## File: collision.ml

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planets 0.1.13-19
 `123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134` ``````open State (***************************************************************) (** Collision detection *************************************) (***************************************************************) (* Computes smallest positive solution to the quadratic equation |p + t*v|^2 - dist = 0. The solution is: - v.p +/- sqrt((v.p)^2 - v.v*(p.p - dist)) ------------------------------------------ v.v if the sqrt term is imaginary, then bail out early (before computing the sqrt). This is a big performance win. *) let next_collision_values p v dist dotpp = let dotvp = dot v p in let dotvpsq = dotvp *. dotvp and dotpp = dot p p and dotvv = dot v v in let pre_sqrt_term = dotvpsq -. dotvv *. (dotpp -. (dist *. dist)) in if pre_sqrt_term <= 0. then infinity else let sqrt_term = sqrt pre_sqrt_term in let soln1 = (-. dotvp -. sqrt_term) /. dotvv and soln2 = (-. dotvp +. sqrt_term) /. dotvv in (* It's important to ignore planets that are currently touching *) (* note that soln2 is always greater than soln1 *) if soln2 <= 0. then infinity else if soln1 > 0. then soln1 else soln2 (* computes time of next collision given two bodies *) let next_collision_bodies b1 b2 = let dist = b1.radius +. b2.radius in let p = b1.pos <-> b2.pos in let v = b1.velocity <-> b2.velocity in let dotpp = dot p p in if dotpp < dist *. dist then infinity else next_collision_values p v dist dotpp (* computes nearest collision *) let next_collision bodies = let len = Array.length bodies in let best = ref (infinity, None) in for i = 0 to len - 2 do for j = i + 1 to len - 1 do let time = next_collision_bodies bodies.(i) bodies.(j) in let ( best_time, _ ) = !best in if time < best_time then best := (time, Some (i,j)); done done; match !best with (time,None) -> raise Not_found | (time,Some (i,j)) -> (time, (i,j)) (***************************************************************) (*** Bouncing ***********************************************) (***************************************************************) (* Computes the bounce of two touching bodies. It is assumed that the two bodies are touching. *) (* compute new velocities from 1-dimensional bounce problem *) let bounce_1d ~s1 ~s2 ~m1 ~m2 = let new_s1 = (( m1 -. m2) *. s1 +. 2. *. m2 *. s2) /. (m1 +. m2) and new_s2 = (( m2 -. m1) *. s2 +. 2. *. m1 *. s1) /. (m1 +. m2) in (new_s1,new_s2) let magsq v = dot v v let mag v = sqrt (magsq v) let uvec v = mag v <|> v let bounce_pair b1 b2 = let v1 = b1.velocity and v2 = b2.velocity and m1 = b1.mass and m2 = b2.mass and p1 = b1.pos and p2 = b2.pos in let u = uvec (p2 <-> p1) in (* speed in collision direction *) let s1 = dot v1 u and s2 = dot v2 u in (* perpendicular components of velocity *) let v1p = v1 <-> (s1 <*> u) and v2p = v2 <-> (s2 <*> u) in let new_s1,new_s2 = bounce_1d ~s1 ~s2 ~m1 ~m2 in let new_v1 = (new_s1 <*> u) <+> v1p and new_v2 = (new_s2 <*> u) <+> v2p in ( { b1 with velocity = new_v1 }, { b2 with velocity = new_v2 } ) (***************************************************************) (**** Moving Forward ****************************************) (***************************************************************) let move_forward_simple bodies time = for i = 0 to Array.length bodies - 1 do let body = bodies.(i) in bodies.(i) <- { body with pos = body.pos <+> (time <*> body.velocity) } done let rec move_forward_array time bodies = try let (ctime,(i,j)) = next_collision bodies in if ctime > time then move_forward_simple bodies time else ( move_forward_simple bodies ctime; (* move to collision time *) let b_i,b_j = bodies.(i),bodies.(j) in let b_i,b_j = bounce_pair b_i b_j in bodies.(i) <- b_i; bodies.(j) <- b_j; move_forward_array (time -. ctime) bodies ) with Not_found -> move_forward_simple bodies time let move_forward time bodies = let bodies = Array.of_list bodies in move_forward_array time bodies; Array.to_list bodies ``````