Gg.v2 * Gg.v2 * point) + -> t + -> t + + val stop + : t -> t + +end diff --git a/script.it/layer/svg.ml b/script.it/layer/svg.ml new file mode 100755 index 0000000..2394cb8 --- /dev/null +++ b/script.it/layer/svg.ml @@ -0,0 +1,64 @@ +(** SVG representation *) + +open Brr + +module V2 = Gg.V2 + +let svg : El.cons + = fun ?d ?at childs -> + El.v ?d ?at (Jstr.v "svg") childs + +let path: El.cons + = fun ?d ?at childs -> + El.v ?d ?at (Jstr.v "path") childs + +type t = Jstr.t + +let create + : unit -> t + = fun () -> Jstr.empty + +(* Start a new path. *) +let move_to + : Gg.v2 -> t -> t + = fun point path -> + let x, y = V2.to_tuple point in + + Jstr.concat ~sep:(Jstr.v " ") + [ path + ; Jstr.v "M" + ; Jstr.of_float x + ; Jstr.of_float y ] + +let line_to + : Gg.v2 -> t -> t + = fun point path -> + let x, y = V2.to_tuple point in + Jstr.concat ~sep:(Jstr.v " ") + [ path + ; (Jstr.v "L") + ; (Jstr.of_float x) + ; (Jstr.of_float y) ] + +let quadratic_to + : Gg.v2 -> Gg.v2 -> Gg.v2 -> t -> t + = fun ctrl0 ctrl1 p1 path -> + let cx, cy = V2.to_tuple ctrl0 + and cx', cy' = V2.to_tuple ctrl1 + and x, y = V2.to_tuple p1 in + Jstr.concat ~sep:(Jstr.v " ") + [ path + ; (Jstr.v "C") + ; (Jstr.of_float cx) + ; (Jstr.of_float cy) + ; (Jstr.v ",") + ; (Jstr.of_float cx') + ; (Jstr.of_float cy') + ; (Jstr.v ",") + ; (Jstr.of_float x) + ; (Jstr.of_float y) ] + +let close + : t -> t + = fun path -> + Jstr.append path (Jstr.v " Z") diff --git a/script.it/layer/wireFramePrinter.ml b/script.it/layer/wireFramePrinter.ml new file mode 100755 index 0000000..81ab271 --- /dev/null +++ b/script.it/layer/wireFramePrinter.ml @@ -0,0 +1,80 @@ +module Point = Path.Point + +module Make(Repr: Repr.PRINTER) = struct + type t = Point.t + + type repr = + { back: (Repr.t -> Repr.t) + ; path: (Repr.t) + ; last_point : Point.t option + } + + let create_path + : 'b -> repr + = fun _ -> + { back = Repr.close + ; path = Repr.create () + ; last_point = None + } + + (* Start a new path. *) + let start + : Point.t -> repr -> repr + = fun t {back; path; _} -> + let path = Repr.move_to (Point.get_coord t) path in + let line' = Repr.line_to (Point.get_coord' t) in + { back = (fun p -> back @@ line' p) + ; path + ; last_point = Some t + } + + let line_to + : Point.t -> Point.t -> repr -> repr + = fun _ t {back; path; _} -> + let line' = Repr.line_to (Point.get_coord' t) in + { back = (fun t -> back @@ line' t) + ; path = Repr.line_to (Point.get_coord t) path + ; last_point = Some t + } + + let quadratic_to + : Point.t -> Gg.v2 -> Gg.v2 -> Point.t -> repr -> repr + = fun p0 ctrl0 ctrl1 p1 t -> + + let ctrl0' = Point.copy p1 ctrl0 + and ctrl1' = Point.copy p1 ctrl1 in + + let line' path = + Repr.quadratic_to + (Point.get_coord' @@ ctrl1') + (Point.get_coord' ctrl0') + (Point.get_coord' p0) path in + + let path = Repr.quadratic_to + (Point.get_coord ctrl0') + (Point.get_coord ctrl1') + (Point.get_coord p1) + t.path in + { back = (fun p -> t.back @@ line' p) + ; path + ; last_point = Some p1 + } + + let stop + : repr -> repr + = fun {back; path; last_point} -> + + let path = + match last_point with + | Some point -> Repr.line_to (Point.get_coord' point) path + | None -> path in + + { back = (fun x -> x) + ; path = back path + ; last_point = None } + + let get + : repr -> Repr.t + = fun {back; path; _} -> + back path +end diff --git a/script.it/layer/wireFramePrinter.mli b/script.it/layer/wireFramePrinter.mli new file mode 100755 index 0000000..b198d58 --- /dev/null +++ b/script.it/layer/wireFramePrinter.mli @@ -0,0 +1,27 @@ +module Make(Repr:Repr.PRINTER): sig + + type repr + + type t = Path.Point.t + + val create_path + : 'b -> repr + + (* Start a new path. *) + val start + : Path.Point.t -> repr -> repr + + val line_to + : Path.Point.t -> Path.Point.t -> repr -> repr + + val quadratic_to + : Path.Point.t -> Gg.v2 -> Gg.v2 -> Path.Point.t -> repr -> repr + + val stop + : repr -> repr + + + val get + : repr -> Repr.t + +end diff --git a/script.it/path/builder.ml b/script.it/path/builder.ml new file mode 100755 index 0000000..4403599 --- /dev/null +++ b/script.it/path/builder.ml @@ -0,0 +1,224 @@ +open StdLabels + +(** Signature for points *) +module type P = sig + type t + + val empty : t + + val get_coord : t -> Gg.v2 + + val copy : t -> Gg.v2 -> t + +end + +module Make(Point:P) = struct + + (** Point creation **) + + type bezier = + { p0:Point.t (* The starting point *) + ; p1:Point.t (* The end point *) + ; ctrl0:Gg.v2 (* The control point *) + ; ctrl1:Gg.v2 } (* The control point *) + + type t = Point.t list * bezier list + + let get_new_segment connexion0 p5 p4 p3 p2 p1 = + let p5' = Point.get_coord p5 + and p4' = Point.get_coord p4 + and p3' = Point.get_coord p3 + and p2' = Point.get_coord p2 + and p1' = Point.get_coord p1 in + + let points_to_link = + [ p1' + ; p2' + ; p3' + ; p4' + ; p5' ] in + Shapes.Bspline.to_bezier ?connexion0 points_to_link + + let empty = ([], []) + + let add_point + : Point.t -> t -> t + = fun lastPoint (path, beziers) -> + let (let*) v f = + match v with + | Ok bezier -> + if Array.length bezier > 0 then + f (Array.get bezier 0) + else + (lastPoint::path, beziers) + | _ -> + (lastPoint::path, beziers) + in + + let connexion0 = match beziers with + | hd::_ -> Some (Point.get_coord hd.p1) + | _ -> None in + + match path with + | p4::p3::p2::p1::_ -> + let* bezier = get_new_segment connexion0 + lastPoint p4 p3 p2 p1 in + + let bezier_point = + { p0 = p2 + ; p1 = p1 + ; ctrl0 = bezier.Shapes.Bezier.ctrl1 + ; ctrl1 = bezier.Shapes.Bezier.ctrl0 + } in + + (* We remove the last point and add the bezier curve in the list*) + let firsts = lastPoint::p4::p3::p2::[] in + (firsts, bezier_point::beziers) + | _ -> + ( lastPoint::path + , beziers) + + let replace_last + : Point.t -> t -> t + = fun lastPoint ((path, beziers) as t) -> + match path, beziers with + | _::(tl), beziers -> + + ( lastPoint::tl + , beziers ) + | _ -> + add_point lastPoint t + + let peek2 + : t -> (Point.t * Point.t) option + = fun (path, _) -> + match path with + | h1::h2::_ -> Some (h1, h2) + | _ -> None + + let peek + : t -> Point.t option + = fun (path, _) -> + match path with + | [] -> None + | hd::_ -> Some hd + + let repr + : t -> (module Repr.M with type point = Point.t and type t = 's) -> 's -> 's + = fun (type s) (points, beziers) (module Repr : Repr.M with type point = Point.t and type t = s) path -> + + (* Represent the last points *) + let path = match points with + | [] -> + ( path ) + | p1::[] -> + ( Repr.start p1 path ) + | p1::p2::[] -> + let path = + Repr.start p1 path + |> Repr.line_to p1 p2 in + ( path ) + | p0::p1::p2::[] -> + + let b0, b1 = Shapes.Bezier.quadratic_to_cubic + @@ Shapes.Bezier.three_points_quadratic + (Point.get_coord p0) + (Point.get_coord p1) + (Point.get_coord p2) + |> Shapes.Bezier.slice 0.5 + in + let p0' = Point.copy p0 b0.Shapes.Bezier.p0 + and p1' = Point.copy p1 b0.Shapes.Bezier.p1 + and p2' = Point.copy p2 b1.Shapes.Bezier.p1 in + + Repr.start p0 path + |> Repr.quadratic_to + ( p0' + , b0.Shapes.Bezier.ctrl0 + , b0.Shapes.Bezier.ctrl1 + , p1' ) + |> Repr.quadratic_to + ( p1' + , b1.Shapes.Bezier.ctrl0 + , b1.Shapes.Bezier.ctrl1 + , p2' ) + | (p0::_ as points) -> + + let (let*) v f = + match v with + | Ok beziers -> f beziers + | _ -> path in + + let points' = List.map ~f:Point.get_coord points in + let connexion = match beziers with + | [] -> None + | hd ::_ -> Some (Point.get_coord hd.p1) in + + let* beziers = Shapes.Bspline.to_bezier ?connexion1:connexion points' in + + (* Stdlib does not provide fold_left_i function and we need to map + each bezier point with the associated point in the curve. + + So I use references here for keeping each result element + + *) + let path = ref path in + let point = ref p0 in + + List.iteri + points + ~f:(fun i pt -> + + (* The first iteration is ignored, as we need both previous and + current point for the two point in the curve. + + Do not forget that there is always n-1 bezier curve for n + points *) + if i > 0 then ( + + let bezier = Array.get beziers (i - 1) in + + path := Repr.quadratic_to + ( !point + , bezier.Shapes.Bezier.ctrl0 + , bezier.Shapes.Bezier.ctrl1 + , pt ) + (!path); + point := pt; + ) + ); + ( !path ) + in + + (* Now represent the already evaluated points. Much easer to do, just + iterate on them *) + Repr.stop @@ List.fold_left beziers + ~init:path + ~f:(fun path bezier -> + Repr.quadratic_to + ( bezier.p0 + , bezier.ctrl0 + , bezier.ctrl1 + , bezier.p1 ) + path + ) + + let map + : t -> (Point.t -> Point.t) -> t + = fun (points, beziers) f -> + let points = List.map + points + ~f + and beziers = List.map + beziers + ~f:(fun bezier -> + + { p0 = f bezier.p0 + ; p1 = f bezier.p1 + ; ctrl0 = Point.