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type spring = { a : int; b : int; rest : float; k : float; damping : float }
let accelerations (bodies : Body.t array) (springs : spring list) : Vec2.t array =
let acc = Array.make (Array.length bodies) (0., 0.) in
springs
|> List.iter (fun s ->
let a = bodies.(s.a) and b = bodies.(s.b) in
let d = Vec2.sub b.pos a.pos in
let length = Vec2.length d in
if length > 0. then (
let u = Vec2.scale (1. /. length) d in
let f = (s.k *. (length -. s.rest)) +. (s.damping *. Vec2.dot (Vec2.sub b.vel a.vel) u) in
acc.(s.a) <- Vec2.add acc.(s.a) (Vec2.scale (f /. a.mass) u);
acc.(s.b) <- Vec2.sub acc.(s.b) (Vec2.scale (f /. b.mass) u)));
acc
let step ~(gravity : Vec2.t) ~(dt : float) (bodies : Body.t array) (springs : spring list) : Body.t array =
let acc = accelerations bodies springs in
bodies
|> Array.mapi (fun i (b : Body.t) ->
if b.mass = infinity then b
else
let vel = Vec2.add b.vel (Vec2.scale dt (Vec2.add acc.(i) gravity)) in
{ b with vel; pos = Vec2.add b.pos (Vec2.scale dt vel) })
let chain ~(from : Vec2.t) ~(towards : Vec2.t) (n : int) ~(k : float) ~(damping : float) : Body.t array * spring list =
let at i = Vec2.add from (Vec2.scale (float_of_int i /. float_of_int (n - 1)) (Vec2.sub towards from)) in
let rest = Vec2.length (Vec2.sub towards from) /. float_of_int (n - 1) in
( Array.init n (fun i -> if i = 0 then Body.make ~mass:infinity (at i) else Body.make (at i)),
List.init (n - 1) (fun i -> { a = i; b = i + 1; rest; k; damping }) )