fix linear solver

editor/DrawingGeom.ml

@@ -2,6 +2,8 @@ open Js_of_ocaml
 
 type point = float * float
 
+let print_point f (x, y) = Printf.fprintf f "(%f,%f)" x y
+
 let ( +.. ) (x1, y1) (x2, y2) = (x2 +. x1, y2 +. y1)
 
 let ( -.. ) (x2, y2) (x1, y1) = (x2 -. x1, y2 -. y1)
@@ -33,6 +35,8 @@ let rot rho (x, y) =
 
 let pi = 4.0 *. atan 1.0
 
+let normal (x, y) = mult (1.0 /. dist (y, -.x)) (y, -.x)
+
 let angle (x, y) =
   if x > 0.0 then atan (y /. x)
   else if x < 0.0 then pi +. atan (y /. x)
@@ -152,7 +156,7 @@ let flipColor ctx =
   setStrokeColor ctx fc;
   setFillColor ctx sc
 
-let solve_linear a b = if a = 0.0 then [] else [ b /. a ]
+let solve_linear a b = if a = 0.0 then [] else [ -.b /. a ]
 
 let solve_quadratic a b c =
   if a = 0.0 then solve_linear b c
@@ -402,8 +406,8 @@ module Line = struct
 
   let point_at t ?(offset = 0.0) (spos, epos) =
     let p0 = spos and p1 = epos in
-    let port = rot (-.pi /. 2.0) (p1 -.. p0) in
-    p0 +.. mult t (p1 -.. p0) +.. mult (offset /. dist port) port
+    let no = normal (p1 -.. p0) in
+    p0 +.. mult t (p1 -.. p0) +.. mult offset no
 end
 
 module Bezier2 = struct
@@ -426,16 +430,21 @@ module Bezier2 = struct
   let is_over tos mouse_pos ~thick bez =
     let (xA, yA), (xB, yB), c = poly_of tos bez in
     let xC, yC = c -.. mouse_pos in
-    let ts = solve_quadratic xA xB xC in
-    let eps t =
+    let epsx t = 
+      let x1 = (xA *. t *. t) +. (xB *. t) +. xC in
+      t >= 0.0 && t <= 1.0 && abs_float x1 <= 1.5 *. thick in
+    let epsy t =
       let y1 = (yA *. t *. t) +. (yB *. t) +. yC in
       t >= 0.0 && t <= 1.0 && abs_float y1 <= 1.5 *. thick
     in
-    List.exists eps ts
+    let b = List.exists epsy (solve_quadratic xA xB xC) || List.exists epsx (solve_quadratic yA yB yC) in
+    
+    b
 
-  let point_at t ?offset:_ bez =
+  let point_at t ?(offset = 0.0) bez =
     let a, b, c = poly_of (fun x -> x) bez in
-    mult (t *. t) a +.. mult t b +.. c
+    let no = normal @@ (mult (2.0 *. t) a +.. b) in
+    mult (t *. t) a +.. mult t b +.. c +.. mult offset no
 end
 
 module Bezier3 = struct
@@ -474,12 +483,17 @@ module Bezier3 = struct
       let x = (xa *. t *. t *. t) +. (xb *. t *. t) +. (xc *. t) +. xd in
       t >= 0.0 && t <= 1.0 && abs_float x <= 1.5 *. thick
     in
-    List.exists epsy (solve_cubic xa xb xc xd)
-    || List.exists epsx (solve_cubic ya yb yc yd)
+    let b = List.exists epsy (solve_cubic xa xb xc xd)
+    || List.exists epsx (solve_cubic ya yb yc yd) in
+    b
 
-  let point_at t ?offset:_ bez =
+  let point_at t ?(offset = 0.0) bez =
     let a, b, c, d = poly_of (fun x -> x) bez in
-    mult (t *. t *. t) a +.. mult (t *. t) b +.. mult t c +.. d
+    let no = normal @@ (mult (3.0 *. t *. t) a +.. mult (2.0 *. t) b +.. c) in
+
+    mult (t *. t *. t) a
+    +.. mult (t *. t) b
+    +.. mult t c +.. d +.. mult offset no
 end
 
 module Arrow = struct
@@ -598,7 +612,6 @@ let draw_shape tos ctx ?(thick = 3.0) = function
   | `SimpleArrow a -> SimpleArrow.draw tos ctx ~thick a
   | `RoundArrow a -> RoundArrow.draw tos ctx ~thick a
 
-let print_point f (x, y) = Printf.fprintf f "(%f,%f)" x y
 
 let print_shape f = function
   | `Empty -> ()