open Graphics ;; Random.self_init () ;; (* use Ctrl+F with 'WALUIGI_TIME' to look for sections *) (* ------------------------------------------------------------------------------------- *) (* ------------------------------------------------------------------------------------- *) (* WALUIGI_TIME Types + Constants *) exception ReturnBool of bool ;; exception ReturnInt of int ;; exception HasEnded ;; type pt_2d = { mutable x : float ; mutable y : float ; } ;; type polygon = { vertexes : pt_2d array ; rgb : int ; xmin : float ; xmax : float ; ymin : float ; ymax : float ; mutable restitution : float ; score : int ; } ;; type sphere = { center : pt_2d ; radius : float ; rgb : int ; xmin : float ; xmax : float ; ymin : float ; ymax : float ; mutable restitution : float ; score : int ; } ;; let default_polygon = { vertexes = [||] ; rgb = 0 ; xmin = 1. ; xmax = -. 1. ; ymin = 1. ; ymax = -. 1. ; restitution = 0. ; score = 0 ; } ;; let default_sphere = { center = {x = 0. ; y = 0.} ; rgb = 0 ; radius = -. 1. ; xmin = 1. ; xmax = -. 1. ; ymin = 1. ; ymax = -. 1. ; restitution = 0. ; score = 0 ; } ;; type ball = { radius : float ; mass : float ; rgb : int ; xy : pt_2d ; v : pt_2d ; a : pt_2d ; fres : pt_2d ; } ;; let univ_dt = 0.05 ;; let univ_friction = 0.8 ;; let univ_g = 800.0 ;; let pi = 3.14159265358979343 ;; let gforce = {x = 0. ; y = -. univ_g} ;; let score = ref 0 ;; (* ------------------------------------------------------------------------------------- *) (* ------------------------------------------------------------------------------------- *) (* WALUIGI_TIME Arithmetical operations *) let rec pw x n = match n with | 0 -> 1 | 1 -> x | k when k mod 2 = 0 -> pw (x*x) (n/2) | k -> x * (pw (x*x) (n/2)) ;; let rec pwf x n = match n with | 0 -> 1. | 1 -> x | k when k mod 2 = 0 -> pwf (x *. x) (n/2) | k -> x *. (pwf (x *. x) (n/2)) ;; let rec ln10 n = match n with | k when k < 0 -> failwith "Are you sure about that ?" | k when k < 10 -> 0 | k -> 1 + ln10 (k/10) ;; let convexf x y theta = (1.0 -. theta) *. x +. theta *. y ;; let absf = function | x when x < 0.0 -> -. x | x -> x ;; let rec expand_fl = function | k when float_of_int (int_of_float k) = k -> int_of_float k | k -> expand_fl (10.0 *. k) ;; let incree = function | k when k < 10 -> 0 | _ -> 1 ;; let round x n = float_of_int (int_of_float (x *. pwf 10. n)) /. (pwf 10. n);; (* ------------------------------------------------------------------------------------- *) (* ------------------------------------------------------------------------------------- *) (* WALUIGI_TIME Dynamic Arrays *) type 'a dynamic = { mutable len : int ; mutable memlen : int ; mutable tab : 'a array } ;; let dyn_create (elt : 'a) = { len = 0 ; memlen = 16 ; tab = Array.make 16 elt } ;; let dyn_add (dyn : 'a dynamic) (elt : 'a) = if dyn.len = dyn.memlen then begin let _new = Array.make (2 * dyn.memlen) dyn.tab.(0) in for i = 0 to dyn.memlen -1 do _new.(i) <- dyn.tab.(i) done; dyn.tab <- _new ; dyn.memlen <- dyn.memlen * 2 ; end; dyn.tab.(dyn.len) <- elt ; dyn.len <- dyn.len +1 ;; let dyn_remove (dyn : 'a dynamic) (elt : 'a) = try for i = 0 to dyn.len -1 do if dyn.tab.