type vector = { x : float; y : float }

let right = { x = 1.0; y = 0.0 }
let up    = { x = 0.0; y = 1.0 }
let zero  = { x = 0.0; y = 0.0 }

let epsilon = 0.000001

let ( -- ) a b =
  { x = a.x -. b.x; y = a.y -. b.y }

let ( ++ ) a b =
  { x = a.x +. b.x; y = a.y +. b.y }

let ( *+ ) s a =
  { x = a.x *. s; y = a.y *. s }

let sqlen a =
  a.x *. a.x +. a.y *. a.y

let len a =  
  sqrt (sqlen a)

let equal a b = 
  sqlen (a -- b) < epsilon

exception ZeroVector

let normalize a = 
  let l = len a in
    if l < epsilon then raise ZeroVector
    else (1. /. l) *+ a

let dot a b = 
  a.x *. b.x +. a.y *. b.y