(get_coord (f ( copy bezier.p0 bezier.ctrl0))) + ; ctrl1 = Point.(get_coord (f ( copy bezier.p1 bezier.ctrl1))) + } + ) in + points, beziers + +end diff --git a/script.it/path/builder.mli b/script.it/path/builder.mli new file mode 100755 index 0000000..2afbd4b --- /dev/null +++ b/script.it/path/builder.mli @@ -0,0 +1,43 @@ +(** Signature for points *) +module type P = sig + type t + + val empty : t + + val get_coord : t -> Gg.v2 + + (** Copy a point and all thoses properties to the given location *) + val copy : t -> Gg.v2 -> t + +end + +module Make(Point:P) : sig + + type t + + (** Create an empty path *) + val empty: t + + val add_point + : Point.t -> t -> t + + (** Replace the last alement in the path by the one given in parameter *) + val replace_last + : Point.t -> t -> t + + (** Retrieve the last element, if any *) + val peek + : t -> Point.t option + + (** Retrieve the last element, if any *) + val peek2 + : t -> (Point.t * Point.t) option + + (** Represent the path *) + val repr + : t -> (module Repr.M with type point = Point.t and type t = 's) -> 's -> 's + + val map + : t -> (Point.t -> Point.t) -> t + +end diff --git a/script.it/path/dune b/script.it/path/dune new file mode 100755 index 0000000..863c768 --- /dev/null +++ b/script.it/path/dune @@ -0,0 +1,7 @@ +(library + (name path) + (libraries + gg + shapes + ) + ) diff --git a/script.it/path/fixed.ml b/script.it/path/fixed.ml new file mode 100755 index 0000000..1362ad3 --- /dev/null +++ b/script.it/path/fixed.ml @@ -0,0 +1,487 @@ +open StdLabels + +(** Signature for points *) +module type P = sig + type t + + val get_coord : t -> Gg.v2 + + val id : t -> int + + val copy : t -> Gg.v2 -> t + +end + +module Make(Point:P) = struct + + type bezier = + { ctrl0:Gg.v2 (* The control point *) + ; ctrl1:Gg.v2 (* The control point *) + ; p1:Point.t (* The end point *) + } + + module type BUILDER = sig + type t + + val repr + : t -> (module Repr.M with type point = Point.t and type t = 's) -> 's -> 's + end + + type path = + | Line of Point.t + | Curve of bezier + + + type step = + { point : Point.t + ; move : path + } + + type t = step array + + module ToFixed = struct + type point = Point.t + + type t = int * step list + + let create_path () = 0, [] + + (* Start a new path. *) + let start point t = + let _ = point in + t + + let line_to + : point -> point -> t -> t + = fun p1 p2 (i, t) -> + ( i + 1 + , { point = p1 + ; move = Line p2 + }:: t ) + + let quadratic_to + : (point * Gg.v2 * Gg.v2 * point) -> t -> t + = fun (p0, ctrl0, ctrl1, p1) (i, t) -> + let curve = Curve + { ctrl0 + ; ctrl1 + ; p1} in + ( i + 1 + , { point = p0 + ; move = curve + } ::t) + + let stop t = t + + let get + : int * step list -> step array + = fun (n, t) -> + + (* The array is initialized with a magic number, and just after + filled with the values from the list in reverse. All the elements are set. + *) + let res = Obj.magic (Array.make n 0) in + List.iteri t + ~f:(fun i elem -> Array.set res (n - i - 1) elem ); + res + end + + let to_fixed + : (module BUILDER with type t = 'a) -> 'a -> t + = fun (type s) (module Builder: BUILDER with type t = s) t -> + Builder.repr t (module ToFixed) (ToFixed.create_path ()) + |> ToFixed.get + + let repr + : t -> (module Repr.M with type point = Point.t and type t = 's) -> 's -> 's + = fun (type s) t (module Repr : Repr.M with type point = Point.t and type t = s) repr -> + let repr_bezier p p0 bezier = + Repr.quadratic_to + ( p0 + , bezier.ctrl0 + , bezier.ctrl1 + , bezier.p1 ) + p in + + let _, repr = Array.fold_left t + ~init:(true, repr) + ~f:(fun (first, path) element -> + let path = if first then + Repr.start element.point path + else path in + match element.move with + | Line p1 -> + ( false + , Repr.line_to element.point p1 path ) + | Curve bezier -> + ( false + , repr_bezier path element.point bezier ) + ) in + Repr.stop repr + + + type approx = + { distance : float + ; closest_point : Gg.v2 + ; ratio : float + ; p0 : Point.t + ; p1 : Point.t } + + (** Return the distance between a given point and the curve. May return + None if the point is out of the curve *) + let distance + : Gg.v2 -> t -> approx option + = fun point t -> + + Array.fold_left t + ~init:None + ~f:(fun res step -> + match step.move with + | Line p1 -> + let box = Gg.Box2.of_pts (Point.get_coord step.point) (Point.get_coord p1) in + begin match Gg.Box2.mem point box with + | false -> res + | true -> + (* TODO Evaluate the normal *) + res + end + | Curve bezier -> + + let bezier' = Shapes.Bezier.( + + { p0 = Point.get_coord step.point + ; p1 = Point.get_coord bezier.p1 + ; ctrl0 = bezier.ctrl0 + ; ctrl1 = bezier.ctrl1 } + ) in + let ratio, point' = Shapes.Bezier.get_closest_point point bezier' in + let distance' = Gg.V2.( norm (point - point') ) in + match res with + | Some {distance; _} when distance < distance' -> res + | _ -> Some + { closest_point = point' + ; distance = distance' + ; p0 = step.point + ; p1 = bezier.p1 + ; ratio } + ) + + let map + : t -> (Point.t -> Point.t) -> t + = fun t f -> + Array.map t + ~f:(fun step -> + match step.move with + | Line p2 -> + { point = f step.point + ; move = Line (f p2) + } + | Curve bezier -> + let point = f step.point in + { point + ; move = Curve + { p1 = f bezier.p1 + ; ctrl0 = Point.get_coord (f (Point.copy step.point bezier.ctrl0)) + ; ctrl1 = Point.get_coord (f (Point.copy bezier.p1 bezier.ctrl1)) + } + } + ) + + let iter + : t -> f:(Point.t -> unit) -> unit + = fun t ~f -> + Array.iter t + ~f:(fun step -> + match step.move with + | Line p2 -> f step.point; f p2 + | Curve bezier -> f step.point ; f bezier.p1 + ) + + let get_point' + : step -> Point.t + = fun { move ; _} -> + match move with + | Line p1 -> p1 + | Curve bezier -> bezier.p1 + + (** Associate the return from the bezier point to an existing path *) + let assoc_point + : Shapes.Bezier.t -> step -> step + = fun bezier step -> + match step.move with + | Line p1 + | Curve {p1; _} -> + let p0' = Point.copy step.point bezier.Shapes.Bezier.p0 + and p1' = Point.copy p1 bezier.Shapes.Bezier.p1 in + { point = p0' + ; move = Curve + { p1 = p1' + ; ctrl0 = bezier.Shapes.Bezier.ctrl0 + ; ctrl1 = bezier.Shapes.Bezier.ctrl1 + } + } + + + let build_from_three_points p0 p1 p2 = + let bezier = + Shapes.Bezier.quadratic_to_cubic + @@ Shapes.Bezier.three_points_quadratic + (Point.get_coord p0) + (Point.get_coord p1) + (Point.get_coord p2) in + + (* The middle point is not exactly at the middle anymore (it can have been + moved), we have the reevaluate it's position *) + let ratio, _ = Shapes.Bezier.get_closest_point + (Point.get_coord p1) + bezier in + + let b0, b1 = Shapes.Bezier.slice ratio bezier in + let p0' = Point.copy p0 b0.Shapes.Bezier.p0 + and p1' = Point.copy p1 b0.Shapes.Bezier.p1 + and p2' = Point.copy p2 b1.Shapes.Bezier.p1 in + + [| { point = p0' + ; move = + Curve { ctrl0 = b0.Shapes.Bezier.ctrl0 + ; ctrl1 = b0.Shapes.Bezier.ctrl1 + ; p1 = p1' + } } + ; { point = p1' + ; move = Curve { ctrl0 = b1.Shapes.Bezier.ctrl0 + ; ctrl1 = b1.Shapes.Bezier.ctrl1 + ; p1 = p2' } + } |] + + (** Rebuild the whole curve by evaluating all the points *) + let rebuild + : t -> t option + = fun t -> + + match Array.length t with + | 0 -> None + | 1 -> + let step = Array.get t 0 in + begin match step.move with + | Curve {p1; _} + | Line p1 -> + Some + [| + { point = step.point + ; move = Line p1 } |] + end + | 2 -> + let p0 = (Array.get t 0).point + and p1 = (Array.get t 1).point + and p2 = get_point' @@ Array.get t 1 in + Some (build_from_three_points p0 p1 p2) + + | _ -> + + (* Convert all the points in list *) + let points = List.init + ~len:((Array.length t) ) + ~f:(fun i -> Point.get_coord @@ get_point' (Array.get t i)) in + let p0 = Point.get_coord @@ (Array.get t 0).point in + + let points = p0::points in + + (* We process the whole curve in a single block *) + begin match Shapes.Bspline.to_bezier points with + | Error `InvalidPath -> None + | Ok beziers -> + + (* Now for each point, reassociate the same point information, + We should have as many points as before *) + let rebuilded = Array.map2 beziers t ~f:assoc_point in + Some rebuilded + end + + let find_pt_index + : Point.t -> step array -> int option + = fun point path -> + (* First search the element to remove. The counter mark the position of + the point to remove, not the segment itself. *) + let idx = ref None + and counter = ref 0 in + + let _ = Array.exists + path + ~f:(fun element -> + let res = + if (Point.id element.point) = (Point.id point) then ( + idx := Some (!counter) ; + true + ) else match element.move with + | Line p1 + | Curve {p1;_} when (Point.id p1) = (Point.id point) -> + idx := Some (!counter+1) ; + true + | _ -> + false + in + incr counter; + res) in + !idx + + let remove_point + : t -> Point.t -> t option + = fun t point -> + + match Array.length t with + | 0 + | 1 -> None + | 2 -> + (* Two segment, we get the points and transform this into a single line *) + let p0 = (Array.get t 0).point + and p1 = (Array.get t 1).point + and p2 = get_point' @@ Array.get t 1 in + let elms = List.filter [p0; p1; p2] + ~f:(fun pt -> Point.id pt != Point.id point) in + begin match elms with + | p0::p1::[] -> + Some + [| { point = p0 + ; move = Line p1 }|] + | _ -> None + end + | l -> + match find_pt_index point t with + | None -> Some t + | Some 0 -> + (* Remove the first point *) + let path = Array.init (l-1) + ~f:( fun i -> Array.get t (i+1)) in + Some path + | Some n when n = (Array.length t) -> + (* Remove the last point *) + let path = Array.init (l-1) + ~f:( fun i -> Array.get t i) in + Some path + | Some n -> + let path' = Array.init (l-1) + ~f:(fun i -> + if i < (n-1) then + Array.get t (i) + else if i = (n-1) then + (* We know that the point is not the first nor the last one. + So it is safe to call n-1 or n + 1 point + + We have to rebuild the point and set that + point_(-1).id = point_(+1).id + *) + let p0 = (Array.get t i).point in + + match (Array.get t (i+1)).move with + | Line p1 -> + { point = p0 + ; move = Line p1 } + | Curve c -> + { point = p0 + ; move = Curve c } + + else + Array.get t (i+1) + ) in + rebuild path' + + let first_point + : step -> Point.t + = fun {point; _} -> point + + let replace_point + : t -> Point.t -> t option + = fun t p -> + + let add_path paths idx f points = + if 0 <= idx && idx < Array.length paths then + let path = Array.get t idx in + Point.get_coord (f path) + :: points + else points in + + match Array.length t with + | 0 -> None + | 1 -> (* Only one point, easy ? *) + let step = Array.get t 0 in + begin match step.move with + | Curve {p1; _} + | Line p1 -> + let p0 = if (Point.id step.point = Point.id p) then p else step.point + and p1 = if (Point.id p1 = Point.id p) then p else p1 in + Some [| + { point = p0 + ; move = Line p1 } + |] + end + + | 2 -> + let p0 = (Array.get t 0).point + and p1 = (Array.get t 1).point + and p2 = get_point' @@ Array.get t 1 in + + let p0 = if (Point.id p0 = Point.id p) then p else p0 + and p1 = if (Point.id p1 = Point.id p) then p else p1 + and p2 = if (Point.id p2 = Point.id p) then p else p2 in + Some (build_from_three_points p0 p1 p2) + + (* More than two segmend, it is ok for a partial reevaluation *) + | _ -> + match find_pt_index p t with + | None -> None + | Some n -> + let path = Array.copy t in + + let p0, p1 = + + if n < Array.length path then + p, get_point' (Array.get path n) + else + (Array.get path (n -1)).point, p + in + + let min_idx = max (n-3) 0 in + + let points = + add_path path (n-3) first_point + @@ add_path path (n-2) first_point + @@ add_path path (n-1) first_point + @@ (fun tl -> (Point.get_coord p)::tl) + @@ add_path path n get_point' + @@ add_path path (n+1) get_point' + @@ add_path path (n+2) get_point' + @@ [] in + + (* It is impressive how fast it is to evaluate the curve ! Maybe is the + worker not required at all… + *) + let bezier_opt = Shapes.Bspline.to_bezier points in + begin match bezier_opt with + | Ok paths -> + Array.iteri paths + ~f:(fun i bezier -> + (* Only take two points before, and two after *) + let idx = min_idx + i in + if (n-2 < idx) && (idx < n +2) && idx < Array.length path then + Array.set path idx (assoc_point bezier (Array.get path idx)) + ); + Some path + | Error _ -> + let bezier', _ = Shapes.Bezier.three_points_quadratic + (Point.get_coord p) + (Point.get_coord @@ get_point' (Array.get path 0)) + (Point.get_coord @@ get_point' (Array.get path 1)) + |> Shapes.Bezier.quadratic_to_cubic + |> Shapes.Bezier.slice 0.5 + in + Array.set path 0 + { point = p0 + ; move = (Curve + { ctrl0 = bezier'.Shapes.Bezier.ctrl0 + ; ctrl1 = bezier'.Shapes.Bezier.ctrl1 + ; p1 + }) + }; + Some path + end +end diff --git a/script.it/path/fixed.mli b/script.it/path/fixed.mli new file mode 100755 index 0000000..111187c --- /dev/null +++ b/script.it/path/fixed.mli @@ -0,0 +1,81 @@ +(** Signature for points *) +module type P = sig + type t + + val get_coord : t -> Gg.v2 + + val id : t -> int + + val copy : t -> Gg.v2 -> t + +end + +module Make(Point:P) : sig + + module type BUILDER = sig + type t + + val repr + : t -> (module Repr.M with type point = Point.t and type t = 's) -> 's -> 's + + end + + type t + + (** Create a path from a builder *) + val to_fixed + : (module BUILDER with type t = 'a) -> 'a -> t + + (** Represent the path *) + val repr + : t -> (module Repr.M with type point = Point.t and type t = 's) -> 's -> 's + + (** Structure to represent all the required information for evaluating the + distance between a point and a path *) + type approx = + { distance : float + ; closest_point : Gg.v2 + ; ratio : float + ; p0 : Point.t + ; p1 : Point.t } + + (** Return the distance between a given point and the curve. May return + None if the point is out of the curve *) + val distance + : Gg.v2 -> t -> approx option + + (** Iterate over a path *) + val iter + : t -> f:(Point.t -> unit) -> unit + + (** Map all the points in the path *) + val map + : t -> (Point.t -> Point.t) -> t + + (** Reevaluate all the control points on the path in order to get a smooth + curve *) + val rebuild + : t -> t option + + (** Delete a point in the path. + + Reconnect the path without the point removed, and reevaluate all the + control points from the nodes + + return None if the point is not present in the curve + *) + val remove_point + : t -> Point.t -> t option + + (** Replace a point by the given one. + + An existing point with the same id shall be present in the path. + + The path is not fully evaluated, and rebuild shall be runned in order to + get the path completely smooth. + + *) + val replace_point + : t -> Point.t -> t option + +end diff --git a/script.it/path/path.ml b/script.it/path/path.ml new file mode 100755 index 0000000..ea90de4 --- /dev/null +++ b/script.it/path/path.ml @@ -0,0 +1,7 @@ +(** Common module for ensuring that the function is evaluated only once *) + +module Point = Point +module Repr = Repr +module Path_Builder = Builder.Make(Point) +module Fixed = Fixed.Make(Point) + diff --git a/script.it/path/point.ml b/script.it/path/point.ml new file mode 100755 index 0000000..ec6f8ad --- /dev/null +++ b/script.it/path/point.ml @@ -0,0 +1,77 @@ +let internal_id = ref 0 + +type t = + { p: Gg.v2 + ; size : float + ; angle: float + ; stamp : float + ; id : int + } + +let empty = + { p = Gg.V2.of_tuple (0., 0.) + ; size = 0. + ; angle = 0. + ; stamp = 0. + ; id = 0 + } + +let create ~angle ~width ~stamp ~x ~y = + + incr internal_id; + { p = Gg.V2.v x y + ; size = width + ; angle = Gg.Float.rad_of_deg (180. -. angle ) + ; stamp + ; id = !internal_id + } + +let copy point p = + { point with + p + } + +let set_angle p angle = + { p with angle = Gg.Float.rad_of_deg (180. -. angle) } + +let get_angle { angle; _} = 180. -. (Gg.Float.deg_of_rad angle) + +let set_width p size = + { p with size } + +let get_width { size; _} = size + +let (+) p1 p2 = + { p1 with p = Gg.V2.(+) p1.p p2 } + +let get_coord { p; _ } = p + +let get_stamp { stamp; _} = stamp + +let get_coord' + : t -> Gg.v2 + = fun t -> + let open Gg.V2 in + let trans = of_polar @@ v t.size t.angle in + t.p + trans + +let mix + : float -> Gg.v2 -> t -> t -> t + = fun f point p0 p1 -> + let angle0 = p0.angle + and angle1 = p1.angle + and width0 = get_width p0 + and width1 = get_width p1 + and stamp0 = get_stamp p0 + and stamp1 = get_stamp p1 in + let angle = angle0 +. f *. ( angle1 -. angle0 ) in + let width = width0 +. f *. ( width1 -. width0 ) in + let stamp = stamp0 +. f *. ( stamp1 -. stamp0 ) in + { p = point + ; size = width + ; angle + ; stamp + ; id = !internal_id + } + +let id { id; _} = id diff --git a/script.it/path/point.mli b/script.it/path/point.mli new file mode 100755 index 0000000..fe4cb45 --- /dev/null +++ b/script.it/path/point.mli @@ -0,0 +1,40 @@ +type t + +(** Return the point id. Each id is unique *) +val id + : t -> int + +val empty : t + +val (+): t -> Gg.v2 -> t + +val get_coord : t -> Gg.v2 + +val get_stamp : t -> float + +val create: angle:float -> width:float -> stamp:float -> x:float -> y:float -> t + +(** Return a copy of the point at given posistion + + This is a true copy, the id will be the same for the two points + TODO : Should this be renamed set_position ? + +*) +val copy : t -> Gg.v2 -> t + +val set_angle : t -> float -> t + +val get_angle : t -> float + +val set_width: t -> float -> t + +val get_width: t -> float + +val get_coord' + : t -> Gg.v2 + +(** [mix f point p0 p1] create a new point at the position point, with the + characteristics from p0 and p1 *) +val mix + : float -> Gg.v2 -> t -> t -> t + diff --git a/script.it/path/repr.ml b/script.it/path/repr.ml new file mode 100755 index 0000000..17fd914 --- /dev/null +++ b/script.it/path/repr.ml @@ -0,0 +1,19 @@ +module type M = sig + + type point + + type t + + (* Start a new path. *) + val start + : point -> t -> t + + val line_to + : point -> point -> t -> t + + val quadratic_to + : (point * Gg.v2 * Gg.v2 * point) -> t -> t + + val stop + : t -> t +end diff --git a/script.it/shapes/bezier.ml b/script.it/shapes/bezier.ml new file mode 100755 index 0000000..f5f288c --- /dev/null +++ b/script.it/shapes/bezier.ml @@ -0,0 +1,228 @@ +(** + + Bezier curve +*) + +module Utils = Tools.Utils + +type quadratic = + { p0:Gg.v2 (* The starting point *) + ; p1:Gg.v2 (* The end point *) + ; ctrl:Gg.v2 } (* The control point *) + + +type t = + { p0:Gg.v2 (* The starting point *) + ; p1:Gg.v2 (* The end point *) + ; ctrl0:Gg.v2 (* The control point *) + ; ctrl1:Gg.v2 } (* The control point *) + + +(** + Build a control point for a quadratic curve for passing throuht 3 points. + taken from https://xuhehuan.com/2608.html + + + also look to https://pomax.github.io/bezierinfo/#pointcurves +*) +let three_points_quadratic + : Gg.v2 -> Gg.v2 -> Gg.v2 -> quadratic + = fun p0 c1 p1 -> + + let open Gg.V2 in + + let vect_1 = p0 - c1 + and vect_2 = p1 - c1 in + let norm1 = norm vect_1 + and norm2 = norm vect_2 in + let v = (Float.sqrt (norm1 *. norm2)) /. 2. in + + let ctrl = c1 - v * (( vect_1 / norm1) + (vect_2 / norm2)) in + {p0; p1; ctrl} + +(** + + Convert a cubic bezier curve into a quadratic one + +*) +let quadratic_to_cubic + : quadratic -> t + = fun {p0; p1; ctrl} -> + + let coef = 2. /. 3. in + + let open Gg.V2 in + { p0 + ; p1 + ; ctrl0 = mix p0 ctrl coef + ; ctrl1 = mix p1 ctrl coef } + + + +let abc_ratio + : int -> float -> float + = fun n t -> + let n' = Float.of_int n in + let bottom = (Float.pow t n') +. (Float.pow (1. -. t) n') in + let top = bottom -. 1. in + Float.abs (top /. bottom) + +let half_cubic_ratio = abc_ratio 3 0.5 + +exception Not_found + +(** + + https://pomax.github.io/bezierinfo/#pointcurves + +*) +let three_points_cubic + : float -> Gg.v2 -> Gg.v2 -> Gg.v2 -> t + = fun f p0 p1 p2 -> + + let open Gg.V2 in + + let c = half ( p0 + p2) in + let a = p1 + ((p1 - c) / half_cubic_ratio) in + + let vect1_0 = p1 - p0 in + let vect2_0 = p2 - p0 in + + let d1 = norm vect1_0 + and d2 = norm (p2 - p1) in + let t = d1 /. (d1 +. d2) in + + let angle_1_0 = angle vect1_0 + and angle_2_0 = angle vect2_0 in + + (* get our e1-e2 distances *) + let angle = mod_float + (Gg.Float.two_pi + +. angle_2_0 + -. angle_1_0) + Gg.Float.two_pi in + + let distance = (norm vect2_0) *. f in + + let bc = + if angle < 0. || angle > Gg.Float.pi then + Float.(neg distance) + else + distance in + let de1 = t *. bc + and de2 = (1. -. t) *. bc in + + (* get the circle-aligned slope as normalized dx/dy *) + let center = Utils.center p0 p1 p2 in + match center with + | None -> raise Not_found + | Some center -> + let t' = p1 - center in + let tangent0 = v + ((x p1) -. (y t')) + ((y p1) +. (x t')) + and tangent1 = v + ((x p1) +. (y t')) + ((y p1) -. (x t')) in + + let d = unit (tangent1 - tangent0) in + + (* then set up an e1 and e2 parallel to the baseline *) + let e1 = p1 + de1 * d + and e2 = p1 - de2 * d in + + (* then use those e1/e2 to derive the new hull coordinates *) + let v1 = a + (e1 - a) / (1. -. t) + and v2 = a + (e2 - a) / t in + + let ctrl0 = p0 + (v1 - p0) / t + and ctrl1 = p2 + (v2 -p2) / (1. -. t) in + + {p0; p1 = p2; ctrl0; ctrl1} + +(** Split a bezier curve in two at a given position *) +let slice + : float -> t -> t * t + = fun t {p0; p1; ctrl0; ctrl1} -> + + let mix p1 p2 = Gg.V2.mix p1 p2 t in + + let p12 = mix p0 ctrl0 + and p23 = mix ctrl0 ctrl1 + and p34 = mix ctrl1 p1 in + + let p123 = mix p12 p23 + and p234 = mix p23 p34 in + + let p1234 = mix p123 p234 in + + ( { p0 + ; ctrl0 = p12 + ; ctrl1 = p123 + ; p1 = p1234 } + , { p0 = p1234 + ; ctrl0 = p234 + ; ctrl1 = p34 + ; p1 } ) + + +let get_closest_point + : Gg.v2 -> t -> float * Gg.v2 + = fun point t -> + + let rec f min max t = + + (* First devide the curve in two *) + let seq_0, seq_1 = slice 0.5 t in + let avg = (min +. max) /. 2. in + + let p0 = t.p0 + and p1 = t.p1 + and p01 = seq_0.p1 in (* seq_0.p1 = seq_1.p0 *) + + let open Gg.V2 in + let center0 = mix p0 p01 0.5 + and center1 = mix p01 p1 0.5 in + + if Tools.Utils.equal_point 0.001 p0 p1 then + avg, p01 + else if (norm (point - center0)) < (norm (point - center1)) then + f min avg seq_0 + else + f avg max seq_1 + + in f 0. 1. t + +let reverse + : t -> t + = fun bezier -> + { + p0 = bezier.p1 + ; p1 = bezier.p0 + ; ctrl0 = bezier.ctrl1 + ; ctrl1 = bezier.ctrl0 } + +(** + + see https://github.com/Pomax/BezierInfo-2/blob/master/docs/js/graphics-element/lib/bezierjs/bezier.js#L504 + + let root + : t -> 'a + = fun bezier -> + + let accept + : float -> bool + = fun t -> + 0. <= t && t <= 1. in + + let cuberoot v = + if v < 0. then + Float.pow (Float.neg v) ( 1. /. 