(i) = elt then raise (ReturnInt i) done; raise (ReturnInt (-1)) with | ReturnInt (-1) -> () | ReturnInt k -> for i = k to dyn.len -2 do dyn.tab.(i) <- dyn.tab.(i+1) done; dyn.len <- dyn.len -1 ; if (dyn.memlen >= 32) && (dyn.len * 4 <= dyn.memlen) then begin let _new = Array.make (dyn.memlen/2) dyn.tab.(0) in for i = 0 to dyn.len -1 do _new.(i) <- dyn.tab.(i) done; dyn.tab <- _new ; dyn.memlen <- dyn.memlen/2 ; end ;; let dyn_fold_left (f : 'b -> 'a -> 'b) (acc0 : 'b) (dyn : 'a dynamic) = let acc = ref acc0 in for i = 0 to dyn.len -1 do acc := f !acc dyn.tab.(i) done; !acc ;; (* ------------------------------------------------------------------------------------- *) (* ------------------------------------------------------------------------------------- *) (* WALUIGI_TIME Arithmetical operations *) let vect_convexf (px : pt_2d) (py : pt_2d) theta = { x = convexf px.x py.x theta ; y = convexf px.y py.y theta ; } ;; let vect_sum_2D (p1 : pt_2d) (p2 : pt_2d) = { x = p1.x +. p2.x ; y = p1.y +. p2.y ; } ;; let vect_diff_2D (p1 : pt_2d) (p2 : pt_2d) = { x = p1.x -. p2.x ; y = p1.y -. p2.y ; } ;; let vect_mult_2D (p1 : pt_2d) (lambda : float) = { x = p1.x *. lambda ; y = p1.y *. lambda ; } ;; let vect_midpoint_2D (p1 : pt_2d) (p2 : pt_2d) = { x = (p1.x +. p2.x) /. 2.0 ; y = (p1.y +. p2.y) /. 2.0 ; } ;; let vect_normal_2D (p1 : pt_2d) (p2 : pt_2d) = { x = -. (p2.y -. p1.y) ; y = (p2.x -. p1.x) ; } ;; let return_proj_of_point (m : pt_2d) (spt : pt_2d) (ept : pt_2d) = match (-. ((ept.x -. spt.x) *. (spt.x -. m.x) +. (ept.y -. spt.y) *. (spt.y -. m.y)) /. ((ept.x -. spt.x) *. (ept.x -. spt.x) +. (ept.y -. spt.y) *. (ept.y -. spt.y))) with | k when k >= 0. && k <= 1. -> (vect_convexf spt ept k) | k when k < 0. -> spt | k -> ept ;; let return_proj_of_point_D (m : pt_2d) (spt : pt_2d) (ept : pt_2d) = let theta = (-. ((ept.x -. spt.x) *. (spt.x -. m.x) +. (ept.y -. spt.y) *. (spt.y -. m.y)) /. ((ept.x -. spt.x) *. (ept.x -. spt.x) +. (ept.y -. spt.y) *. (ept.y -. spt.y))) in (vect_convexf spt ept theta) ;; let vect_dot_product_2D (p1 : pt_2d) (p2 : pt_2d) = p1.x *. p2.x +. p1.y *. p2.y ;; let vect_norm_2D (p1 : pt_2d) = Float.sqrt (vect_dot_product_2D p1 p1) ;; let vect_dist_2D (p1 : pt_2d) (p2 : pt_2d) = vect_norm_2D (vect_diff_2D p1 p2) ;; let vect_scale_2D (v1 : pt_2d) (v2 : pt_2d) = vect_mult_2D v1 ((vect_norm_2D v2) /. (vect_norm_2D v1)) ;; let vect_normalize_2D (v1 : pt_2d) = vect_mult_2D v1 (1.0 /. (vect_norm_2D v1)) ;; let vect_symmetry (m : pt_2d) (p1 : pt_2d) (p2 : pt_2d) = let proj = return_proj_of_point_D m p1 p2 in let ortho = vect_diff_2D proj m in vect_sum_2D (vect_sum_2D ortho ortho) m ;; (* ------------------------------------------------------------------------------------- *) (* ------------------------------------------------------------------------------------- *) (* WALUIGI_TIME Physics functions *) let step_one_ball (b : ball) (dt : float) = { x = b.xy.x +. b.v.x *. dt ; y = b.xy.y +. b.v.y *. dt ; } ;; let is_in_bounding_box_p (b : ball) (poly : polygon) = (b.xy.x +. b.radius >= poly.xmin) && (b.xy.x -. b.radius <= poly.xmax) && (b.xy.y +. b.radius >= poly.ymin) && (b.xy.y -. b.radius <= poly.ymax) ;; let is_in_bounding_box_s (b : ball) (s : sphere) = (b.xy.x +. b.radius >= s.xmin) && (b.xy.x -. b.radius <= s.xmax) && (b.xy.y +. b.radius >= s.ymin) && (b.xy.y -. b.radius <= s.ymax) ;; let distance_line_segment (m : pt_2d) (spt : pt_2d) (ept : pt_2d) = match (-. ((ept.x -. spt.x) *. (spt.x -. m.x) +. (ept.y -. spt.y) *. (spt.y -. m.y)) /. ((ept.x -. spt.x) *. (ept.x -. spt.x) +. (ept.y -. spt.y) *. (ept.y -. spt.y))) with | k when k >= 0. && k <= 1. -> vect_dist_2D (vect_convexf spt ept k) m | k when k < 0. -> vect_dist_2D spt m | k -> vect_dist_2D ept m ;; let is_collision_p (b : ball) (poly : polygon) (dt : float) = (* returns the 1st point of the closest line that the ball collides with *) if not (is_in_bounding_box_p b poly) then (-1) else begin try let mind = ref b.radius and minidx = ref (-1) in for i = 0 to Array.length poly.vertexes - 1 do let dst = (distance_line_segment (step_one_ball b dt) poly.vertexes.(i) poly.vertexes.((i+1) mod Array.length poly.vertexes)) in if dst <= !mind then begin mind := dst ; minidx := i ; end done; raise (ReturnInt (!minidx)) with | ReturnInt b -> b end ;; let is_collision_s (b : ball) (s : sphere) (dt : float) = if not (is_in_bounding_box_s b s) then false else vect_dist_2D (step_one_ball b dt) (s.center) <= (s.radius +. b.radius) ;; let update_ball_data (b : ball) (polys : polygon array) (spheres : sphere array) (dt : float) = b.fres.x <- 0. ; b.fres.y <- 0. ; for p = 0 to (Array.length polys -1) do let hit = (is_collision_p b polys.(p) dt) in if hit <> -1 then begin score := !score + polys.(p).score ; (* apply normal reaction force *) let hit2 = (hit +1) mod (Array.length polys.(p).vertexes) in let proj = return_proj_of_point b.xy polys.(p).vertexes.(hit) polys.(p).vertexes.(hit2) in let proj_n = vect_normalize_2D (vect_diff_2D b.xy proj) in let reaction_force_2 = vect_mult_2D proj_n (univ_g *. b.mass *. (vect_dot_product_2D (vect_normalize_2D gforce) proj_n)) in b.fres.x <- b.fres.x +. reaction_force_2.x *. polys.(p).restitution ; b.fres.y <- b.fres.y +. reaction_force_2.y *. polys.(p).restitution ; (* change velocity according to angle *) let director = vect_diff_2D polys.(p).vertexes.(hit2) polys.(p).vertexes.(hit) in let symmetric = vect_symmetry b.v {x = 0. ; y = 0.} director in b.v.x <- symmetric.x ; b.v.y <- symmetric.y ; end done ; for s = 0 to (Array.length spheres -1) do if is_collision_s b spheres.(s) dt then begin score := !score + spheres.(s).score ; (* apply normal reaction force *) let proj_n = vect_normalize_2D (vect_diff_2D b.xy spheres.(s).center) in let reaction_force_2 = vect_mult_2D proj_n (univ_g *. b.mass *. (vect_dot_product_2D (vect_normalize_2D gforce) proj_n)) in b.fres.x <- b.fres.x +. reaction_force_2.x *. spheres.(s).restitution ; b.fres.y <- b.fres.y +. reaction_force_2.y *. spheres.(s).restitution ; (* change velocity according to angle *) let theta = b.radius /. (vect_norm_2D (vect_diff_2D b.xy spheres.(s).center)) in let intersection = (vect_convexf b.xy spheres.(s).center theta) in let director = vect_normal_2D intersection (vect_sum_2D intersection proj_n) in let symmetric = vect_symmetry b.v {x = 0. ; y = 0.