diff options
Diffstat (limited to 'curves/bezier.ml')
| -rwxr-xr-x | curves/bezier.ml | 197 |
1 files changed, 0 insertions, 197 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 } |