open Point

type t = {dx:float; dy:float; dz:float}

let dotproduct a b =
  a.dx *. b.dx +. a.dy *. b.dy +. a.dz *. b.dz

let between p q =
  {dx = q.x -. p.x; dy = q.y -. p.y; dz = q.z -. p.z}

let opposite v =
  {dx = -. v.dx; dy = -. v.dy; dz = -. v.dz}

let point_along p v ac =
  { x = p.x +. v.dx *. ac;
    y = p.y +. v.dy *. ac;
    z = p.z +. v.dz *. ac }

let product a b =
  { dx = a.dy *. b.dz -. a.dz *. b.dy;
    dy = a.dz *. b.dx -. a.dx *. b.dz;
    dz = a.dx *. b.dy -. a.dy *. b.dx }

let length a =
  sqrt(a.dx *. a.dx +. a.dy *. a.dy +. a.dz *. a.dz)

let length2 a =
  a.dx *. a.dx +. a.dy *. a.dy +. a.dz *. a.dz

let scale a s =
  {dx = a.dx *. s; dy = a.dy *. s; dz = a.dz *. s}

let normalize a =
  scale a (1.0 /. length a)

let sub a b =
  {dx = a.dx -. b.dx; dy = a.dy -. b.dy; dz = a.dz -. b.dz}