} director in b.v.x <- symmetric.x ; b.v.y <- symmetric.y ; end done ; (* P = mg *) b.fres.y <- b.fres.y -. univ_g *. b.mass ; (* PFD : ma = sum(F) *) b.a.x <- b.fres.x /. b.mass ; b.a.y <- b.fres.y /. b.mass ; b.v.x <- b.v.x +. b.a.x *. dt ; b.v.y <- b.v.y +. b.a.y *. dt ; b.xy.x <- b.xy.x +. b.v.x *. dt ; b.xy.y <- b.xy.y +. b.v.y *. dt ;; (* ------------------------------------------------------------------------------------- *) (* ------------------------------------------------------------------------------------- *) (* WALUIGI_TIME Graphics fcts *) let draw_integer x0 y n0 r = (* 7-seg display *) let n = ref n0 in let size = ln10 n0 in let len = r/3 in let offset = size*(len*11/7)/2 in for i = 0 to size do let x = x0 + offset - i*(len*11/7) in if Array.mem (!n mod 10) [|0; 4; 5; 6; 7; 8; 9|] then draw_poly_line [|(x-len/2, y+len); (x-len/2, y)|]; if Array.mem (!n mod 10) [|0; 2; 3; 5; 6; 7; 8; 9|] then draw_poly_line [|(x-len/2, y+len); (x+len/2, y+len)|]; if Array.mem (!n mod 10) [|0; 1; 2; 3; 4; 7; 8; 9|] then draw_poly_line [|(x+len/2, y+len); (x+len/2, y)|]; if Array.mem (!n mod 10) [|2; 3; 4; 5; 6; 8; 9|] then draw_poly_line [|(x-len/2, y); (x+len/2, y)|]; if Array.mem (!n mod 10) [|0; 1; 3; 4; 5; 6; 7; 8; 9|] then draw_poly_line [|(x+len/2, y-len); (x+len/2, y)|]; if Array.mem (!n mod 10) [|0; 2; 3; 5; 6; 8; 9|] then draw_poly_line [|(x-len/2, y-len); (x+len/2, y-len)|]; if Array.mem (!n mod 10) [|0; 2; 6; 8|] then draw_poly_line [|(x-len/2, y-len); (x-len/2, y)|]; n := !n/10; done ;; let draw_integer_alignedleft x0 y n0 len = (* 7-seg display 2 *) set_line_width (max 1 (len/4)); let n = ref n0 in let size = ln10 (abs n0) in let cur_x = ref (x0 + size*(len*11/7)) in if !n < 0 then begin n := !n * (-1); draw_poly_line [|(x0, y); (x0+len, y)|]; cur_x := !cur_x + (len*11/7) end; for i = 0 to size do let x = !cur_x in if Array.mem (!n mod 10) [|0; 4; 5; 6; 7; 8; 9|] then draw_poly_line [|(x, y+len); (x, y)|]; if Array.mem (!n mod 10) [|0; 2; 3; 5; 6; 7; 8; 9|] then draw_poly_line [|(x, y+len); (x+len, y+len)|]; if Array.mem (!n mod 10) [|0; 1; 2; 3; 4; 7; 8; 9|] then draw_poly_line [|(x+len, y+len); (x+len, y)|]; if Array.mem (!n mod 10) [|2; 3; 4; 5; 6; 8; 9|] then draw_poly_line [|(x, y); (x+len, y)|]; if Array.mem (!n mod 10) [|0; 1; 3; 4; 5; 6; 7; 8; 9|] then draw_poly_line [|(x+len, y-len); (x+len, y)|]; if Array.mem (!n mod 10) [|0; 2; 3; 5; 6; 8; 9|] then draw_poly_line [|(x, y-len); (x+len, y-len)|]; if Array.mem (!n mod 10) [|0; 2; 6; 8|] then draw_poly_line [|(x, y-len); (x, y)|]; n := !n/10; cur_x := !cur_x - (len*11/7); done ;; let draw_float x y n0 r = let n = absf n0 in let ent = int_of_float n in let frac = expand_fl (n -. float_of_int ent) in draw_integer_alignedleft x y ent r ; fill_circle (x + (ln10 ent) * r * 11/7 + 3*r/2) (y - r) 3 ; draw_integer_alignedleft (x + 3*r/5 + (ln10 ent + 1)*r*11/7) y ((100 * frac) / (pw 10 (1+ ln10 frac))) r ;; let draw_polygon (poly : polygon) = set_color (rgb (poly.rgb mod 256) ((poly.rgb / 256) mod 256) ((poly.rgb / (256*256)) mod 256)) ; fill_poly (Array.init (Array.length poly.vertexes) (fun i -> (int_of_float poly.vertexes.(i).x, int_of_float poly.vertexes.