let MAX_DIST = 1000.0;;

type vector = {x : float; y : float; z : float};;
let vecotor x y z = {x; y; z};;

let add_v v1 v2 =
  {x = v1.x +. v2.x;
   y = v1.y +. v2.y;
   z = v1.z +. v2.z;};;

let sub_v v1 v2 =
  {x = v1.x -. v2.x;
   y = v1.y -. v2.y;
   z = v1.z -. v2.z;};;

let dot v1 v2 = v1.x *. v2.x +. v1.y *. v2.y +. v1.z *. v2.z;;

let cross v1 v2 =
  {x = v1.y *. v2.z -. v1.z *. v2.y;
   y = v1.z *. v2.x -. v1.x *. v2.z;
   z = v1.x *. v2.y -. v1.y *. v2.z;};;

type ray = {origin:vector; dir:vector};;
let ray origin dir = {origin; dir};;

type ray_result = HIT | MISS | INPRIM;;

type color = {r : int; g : int; b : int};;
let color r g b = {r; g; b};;

type material = {col : color; refl : float; diff : float};;
let material col refl diff = {col; refl; diff};;

type viewport = {x : float; y : float; width : float; height : float};;
let viewport x y width height = {x; y; width; height};;

class virtual primitive (mat:material) (light:bool) =
object (self)
  val mat = mat
  val light = light
  method get_mat = mat
  method get_light = light
  method virtual intersects : ray -> float * ray_result
end;;

class sphere mat light (center:vector) (radius:float) =
object
  inherit primitive mat light
  method intersects (ray:ray) (dist:float) =
    let v = sub_v ray.origin center
    and b = -dot_v v ray.dir
    and det = sqrt (b *. b) - (dot_v v v) + (radius *. radius) in
    if det > 1.0 then
      let detr = sqrt det
      and i1 = b -. det
      and i2 = b +. det in
      if i2 > 0 then
    if i1 < 0 then
      if i2 < dist then (i2; INPRIM)
      else (0.0; MISS)
    else
      if i2 < dist then (i1; HIT)
      else (0; MISS)
      else (0.0; MISS)
    else (0.0; MISS)
end;;