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-rwxr-xr-xcurves/bezier.ml197
-rwxr-xr-xcurves/bezier.mli40
-rwxr-xr-xcurves/bspline.ml149
-rwxr-xr-xcurves/bspline.mli24
-rwxr-xr-xcurves/dd_splines.pdfbin184248 -> 0 bytes
-rwxr-xr-xcurves/dune7
6 files changed, 0 insertions, 417 deletions
diff --git a/curves/bezier.ml b/curves/bezier.ml
deleted file mode 100755
index 3dedc70..0000000
--- a/curves/bezier.ml
+++ /dev/null
@@ -1,197 +0,0 @@
-(**
-
- 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 rec get_closest_point
- : Gg.v2 -> t -> Gg.v2
- = fun point t ->
- (* First devide the curve in two *)
- let seq_0, seq_1 = slice 0.5 t 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
- p01
- else if (norm (point - center0)) < (norm (point - center1)) then
- get_closest_point point seq_0
- else
- get_closest_point point seq_1
-
-let reverse
- : t -> t
- = fun bezier ->
- {
- p0 = bezier.p1
- ; p1 = bezier.p0
- ; ctrl0 = bezier.ctrl1
- ; ctrl1 = bezier.ctrl0 }
diff --git a/curves/bezier.mli b/curves/bezier.mli
deleted file mode 100755
index e90163c..0000000
--- a/curves/bezier.mli
+++ /dev/null
@@ -1,40 +0,0 @@
-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 -> Gg.v2
-
-val reverse: t -> t
diff --git a/curves/bspline.ml b/curves/bspline.ml
deleted file mode 100755
index bb60227..0000000
--- a/curves/bspline.ml
+++ /dev/null
@@ -1,149 +0,0 @@
-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/curves/bspline.mli b/curves/bspline.mli
deleted file mode 100755
index 074658d..0000000
--- a/curves/bspline.mli
+++ /dev/null
@@ -1,24 +0,0 @@
-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/curves/dd_splines.pdf b/curves/dd_splines.pdf
deleted file mode 100755
index 2618162..0000000
--- a/curves/dd_splines.pdf
+++ /dev/null
Binary files differ
diff --git a/curves/dune b/curves/dune
deleted file mode 100755
index 34c87fb..0000000
--- a/curves/dune
+++ /dev/null
@@ -1,7 +0,0 @@
-(library
- (name curves)
- (libraries
- tools
- matrix
- )
- )
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-23 12:24:54 +0000