(i).y))) ;; let draw_sphere (s : sphere) = set_color (rgb (s.rgb mod 256) ((s.rgb / 256) mod 256) ((s.rgb / (256*256)) mod 256)) ; fill_circle (int_of_float s.center.x) (int_of_float s.center.y) (int_of_float s.radius) ;; let draw_ball (b : ball) = set_color (rgb (b.rgb mod 256) ((b.rgb / 256) mod 256) ((b.rgb / (256*256)) mod 256)) ; fill_circle (int_of_float b.xy.x) (int_of_float b.xy.y) (int_of_float b.radius) ; set_line_width 4 ; draw_circle (int_of_float b.xy.x) (int_of_float b.xy.y) (int_of_float b.radius) ;; (* ------------------------------------------------------------------------------------- *) (* ------------------------------------------------------------------------------------- *) (* WALUIGI_TIME Misc fcts *) let get1char_plus () = if key_pressed () then read_key () else '@' ;; let create_ball (r : float) (x0 : int) (y0 : int) (m : float) (red : int) (green : int) (blue : int) = { radius = r ; rgb = red + 256 * green + 256 * 256 * blue ; mass = m; xy = {x = float_of_int x0 +. (Random.float 10.0 -. 5.0); y = float_of_int y0 +. (Random.float 10.0 -. 5.0)} ; v = {x = 0. ; y = 0.} ; a = {x = 0. ; y = 0.} ; fres = {x = 0. ; y = 0.} ; } ;; let create_polygon (arr : (int * int) array) (rest : float) (pts : int) (red : int) (green : int) (blue : int) = { vertexes = Array.init (Array.length arr) (fun k -> {x = float_of_int (fst arr.(k)); y = float_of_int (snd arr.(k))}) ; rgb = red + 256 * green + 256 * 256 * blue ; xmin = float_of_int (Array.fold_left (fun acc k -> min acc (fst k)) 99999 arr) ; xmax = float_of_int (Array.fold_left (fun acc k -> max acc (fst k)) (-99999) arr) ; ymin = float_of_int (Array.fold_left (fun acc k -> min acc (snd k)) 99999 arr) ; ymax = float_of_int (Array.fold_left (fun acc k -> max acc (snd k)) (-99999) arr) ; restitution = rest ; score = pts ; } ;; let create_sphere (x00 : int) (y00 : int) (rd : float) (rest : float) (pts : int) (red : int) (green : int) (blue : int) = let x0 = float_of_int x00 and y0 = float_of_int y00 in { center = {x = x0 ; y = y0}; rgb = red + 256 * green + 256 * 256 * blue ; radius = rd ; xmin = x0 -. rd ; xmax = x0 +. rd ; ymin = y0 -. rd ; ymax = y0 +. rd ; restitution = rest ; score = pts ; } ;; (* ------------------------------------------------------------------------------------- *) (* ------------------------------------------------------------------------------------- *) (* WALUIGI_TIME Edition functions *) let customize lvl_name = open_graph " 1200x800" ; set_window_title "WAH" ; let (res : polygon dynamic) = dyn_create default_polygon in let stopped = ref false in let refresh = ref true in let (cpoly : pt_2d dynamic) = dyn_create {x = 0. ; y = 0.} in while not !stopped do Unix.sleepf 0.005 ; if !refresh then begin auto_synchronize false ; clear_graph () ; refresh := false ; for p = 0 to res.len -1 do draw_polygon res.tab.(p) done; auto_synchronize true ; end; match (get1char_plus ()) with | 'a' -> (* add current polygon *) (*Printf.printf "+polygon\n" ;*) if cpoly.len >= 2 then begin refresh := true ; let newVTX = Array.init cpoly.len (fun k -> cpoly.tab.