3.) + |> Float.neg + else Float.pow v (1. /. 3.) in + + + + + failwith "Non implemented" +*) diff --git a/script.it/shapes/bezier.mli b/script.it/shapes/bezier.mli new file mode 100755 index 0000000..2f5bbcf --- /dev/null +++ b/script.it/shapes/bezier.mli @@ -0,0 +1,40 @@ +type t = + { p0:Gg.v2 (* The starting point *) + ; p1:Gg.v2 (* The end point *) + ; ctrl0:Gg.v2 (* The control point *) + ; ctrl1:Gg.v2 } (* The control point *) + +type quadratic + +(** + Build a control point for a quadratic curve for passing throuht 3 points. + taken from https://xuhehuan.com/2608.html + + + also look to https://pomax.github.io/bezierinfo/#pointcurves +*) +val three_points_quadratic + : Gg.v2 -> Gg.v2 -> Gg.v2 -> quadratic + +(** + Create a curve from three points. + + This is an implementation for + https://pomax.github.io/bezierinfo/#pointcurves + +*) +val three_points_cubic + : float -> Gg.v2 -> Gg.v2 -> Gg.v2 -> t + +val quadratic_to_cubic + : quadratic -> t + +(** Split a bezier curve in two at a given position *) +val slice + : float -> t -> t * t + +(** Return the closest point to the curve by approximation *) +val get_closest_point + : Gg.v2 -> t -> float * Gg.v2 + +val reverse: t -> t diff --git a/script.it/shapes/bspline.ml b/script.it/shapes/bspline.ml new file mode 100755 index 0000000..bb60227 --- /dev/null +++ b/script.it/shapes/bspline.ml @@ -0,0 +1,149 @@ +open StdLabels + +type err = [`InvalidPath ] + +module M = Matrix.MakeMatrix (struct + + type t = Float.t + + let compare a b = + + let v = Float.compare a b in + if v = 0 then Matrix.Order.Equal + else if v > 0 then Matrix.Order.Greater + else Matrix.Order.Less + + let zero = Float.zero + let one = Float.one + + let divide = (/.) + let multiply = ( *. ) + let add = (+.) + let subtract = (-.) + exception NonElt + + + end) + +type t = Gg.v2 list + +let from_points + : Gg.v2 array -> (Gg.v2 array, [> `InvalidPath]) Result.t + = fun points -> + + let n = (Array.length points - 2) in + + if n <= 1 then + Result.error `InvalidPath + else + + (* Create the initial matrix. + + The matrix is augmented with two additionals columns, which will be + populated with the points from the path. + *) + let arr = Array.init n ~f:(fun line -> + Array.init (n +2) ~f:(fun row -> + match row - line with + | (-1) -> 1. + | 0 -> 4. + | 1 -> 1. + | _ -> 0. + ) + ) in + let matrix = M.from_array arr in + + (* Add the points from the augmented matrix *) + let points_array = points in + for line = 0 to (n -1) do + + let point = + if line = 0 then + let p0 = points_array.(0) + and p1 = points_array.(1) in + Gg.V2.(6. * p1 - p0) + else if (line + 1) = n then + let p_n_2 = points_array.(n) + and p_n_1 = points_array.(n + 1) in + Gg.V2.(6. * p_n_2 - p_n_1) + else + let n' = line + 1 in + Gg.V2.(6. * points_array.(n')) + in + let x = (Gg.V2.x point) + and y = (Gg.V2.y point) in + + + M.set_elt matrix (line + 1, n + 1) x; + M.set_elt matrix (line + 1, n + 2) y; + done; + + (* Resolve the matrix *) + let res' = M.row_reduce matrix in + + (* Extract the result as points *) + let _, col_x = M.get_column res' (n + 1) + and _, col_y = M.get_column res' (n + 2) in + + (* Build the result *) + let res = Array.make (n + 2) (Array.get points_array (n + 1) ) in + for i = 1 to n do + let point = Gg.V2.v col_x.(i - 1) col_y.(i - 1) in + Array.set res i point; + done; + Array.set res 0 (Array.get points_array 0); + Result.ok res + +let (let*) = Result.bind + +(** Build a continue curve from path + + see https://www.math.ucla.edu/~baker/149.1.02w/handouts/dd_splines.pdf +*) +let to_bezier + : ?connexion0:Gg.v2 -> ?connexion1:Gg.v2 -> t -> (Bezier.t array, [> `InvalidPath]) Result.t + = fun ?connexion0 ?connexion1 points -> + + let points' = match connexion0 with + | None -> points + | Some pt -> pt::points in + + let arr_points = match connexion1 with + | None -> Array.of_list points' + | Some pt -> + let arr = Array.make (1 + (List.length points')) pt in + List.iteri points' + ~f:(fun i value -> Array.set arr i value); + arr in + + let* bspline_points = from_points arr_points in + + let start = match connexion0 with + | None -> 1 + | Some _ -> 2 + and end_ = match connexion1 with + | None -> (Array.length bspline_points) - 1 + | Some _ -> (Array.length bspline_points) - 2 in + + let result = Array.init (end_ - start + 1) ~f:(fun i -> + + let i = i + start in + + let prev_b = Array.get bspline_points (i - 1) + and bpoint = Array.get bspline_points i + and prev_p = Array.get arr_points (i - 1) + and point = Array.get arr_points i in + let ctrl0 = Gg.V2.(mix prev_b bpoint (1. /. 3.)) + and ctrl1 = Gg.V2.(mix prev_b bpoint (2. /. 3.)) in + + let bezier = + { Bezier.p0 = prev_p + ; Bezier.p1 = point + ; Bezier.ctrl0 + ; Bezier.ctrl1 } in + + bezier + + ) in + Result.Ok result + diff --git a/script.it/shapes/bspline.mli b/script.it/shapes/bspline.mli new file mode 100755 index 0000000..a36aa22 --- /dev/null +++ b/script.it/shapes/bspline.mli @@ -0,0 +1,24 @@ +type t + +type err = + [ `InvalidPath (* Too few points in the path for building the curve *) + ] + +(** Convert a list of points into a beziers curves. + + At least 4 points are required for building the path. + + [to_bezier ~connexion points] create a list of beziers segments joining all + the points together. + + [connexion0] add a virtual point in the begining for helping to get the + appropriate tangent when connecting path together + + [connexion1] does the same at the end + +*) +val to_bezier + : ?connexion0:Gg.v2 + -> ?connexion1:Gg.v2 + -> Gg.v2 list + -> (Bezier.t array, [> err]) Result.t diff --git a/script.it/shapes/dd_splines.pdf b/script.it/shapes/dd_splines.pdf new file mode 100755 index 0000000..2618162 Binary files /dev/null and b/script.it/shapes/dd_splines.pdf differ diff --git a/script.it/shapes/dune b/script.it/shapes/dune new file mode 100755 index 0000000..d03a217 --- /dev/null +++ b/script.it/shapes/dune @@ -0,0 +1,7 @@ +(library + (name shapes) + (libraries + tools + matrix + ) + ) diff --git a/script.it/shapes/matrix/EltsI.ml b/script.it/shapes/matrix/EltsI.ml new file mode 100755 index 0000000..fcfdb50 --- /dev/null +++ b/script.it/shapes/matrix/EltsI.ml @@ -0,0 +1,28 @@ +module type ORDERED_AND_OPERATIONAL = +sig + + (* Exception for from_string. Is raised when from_string is passed something + * that is not an elt *) + exception NonElt + + type t + + (* The zero element *) + val zero : t + + (* The one element *) + val one: t + + (* ts must be comparable *) + val compare : t -> t -> Order.order + + (* Basic mathematical operations must be possible *) + val add: t -> t -> t + + val subtract: t -> t -> t + + val multiply: t -> t -> t + + val divide: t -> t -> t + +end diff --git a/script.it/shapes/matrix/Helpers.ml b/script.it/shapes/matrix/Helpers.ml new file mode 100755 index 0000000..6980052 --- /dev/null +++ b/script.it/shapes/matrix/Helpers.ml @@ -0,0 +1,16 @@ +(* Takes in a string and a separator, and separates the string into a list of + * substrings where each substring is between two separators or between a + * separator and the beginning/end of the string *) +let explode (s: string) (space: string) : string list = + let rec build (curr: string) (buffer: string) (lst: string list) : string list = + let len = String.length curr in + if len = 0 then buffer::lst + else + let c = String.sub curr (len - 1) 1 in + if len = 1 then (c ^ buffer)::lst + else + let s' = String.sub curr 0 (len - 1) in + if c = space then build s' "" (buffer::lst) + else build s' (c ^ buffer) lst in + build (String.trim s) "" [] + diff --git a/script.it/shapes/matrix/Matrix.ml b/script.it/shapes/matrix/Matrix.ml