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(* Planets: A celestial simulator
Copyright (C) 2001-2003 Yaron M. Minsky
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*)
open StdLabels
open MoreLabels
open Printf
open State
open Constants
open Common
(* Faster physics implementation that is array-based *)
(* Only implements the act_all_on_all function. *)
(* Another useful thing to implement faster would be collision detection *)
(* all-float record, to let the compiler unbox in a loop *)
type fbody = { mutable x_pos: float;
mutable y_pos: float;
mutable x_vel: float;
mutable y_vel: float;
fb_radius: float;
fb_mass: float;
}
let cube x = x *. x *. x
let square x = x *. x
(* let sqrtcube x = sqrt (x *. x *. x) (* Faster but less flexible
implementaqtion of sqrtcube *) *)
let body_to_fbody body =
let (x_pos,y_pos) = body.pos
and (x_vel,y_vel) = body.velocity
(*and (x_accel,y_accel) =
match body.i with None -> (0.,0.) | Some accel -> accel *)
in
{ x_pos = x_pos;
y_pos = y_pos;
fb_radius = body.radius;
fb_mass = body.mass;
x_vel = x_vel;
y_vel = y_vel;
}
let build_fbody_array bodies =
Array.of_list (List.map ~f:body_to_fbody bodies)
(* convert a body and a b to an updated body *)
let fbody_and_body_to_body body b =
{ body with
velocity = (b.x_vel,b.y_vel);
pos = (b.x_pos,b.y_pos);
}
(******** List iterator w/index ********)
let rec list_iteri_rec ~f list i = match list with
[] -> ()
| hd::tl -> f ~i hd; list_iteri_rec ~f tl (i+1)
let list_iteri ~f list =
list_iteri_rec ~f list 0
(**************************************************)
let array_to_bodies bodies array =
let b_list = Array.to_list array in
List.map2 ~f:fbody_and_body_to_body bodies b_list
(**********************************************************************)
let timer = MTimer.create ()
let sqrtcube x = sqrt (x *. x *. x)
let act_all_on_all_rk ~bounce bodies =
let gexp = grav_exp#v in
let exp = ((1.0 +. gexp)/.2.0) in
let sqrtcube =
if gexp = 2.0 then sqrtcube else (fun x -> x ** exp) in
let const = gconst#v in
(* t is the time. This function has no time dependence.
s is the position is state space
dsdt is the array of derivatives
*)
let deriv t s dsdt =
(* initialize derivatives to 0 *)
for i = 0 to Array.length dsdt - 1 do dsdt.(i) <- 0. done;
for i = 0 to Array.length bodies - 1 do
(* x and y pos derivative *)
dsdt.(i*4) <- s.(i*4 + 2);
dsdt.(i*4 + 1) <- s.(i*4 + 3);
done;
for i = 0 to Array.length bodies - 1 do
for j = i+1 to Array.length bodies - 1 do
(* compute i's action on j and vice-versa. That way you only need to
* compute the force once. It's nearly twice as fast that way. *)
let x_pos_i = s.(i*4) and y_pos_i = s.(i*4 + 1) in
let x_pos_j = s.(j*4) and y_pos_j = s.(j*4 + 1) in
let xdiff = x_pos_i -. x_pos_j
and ydiff = y_pos_i -. y_pos_j in
let dist_sq = xdiff *. xdiff +. ydiff *. ydiff in
let mult = const /. sqrtcube dist_sq in
let mult_i = -. mult *. bodies.(j).fb_mass
and mult_j = mult *. bodies.(i).fb_mass
in
(* x vel derivative *)
dsdt.(i*4 + 2) <- dsdt.(i*4 + 2) +. xdiff *. mult_i;
dsdt.(j*4 + 2) <- dsdt.(j*4 + 2) +. xdiff *. mult_j;
(* y vel derivative *)
dsdt.(i*4 + 3) <- dsdt.(i*4 + 3) +. ydiff *. mult_i;
dsdt.(j*4 + 3) <- dsdt.(j*4 + 3) +. ydiff *. mult_j;
if bounce &&
(let total_radius = bodies.(j).fb_radius +. bodies.(i).fb_radius in
dist_sq < total_radius *. total_radius )
then (
let total_radius = bodies.(j).fb_radius +. bodies.(i).fb_radius in
let mult = -. mult *. bodies.(i).fb_mass *. bodies.(j).fb_mass
*. (total_radius *. total_radius /. dist_sq) in
let mult_i = -. mult /. bodies.(i).fb_mass
and mult_j = mult /. bodies.(j).fb_mass
in
(* x vel derivative *)
dsdt.(i*4 + 2) <- dsdt.(i*4 + 2) +. xdiff *. mult_i;
dsdt.(j*4 + 2) <- dsdt.(j*4 + 2) +. xdiff *. mult_j;
(* y vel derivative *)
dsdt.(i*4 + 3) <- dsdt.(i*4 + 3) +. ydiff *. mult_i;
dsdt.(j*4 + 3) <- dsdt.(j*4 + 3) +. ydiff *. mult_j;
)
done
done
in
let s =
Array.init (4 * Array.length bodies)
~f:(fun i -> match i mod 4 with
| 0 -> bodies.(i / 4).x_pos
| 1 -> bodies.(i / 4).y_pos
| 2 -> bodies.(i / 4).x_vel
| _ -> bodies.(i / 4).y_vel
)
in
(* dumb_solver s state.delta#v deriv; *)
Rk4.step s 0.0 state.delta#v s deriv;
for i = 0 to Array.length bodies - 1 do
bodies.(i).x_pos <- s.(4 * i);
bodies.(i).y_pos <- s.(4 * i + 1);
bodies.(i).x_vel <- s.(4 * i + 2);
bodies.(i).y_vel <- s.(4 * i + 3);
done
let act_all_on_all ~bounce bodies =
let array = build_fbody_array bodies in
act_all_on_all_rk ~bounce array;
array_to_bodies bodies array
|