(k)) in dyn_add res { vertexes = newVTX ; rgb = 128 + 255*128 + 255*255*128 ; xmin = Array.fold_left (fun acc k -> min acc k.x) (999999.) newVTX ; xmax = Array.fold_left (fun acc k -> max acc k.x) (-.999999.) newVTX ; ymin = Array.fold_left (fun acc k -> min acc k.y) (999999.) newVTX ; ymax = Array.fold_left (fun acc k -> max acc k.y) (-.999999.) newVTX ; restitution = 1. ; score = 0 ; } ; cpoly.len <- 0 ; end | 'v' -> (* add a vertex *) (*Printf.printf "+vertex\n" ;*) let (mx, my) = mouse_pos () in dyn_add cpoly {x = float_of_int mx ; y = float_of_int my} ; | 'c' -> (* clear current polygon *) (*Printf.printf "cleared\n" ;*) cpoly.len <- 0 ; | 'h' -> stopped := true ; | _ -> () done; close_graph (); res ;; (* ------------------------------------------------------------------------------------- *) (* ------------------------------------------------------------------------------------- *) (* WALUIGI_TIME Main *) let simulate (data : polygon dynamic) (dats : sphere dynamic) = open_graph " 1200x800" ; set_window_title "WAH" ; let pinball = create_ball 25.0 600 800 0.15 169 169 169 in let stime = Unix.gettimeofday () in let ctime = ref (Unix.gettimeofday ()) in while true do let __start = Unix.gettimeofday () in auto_synchronize false ; clear_graph () ; set_color black ; set_line_width 4 ; draw_integer 600 770 !score 50 ; set_line_width 1 ; for d = 0 to data.len -1 do draw_polygon data.tab.(d) done; for d = 0 to dats.len -1 do draw_sphere dats.tab.(d) done; draw_ball pinball ; set_color (rgb 128 128 32) ; draw_float 25 770 (round (!ctime -. stime) 3) 25 ; auto_synchronize true ; Unix.sleepf 0.005 ; let __end = Unix.gettimeofday () in ctime := !ctime +. (__end -. __start) ; update_ball_data pinball data.tab dats.tab (__end -. __start) ; done; close_graph () ;; (*let polygons = customize () ;;*) let polygons = dyn_create default_polygon ;; dyn_add polygons (create_polygon [|(0, 0); (50, 0); (50, 775); (0, 775)|] 1.0 0 32 32 255) ;; dyn_add polygons (create_polygon [|(1150, 0); (1200, 0); (1200, 775); (1150, 775)|] 1.0 0 32 32 255) ;; dyn_add polygons (create_polygon [|(50, 0); (50, 200); (500, 25); (500, 0)|] 1.0 0 32 32 255) ;; dyn_add polygons (create_polygon [|(1150, 0); (1150, 200); (700, 25); (700, 0)|] 1.0 0 32 32 255) ;; dyn_add polygons (create_polygon [|(500, 0); (700, 0); (700, 25); (500, 25)|] 1.0 (-10) 192 64 64) ;; let spheres = dyn_create default_sphere ;; dyn_add spheres (create_sphere 200 400 20. 1. 5 220 32 220) ;; dyn_add spheres (create_sphere 300 200 20. 1. 3 192 0 192) ;; dyn_add spheres (create_sphere 400 450 20. 1. 3 192 0 192) ;; dyn_add spheres (create_sphere 600 350 20. 1. 10 255 64 255) ;; dyn_add spheres (create_sphere 800 450 20. 1. 3 192 0 192) ;; dyn_add spheres (create_sphere 900 200 20. 1. 3 192 0 192) ;; dyn_add spheres (create_sphere 1000 400 20. 1. 5 220 32 220) ;; dyn_add spheres (create_sphere 50 200 15. 1. 20 255 255 32) ;; dyn_add spheres (create_sphere 1150 200 15. 1. 20 255 255 32) ;; simulate polygons spheres ;; (* let create_polygon (arr : (int * int) array) (rest : float) (pts : int) (red : int) (green : int) (blue : int) let create_sphere (x00 : int) (y00 : int) (radius : float) (rest : float) (pts : int) *) (* ocamlfind ocamlopt -linkpkg -package unix -linkpkg -package graphics -thread -package threads -linkpkg main.ml *)