type vec3 = {
  x: float;
  y: float;
  z: float;
}

let of_floats (e1, e2, e3) = { x = e1; y = e2; z = e3 }
let add v w = { x = v.x +. w.x; y = v.y +. w.y; z = v.z +. w.z }
let sub v w = { x = v.x -. w.x; y = v.y -. w.y; z = v.z -. w.z }
let neg v = sub { x = 0.0; y = 0.0; z = 0.0 } v
let dot v w = (v.x *. w.x) +. (v.y *. w.y) +. (v.z *. w.z)

let cross v w =
  {
    x = (v.y *. w.z) -. (v.z *. w.y);
    y = (v.z *. w.x) -. (v.x *. w.z);
    z = (v.x *. w.y) -. (v.y *. w.x);
  }

let length v = sqrt (dot v v)

let unit_vector v =
  let l = length v in
  { x = v.x /. l; y = v.y /. l; z = v.z /. l }

let mul t v = { x = t *. v.x; y = t *. v.y; z = t *. v.z }

(* pairwise multiplication *)
let pmul v w = { x = v.x *. w.x; y = v.y *. w.y; z = v.z *. w.z }