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TWEET # Untitled a guest Oct 21st, 2019 57 Never
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1.
2. (* auto eval 4.2 *)
3.
4.
5. (* 1. *)
6. type t_point_vector = {x : float; y : float};;
7. (* type vector & type point didn't has any difference *)
8. type t_ball = {pos : t_point_vector; speed : t_point_vector};;
9. (* the ball have a position and a speed (due to gravity) *)
10.
11. (* 2. *)
12.
13. let gravity : t_point_vector = {x = 0.; y = -9.80665};;
14. (* the gravity is a vector *)
15.
16.
17. (* 3. *)
18.
19. let sum_vector(vector_1, vector_2 : t_point_vector * t_point_vector) :
20. t_point_vector =
21.    {x = vector_1.x +. vector_2.x; y = vector_1.y +. vector_2.y}
22. ;;
23. (* sum_vector is a function used to add vector 1 and vector 2, can be used to add vector to position or position to position *)
24.
25. let init_ball(height, speed : float * t_point_vector) : t_ball =
26.   let init_point : t_point_vector = {x = 0.; y = height} in {pos =
27. init_point; speed = speed}
28. ;;
29. (* assign the speed and the height to a ball *)
30.
31. let rec compute_next_speed(ball, t : t_ball * int) : t_point_vector =
32.   if t = 0
33.   then ball.speed
34.   else
35.     sum_vector(compute_next_speed(ball, t-1), gravity)
36. ;;
37. (* a recursive function who add 't' times gravity to the speed *)
38.
39. (* 4. *)
40.
41. let rec compute_next_pos(ball , t: t_ball * int) : t_point_vector =
42.   if t = 0
43.   then ball.pos
44.   else
45.     sum_vector(compute_next_pos(ball, t-1), compute_next_speed(ball, t))
46. ;;
47. (* give the position after 't' seconds, due to speed changes *)
48.
49. (* 5. *)
50.
51. let rec compute_end_point(ball, t : t_ball * int) : t_point_vector =
52.   let pos : t_point_vector = compute_next_pos(ball, t) in
53.   if pos.y < 0.
54.   then compute_next_pos(ball, t)
55.   else
56.     compute_end_point(ball, t+1)
57. ;;
58.
59.
60. compute_end_point({pos = {x = 0.; y = 100.}; speed = {x = 10.; y = 10.}}, 0);;
61. (* exemple for a ball *)
62.
63. #trace compute_end_point
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