new file mode 100755 index 0000000..7f1d54b --- /dev/null +++ b/script.it/shapes/matrix/Matrix.ml @@ -0,0 +1,529 @@ +open Order + +module Order = Order + +(*************** Exceptions ***************) + +exception NonSquare +exception ImproperDimensions + +(* Functor so we can Abstract away! *) +module MakeMatrix (C: EltsI.ORDERED_AND_OPERATIONAL) : + (MatrixI.MATRIX with type elt = C.t) = +struct + + + (*************** End Exceptions ***************) + + (*************** Types ***************) + + type elt = C.t + + (* A matrix is a pair of dimension (n x p) and a array of arrays + * the first array is the row (n) and the second the column (p) *) + type matrix = (int * int) * (elt array array) + + (*************** End Types ***************) + + (*************** Base Functions ***************) + + (* catching negative dimensions AND 0 dimensions and too large + * of a dimension so we don't have to worry about it later *) + let empty (rows: int) (columns: int) : matrix = + if rows > 0 && columns > 0 then + try + let m = Array.make_matrix rows columns C.zero in ((rows,columns),m) + with _ -> + raise ImproperDimensions + else (* dimension is negative or 0 *) + raise ImproperDimensions + + (*************** End Base Functions ***************) + + (*************** Helper Functions ***************) + + (* get's the nth row of a matrix and returns (r, row) where r is the length + * of the row and row is a COPY of the original row. For example, calling + * calling get_row m 1 will return (3, |1 3 4 |) + * ________ + * m = | 1 3 4 | + * |*2 5 6 | + *) + (* aside: we don't check whether n < 1 because of our matrix invariant *) + let get_row (((n,p),m): matrix) (row: int) : int * elt array = + if row <= n then + let row' = Array.map (fun x -> x) m.(row - 1) in + (p, row') + else + raise (Failure "Row out of bounds.") + + (* similar to get_row. For m, get_column m 1 will return (2, |1 2|) *) + let get_column (((n,p),m): matrix) (column: int) : int * elt array = + if column <= p then + begin + let column' = Array.make n C.zero in + for i = 0 to n - 1 do + column'.(i) <- m.(i).(column - 1) + done; + (n, column') + end + else + raise (Failure "Column out of bounds.") + + (* sets the nth row of the matrix m to the specified array a. + * This is done IN-PLACE. Therefore the function returns unit. You should + * nonetheless enfore immutability whenever possible. For a clarification on + * what nth row means, look at comment for get_row above. *) + let set_row (((n, p), m): matrix) (row: int) (a: elt array) : unit = + if row <= n then + begin + assert(Array.length a = p); + for i = 0 to p - 1 do + m.(row - 1).(i) <- a.(i) + done; + end + else + raise (Failure "Row out of bounds.") + + (* Similar to set_row but sets the nth column instead *) + let set_column (((n,p),m): matrix) (column: int) (a: elt array) : unit = + if column <= p then + begin + assert(Array.length a = n); + for i = 0 to n - 1 do + m.(i).(column - 1) <- a.(i) + done; + end + else + raise (Failure "Column out of bounds.") + + (* returns the ij-th element of a matrix (not-zero indexed) *) + let get_elt (((n,p),m): matrix) ((i,j): int*int) : elt = + if i <= n && j <= p then + m.(i - 1).(j - 1) + else + raise ImproperDimensions + + (* Changes the i,j-th element of a matrix to e. Is not zero-indexed, and + * changes the matrix in place *) + let set_elt (((n,p),m): matrix) ((i,j): int*int) (e: elt) : unit = + if i <= n && j <= p then + m.(i - 1).(j - 1) <- e + else + raise ImproperDimensions + + (* similar to map, but applies to function to the entire matrix + * Returns a new matrix *) + let map (f: elt -> elt) (mat: matrix) : matrix = + let (dim,m) = mat in + (dim, Array.map (Array.map f) m) + + (* Just some wrapping of Array.iter made for Matrices! *) + let iter (f: elt -> unit) (mat: matrix) : unit = + let _, m = mat in + Array.iter (Array.iter f) m + + (* Just some wrapping of Array.iteri. Useful for pretty + * printing matrix. The index is (i,j). NOT zero-indexed *) + let iteri (f: int -> int -> elt -> unit) (mat: matrix) : unit = + let _, m = mat in + Array.iteri (fun i row -> Array.iteri (fun j e -> f i j e) row) m + + (* folds over each row using base case u and function f *) + (* could be a bit more efficient? *) + let reduce (f: 'a -> elt -> 'a) (u: 'a) (((p,q),m): matrix) : 'a = + let total = ref u in + for i = 0 to p - 1 do + for j = 0 to q - 1 do + total := f (!total) m.(i).(j) + done; + done; + !total + + let fold_row ~(f: elt array -> 'b) ((_,m): matrix) : 'b list = + + let call_row acc v = (f v)::acc in + Array.fold_left call_row [] m + |> List.rev + + + + + (* given two arrays, this will calculate their dot product *) + (* It seems a little funky, but this is done for efficiency's sake. + * In short, it tries to multiply each element by it's respective + * element until the one array is indexed out of bounds. If the + * other array is also out of bounds, then it returns their value. + * Otherwise, the arrays were the wrong size and raises ImproperDimension + + THE ABOVE COMMENT HAS NOT BEEN IMPLEMENTED + + Instead we calculate the length before starting + *) + let dot (v1: elt array) (v2: elt array) : elt = + let rec dotting (i: int) (total: elt) : elt = + if i = 0 then total + else + let curr = C.multiply v1.(i-1) v2.(i-1) in + dotting (i - 1) (C.add curr total) in + let len1, len2 = Array.length v1, Array.length v2 in + if len1 = len2 then dotting len1 C.zero + else raise ImproperDimensions + + (* function to expose the dimensions of a matrix *) + let get_dimensions (m: matrix) : (int * int) = + let ((x,y), _) = m in (x,y) + + (*************** End Helper Functions ***************) + + + (*************** Primary Matrix Functions ***************) + + (* scales a matrix by the appropriate factor *) + let scale (m: matrix) (sc: elt) : matrix = map (C.multiply sc) m + + (* Generates a matrix from a list of lists. The inners lists are the rows *) + let from_list (lsts : elt list list) : matrix = + let check_length (length: int) (lst: elt list) : int = + if List.length lst = length then length + else raise ImproperDimensions in + let p = List.length lsts in + match lsts with + | [] -> raise ImproperDimensions + | hd::tl -> + let len = List.length hd in + if List.fold_left check_length len tl = len then + ((p,len),Array.map Array.of_list (Array.of_list lsts)) + else + raise ImproperDimensions + + (* Generates a matrix from a list of lists. The inners lists are the rows *) + let from_array (arrs : elt array array) : matrix = + let check_length (length: int) (arr: elt array) : unit = + if Array.length arr = length then () + else raise ImproperDimensions in + let p = Array.length arrs in + match Array.length arrs with + | 0 -> raise ImproperDimensions + | _ -> + let len = Array.length (Array.get arrs 0) in + Array.iter (check_length len) arrs; + ((p, len), arrs) + + (* Adds two matrices. They must have the same dimensions *) + let add ((dim1,m1): matrix) ((dim2,m2): matrix) : matrix = + if dim1 = dim2 then + let n, p = dim1 in + let (dim', sum_m) = empty n p in + for i = 0 to n - 1 do + for j = 0 to p - 1 do + sum_m.(i).(j) <- C.add m1.(i).(j) m2.(i).(j) + done; + done; + (dim',sum_m) + else + raise ImproperDimensions + + + (* Multiplies two matrices. If the matrices have dimensions m x n and p x q, n + * and p must be equal, and the resulting matrix will have dimension n x q *) + let mult (matrix1: matrix) (matrix2: matrix) : matrix = + let ((m,n), _), ((p,q), _) = matrix1, matrix2 in + if n = p then + let (dim, result) = empty m q in + for i = 0 to m - 1 do + for j = 0 to q - 1 do + let (_,row), (_,column) = get_row matrix1 (i + 1), + get_column matrix2 (j + 1) in + result.(i).