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open V
let arc
?(rev = false)
?fn
?fa
?fs
?(wedge = false)
~centre:(c : V2.t)
~radius
~start
angle
=
let fn = Util.helical_fragments ?fn ?fa ?fs radius in
let a_step = angle /. Float.of_int fn *. if rev then 1. else -1. in
let f _ (acc, a) =
let p = v2 ((Float.cos a *. radius) +. c.x) ((Float.sin a *. radius) +. c.y) in
p :: acc, a +. a_step
and init = if wedge then [ c ] else [] in
fst @@ Util.fold_init (fn + 1) f (init, if rev then start else start +. angle)
let arc_about_centre ?rev ?fn ?fa ?fs ?dir ?wedge ~centre p1 p2 =
let radius = V2.distance centre p1
and start =
let { x; y } = V2.sub p1 centre in
Float.atan2 y x
and angle =
let a = V2.angle_points p1 centre p2
and d = V2.clockwise_sign p1 p2 centre in
match d, dir with
| 0., None ->
invalid_arg "Co-linear points don't define unique arc. Must specify dir."
| 0., Some `CW -> (2. *. Float.pi) -. a
| 0., Some `CCW -> ((2. *. Float.pi) -. a) *. -1.
| -1., Some `CW | 1., Some `CCW -> ((2. *. Float.pi) -. a) *. Float.neg d
| _ -> d *. a
in
arc ?rev ?fn ?fa ?fs ?wedge ~centre ~radius ~start angle
let arc_through ?rev ?fn ?fa ?fs ?wedge p1 p2 p3 =
if V2.collinear p1 p2 p3 then invalid_arg "Arc points must form a valid triangle.";
let centre =
let d =
(2. *. (p1.x -. p3.x) *. (p3.y -. p2.y)) +. (2. *. (p2.x -. p3.x) *. (p1.y -. p3.y))
and m1 = V2.dot p1 p1 -. V2.dot p3 p3
and m2 = V2.dot p3 p3 -. V2.dot p2 p2 in
let nx = (m1 *. (p3.y -. p2.y)) +. (m2 *. (p3.y -. p1.y))
and ny = (m1 *. (p2.x -. p3.x)) +. (m2 *. (p1.x -. p3.x)) in
v2 (nx /. d) (ny /. d)
and dir = if Float.equal (V2.clockwise_sign p1 p2 p3) 1. then `CW else `CCW in
arc_about_centre ?rev ?fn ?fa ?fs ?wedge ~dir ~centre p1 p3