(j) <- dot row column + done; + done; + (dim,result) + else + raise ImproperDimensions + + (*************** Helper Functions for Row Reduce ***************) + + (* + (* returns the index of the first non-zero elt in an array*) + let zero (arr: elt array) : int option = + let index = ref 1 in + let empty (i: int option) (e: elt) : int option = + match i, C.compare e C.zero with + | None, Equal -> (index := !index + 1; None) + | None, _ -> Some (!index) + | _, _ -> i in + Array.fold_left empty None arr + + (* returns the the location of the nth non-zero + * element in the matrix. Scans column wise. So the nth non-zero element is + * the FIRST non-zero element in the nth non-zero column *) + let nth_nz_location (m: matrix) (_: int): (int*int) option = + let ((n,p), _) = m in + let rec check_col (to_skip: int) (j: int) = + if j <= p then + let (_,col) = get_column m j in + match zero col with + | None -> check_col to_skip (j + 1) + | Some i -> + if to_skip = 0 then + Some (i,j) + else (* we want a later column *) + check_col (to_skip - 1) (j + 1) + else None in + check_col (n - 1) 1 + + (* returns the the location of the first + * non-zero and non-one elt. Scans column wise, from + * left to right. Basically, it ignores columns + * that are all zero or that *) + let fst_nz_no_loc (m: matrix): (int*int) option = + let ((_, p), _) = m in + let rec check_col (j: int) = + if j <= p then + let (_,col) = get_column m j in + match zero col with + | None -> check_col (j + 1) + | Some i -> + match C.compare col.(i-1) C.one with + | Equal -> check_col (j + 1) + | _ -> Some (i,j) + else None in + check_col 1 + *) + + (* Compares two elements in an elt array and returns the greater and its + * index. Is a helper function for find_max_col_index *) + let compare_helper (e1: elt) (e2: elt) (ind1: int) (ind2: int) : (elt*int) = + match C.compare e1 e2 with + | Equal -> (e2, ind2) + | Greater -> (e1, ind1) + | Less -> (e2, ind2) + + (* Finds the element with the greatest absolute value in a column. Is not + * 0-indexed. If two elements are both the maximum value, returns the one with + * the lowest index. Returns None if this element is zero (if column is all 0) + *) + let find_max_col_index (array1: elt array) (start_index: int) : int option = + let rec find_index (max_index: int) (curr_max: elt) (curr_index: int) + (arr: elt array) = + if curr_index = Array.length arr then + (if curr_max = C.zero then None + else Some (max_index+1)) (* Arrays are 0-indexed but matrices aren't *) + else + (match C.compare arr.(curr_index) C.zero with + | Equal -> find_index max_index curr_max (curr_index+1) arr + | Greater -> + (let (el, index) = compare_helper (arr.(curr_index)) + curr_max curr_index max_index in + find_index index el (curr_index+1) arr) + | Less -> + (let abs_curr_elt = C.subtract C.zero arr.(curr_index) in + let (el, index) = compare_helper abs_curr_elt curr_max curr_index + max_index in + find_index index el (curr_index+1) arr)) + in + find_index 0 C.zero (start_index -1) array1 + + (* Basic row operations *) + (* Scales a row by sc *) + let scale_row (m: matrix) (num: int) (sc: elt) : unit = + let (_, row) = get_row m num in + let new_row = Array.map (C.multiply sc) row in + set_row m num new_row + + (* Swaps two rows of a matrix *) + let swap_row (m: matrix) (r1: int) (r2: int) : unit = + let (len1, row1) = get_row m r1 in + let (len2, row2) = get_row m r2 in + let _ = assert (len1 = len2) in + let _ = set_row m r1 row2 in + let _ = set_row m r2 row1 in + () + + (* Subtracts a multiple of r2 from r1 *) + let sub_mult (m: matrix) (r1: int) (r2: int) (sc: elt) : unit = + let (len1, row1) = get_row m r1 in + let (len2, row2) = get_row m r2 in + let _ = assert (len1 = len2) in + for i = 0 to len1 - 1 do (* Arrays are 0-indexed *) + row1.(i) <- C.subtract row1.(i) (C.multiply sc row2.(i)) + done; + set_row m r1 row1 + + (*************** End Helper Functions for Row Reduce ***************) + + (* Returns the row reduced form of a matrix. Is not done in place, but creates + * a new matrix *) + let row_reduce (mat: matrix) : matrix = + let[@tailcall] rec row_reduce_h (n_row: int) (n_col: int) (mat2: matrix) : unit = + let ((num_row, _), _) = mat2 in + if (n_col = num_row + 1) then () + else + let (_,col) = get_column mat2 n_col in + match find_max_col_index col n_row with + | None (* Column all 0s *) -> row_reduce_h n_row (n_col+1) mat2 + | Some index -> + begin + swap_row mat2 index n_row; + let pivot = get_elt mat2 (n_row, n_col) in + scale_row mat2 (n_row) (C.divide C.one pivot); + for i = 1 to num_row do + if i <> n_row then sub_mult mat2 i n_row (get_elt mat2 (i,n_col)) + done; + row_reduce_h (n_row+1) (n_col+1) mat2 + end + in + (* Copies the matrix *) + let ((n,p),m) = mat in + let (dim,mat_cp) = empty n p in + for i = 0 to n - 1 do + for j = 0 to p - 1 do + mat_cp.(i).(j) <- m.(i).(j) + done; + done; + let _ = row_reduce_h 1 1 (dim,mat_cp) in (dim,mat_cp) + + (*************** End Main Functions ***************) + + (*************** Optional module functions ***************) + + (* calculates the trace of a matrix *) + let trace (((n,p),m): matrix) : elt = + let rec build (elt: elt) (i: int) = + if i > -1 then + build (C.add m.(i).(i) elt) (i - 1) + else + elt in + if n = p then build C.zero (n - 1) + else raise ImproperDimensions + + (* calculates the transpose of a matrix and retuns a new one *) + let transpose (((n,p),m): matrix) = + let (dim,m') = empty p n in + for i = 0 to n - 1 do + for j = 0 to p - 1 do + m'.(j).(i) <- m.(i).(j) + done; + done; + assert(dim = (p,n)); + ((p,n),m') + + (* Returns the inverse of a matrix. Uses a pretty simple algorithm *) + let inverse (mat: matrix) : matrix = + let ((n, p), _) = mat in + if n = p then + (* create augmented matrix *) + let augmented = empty n (2*n) in + for i = 1 to n do + let (dim,col) = get_column mat i in + let arr = Array.make n C.zero in + begin + assert(dim = n); + arr.(i-1) <- C.one; + set_column augmented i col; + set_column augmented (n + i) arr + end + done; + let augmented' = row_reduce augmented in + (* create the inverted matrix and fill in with appropriate values *) + let inverse = empty n n in + for i = 1 to n do + let (dim, col) = get_column augmented' (n + i) in + let _ = assert(dim = n) in + let _ = set_column inverse i col in + () + done; + inverse + else + raise NonSquare + + (***************** HELPER FUNCTIONS FOR DETERMINANT *****************) + (* creates an identity matrix of size n*) + let create_identity (n:int) : matrix = + let (dim,m) = empty n n in + for i = 0 to n - 1 do + m.(i).(i) <- C.one + done; + (dim,m) + + (* Finds the index of the maximum value of an array *) + let find_max_index (arr: elt array) (start_index : int) : int = + let rec find_index (max_index: int) (curr_index: int) = + if curr_index = Array.length arr then max_index+1 + else + match C.compare arr.(curr_index) arr.(max_index) with + | Equal | Less -> find_index max_index (curr_index + 1) + | Greater -> find_index curr_index (curr_index + 1) in + find_index (start_index - 1) start_index + + (* Creates the pivoting matrix for A. Returns swqps. Adapted from + * http://rosettacode.org/wiki/LU_decomposition#Common_Lisp *) + let pivotize (((n,p),m): matrix) : matrix * int = + if n = p then + let swaps = ref 0 in + let pivot_mat = create_identity n in + for j = 1 to n do + let (_,col) = get_column ((n,p),m) j in + let max_index = find_max_index col j in + if max_index <> j then + (swaps := !swaps + 1; swap_row pivot_mat max_index j) + else () + done; + (pivot_mat,!swaps) + else raise ImproperDimensions + + (* decomposes a matrix into a lower triangualar, upper triangualar + * and a pivot matrix. It returns (L,U,P). Adapted from + * http://rosettacode.org/wiki/LU_decomposition#Common_Lisp *) + let lu_decomposition (((n,p),m): matrix) : (matrix*matrix*matrix)*int = + if n = p then + let mat = ((n,p),m) in + let lower, upper, (pivot,s) = empty n n, empty n n, pivotize mat in + let (_ ,l),(_ ,u), _ = lower,upper,pivot in + let ((_, _),mat') = mult pivot mat in + for j = 0 to n - 1 do + l.(j).(j) <- C.one; + for i = 0 to j do + let sum = ref C.zero in + for k = 0 to i - 1 do + sum := C.add (!sum) (C.multiply u.(k).(j) l.(i).(k)) + done; + u.(i).(j) <- C.subtract mat'.(i).(j) (!sum) + done; + for i = j to n - 1 do + let sum = ref C.zero in + for k = 0 to j - 1 do + sum := C.add (!sum) (C.multiply u.(k).(j) l.(i).(k)) + done; + let sub = C.subtract mat'.(i).(j) (!sum) in + l.(i).(j) <- C.divide sub u.(j).(j) + done; + done; + (lower,upper,pivot),s + else raise ImproperDimensions + + (* Computes the determinant of a matrix *) + let determinant (m: matrix) : elt = + try + let ((n,p), _) = m in + if n = p then + let rec triangualar_det (a,mat) curr_index acc = + if curr_index < n then + let acc' = C.multiply mat.(curr_index).(curr_index) acc in + triangualar_det (a,mat) (curr_index + 1) acc' + else acc in + let ((dim1,l),(dim2,u), _),s = lu_decomposition m in + let det1, det2 = triangualar_det (dim1,l) 0 C.one, + triangualar_det (dim2,u) 0 C.one in + if s mod 2 = 0 then C.multiply det1 det2 + else C.subtract C.zero (C.multiply det1 det2) + else raise ImproperDimensions + with + | _ -> C.zero + + + (*************** Optional module functions ***************) + + +end diff --git a/script.it/shapes/matrix/MatrixI.ml b/script.it/shapes/matrix/MatrixI.ml new file mode 100755 index 0000000..fbc4e21 --- /dev/null +++ b/script.it/shapes/matrix/MatrixI.ml @@ -0,0 +1,105 @@ +exception NonSquare +exception ImproperDimensions + +module type MATRIX = +sig + + (******** TYPES ********) + type elt + + type matrix + + (* empty matrix of nxp dimensions *) + val empty : int -> int -> matrix + + (* Takes a list of lists and converts that to a matrix *) + val from_list : (elt list list) -> matrix + + val from_array: elt array array -> matrix + + (******** OPERATIONS ON ONE MATRIX ********) + (* Takes in a matrix and returns its dimensions. ie, nxp *) + val get_dimensions : matrix -> (int * int) + + (* get's the row of a matrix: Not zero-indexed. *) + val get_row : matrix -> int -> (int * elt array) + + (* similar to get_row *) + val get_column: matrix -> int -> (int * elt array) + + (* sets the row of a matrix in place! Not zero-index *) + val set_row: matrix -> int -> elt array -> unit + + (* similar to set_row, but for a column *) + val set_column: matrix -> int -> elt array -> unit + + (* gets the element at the specified index. *) + val get_elt: matrix -> (int * int) -> elt + + (* sets the element at the specified index *) + val set_elt: matrix -> (int * int) -> elt -> unit + + (* Scales every element in the matrix by another elt *) + val scale : matrix -> elt -> matrix + + + (******** MORE ADVANCED SINGLE MATRIX OPERATIONS ********) + (* Returns the row reduced form of a matrix *) + val row_reduce: matrix -> matrix + (* We will implement the algorithm found in the link above *) + + (* Returns the inverse of a matrix *) + val inverse: matrix -> matrix + + (*Transposes a matrix. If the input has dimensions m x n, the output will + * have dimensions n x m *) + val transpose: matrix -> matrix + + (* Returns the trace of the matrix *) + val trace: matrix -> elt + + (******** OPERATIONS ON TWO MATRICES ********) + (* Adds two matrices. They must have the same dimensions *) + val add : matrix -> matrix -> matrix + + (* Multiplies two matrices. If the matrices have dimensions m x n and p x q, n + * and p must be equal, and the resulting matrix will have dimension m x q *) + val mult: matrix -> matrix -> matrix + + (**** Other Library Functions ***) + (* Function to make over our matrices *) + val map : (elt -> elt) -> matrix -> matrix + + (*val iter : (elt -> unit) -> matrix -> unit*) + + (* Returns the LUP decomposition of a matrix *) + val lu_decomposition : matrix -> (matrix * matrix * matrix) * int + + (* Returns the determinant of the matrix *) + val determinant: matrix -> elt + + (************** Other Library Functions *************) + val iter : (elt -> unit) -> matrix -> unit + + val iteri : (int -> int -> elt -> unit) -> matrix -> unit + + (* folds over each row using base case u and function f *) + val reduce: ('a -> elt -> 'a) -> 'a -> matrix -> 'a + + val fold_row: f:(elt array -> 'b) -> matrix -> 'b list + + (********** Specific for Simplex Algorithm ***********) + (** All of the following functions will raise ImproperDimensions + * Exception if the matrix is not the right size for the operation + **) + + (* Scales a row *) + val scale_row: matrix -> int -> elt -> unit + + (* Swaps two rows *) + val swap_row: matrix -> int -> int -> unit + + (* Subtracts a multiple of one row (the 2nd int) from another (the 1st int) *) + val sub_mult: matrix -> int -> int -> elt -> unit + +end diff --git a/script.it/shapes/matrix/Order.ml b/script.it/shapes/matrix/Order.ml new file mode 100755 index 0000000..5f2aa22 --- /dev/null +++ b/script.it/shapes/matrix/Order.ml @@ -0,0 +1,2 @@ +(* Defines a general ordering type *) +type order = Equal | Less | Greater diff --git a/script.it/shapes/matrix/dune b/script.it/shapes/matrix/dune new file mode 100755 index 0000000..1c0cab6 --- /dev/null +++ b/script.it/shapes/matrix/dune @@ -0,0 +1,3 @@ +(library + (name matrix) +) diff --git a/script.it/shapes/tools/dune b/script.it/shapes/tools/dune new file mode 100755 index 0000000..a2c3fdb --- /dev/null +++ b/script.it/shapes/tools/dune @@ -0,0 +1,6 @@ +(library + (name tools) + (libraries + gg + ) + ) diff --git a/script.it/shapes/tools/utils.ml b/script.it/shapes/tools/utils.ml new file mode 100755 index 0000000..b8a473f --- /dev/null +++ b/script.it/shapes/tools/utils.ml @@ -0,0 +1,63 @@ +open Gg.V2 + +let norm_angle vect = + mod_float + ((angle vect) +. Gg.Float.two_pi) + Gg.Float.two_pi + + +let intersection + : (Gg.v2 * Gg.v2) -> (Gg.v2 * Gg.v2) -> Gg.v2 option + = fun (p0, p1) (p2, p3) -> + let i = p1 - p0 + and j = p3 - p2 in + + let d = (x i *. y j) -. (y i *. x j) in + if Float.( (abs d) <= 0.01 ) then + None + else + let m = ((x i) *. (y p0) + -. (x i) *. (y p2) + -. (y i) *. (x p0) + +. (y i) *. (x p2)) /. d in + Some (p2 + m * j) + (* + let k = ((x j) *. (y p0) + -. (x j) *. (y p2) + -. (y j) *. (x p0) + +. (y j) *. (x p2)) /. d in + Some (p0 + k * i) + *) + + +let center + : Gg.v2 -> Gg.v2 -> Gg.v2 -> Gg.v2 option + = fun p0 p1 p2 -> + (* deltas *) + let d1 = p1 - p0 + and d2 = p2 - p1 in + + (* perpendiculars *) + let d1p = ortho d1 + and d2p = ortho d2 in + + (* Chord midpoints *) + let m1 = half (p0 + p1) + and m2 = half (p1 + p2) in + + (* midpoint offsets *) + let m1n = m1 + d1p + and m2n = m2 + d2p in + + intersection (m1, m1n) (m2, m2n) + +let rotate + : Gg.v2 -> float -> Gg.v2 + = fun p0 theta -> + let r = x (to_polar p0) in + of_polar (v r theta) + +let equal_point + : float -> Gg.v2 -> Gg.v2 -> bool + = fun eps p0 p1 -> + Gg.V2.equal_f (fun v0 v1 -> (Float.abs (v1 -. v0)) <= eps ) p0 p1 diff --git a/script.it/shapes/tools/utils.mli b/script.it/shapes/tools/utils.mli new file mode 100755 index 0000000..4e12906 --- /dev/null +++ b/script.it/shapes/tools/utils.mli @@ -0,0 +1,21 @@ +(** Return a normalize angle *) +val norm_angle + : Gg.v2 -> float + +(** return the interesction for two segments *) +val intersection + : (Gg.v2 * Gg.v2) -> (Gg.v2 * Gg.v2) -> Gg.v2 option + +(** Return the center of the cercle for three points + None if the point cannot be evaluated +*) +val center + : Gg.v2 -> Gg.v2 -> Gg.v2 -> Gg.v2 option + +(** Rotate the vector by the given angle *) +val rotate + : Gg.v2 -> float -> Gg.v2 + +(** Test equality between two points *) +val equal_point + : float -> Gg.v2 -> Gg.v2 -> bool -- cgit v1.2.3