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1 (**********************************************************************) (* Corrige du TD "Graphisme" *) (**********************************************************************) (************************ Instructions de base ************************) #load "graphics.cma" open Graphics open_graph " 800x " for i = 0 to 255 do for j = 0 to 255 do set_color (rgb i 0 j); plot i j; done let rose = and mandarine = and orange = and jaunefaible = and saumon = and violet = and indigo = and turquoise = and vertjaune = (* SORTIE : rose : int = mandarine : int = orange : int = jaunefaible : int = saumon : int = violet : int = indigo : int = turquoise : int = vertjaune : int = *) let message= "Titre" in moveto 0 0; draw_string message (***************************** Exercice 1 *****************************) let cadre = open_graph " "; set_color magenta; moveto 5 5; lineto 400 5; lineto ; lineto 5 40; lineto 5 5; moveto ;
2 set_text_size 18; set_color blue; draw_string "Pressez a nouveau sur une touche..."; (* SORTIE : cadre : unit = () *) (***************************** Exercice 2 *****************************) open_graph " 800x " (* Pour la fonction "coord", il s'agit de trouver y = a x + b tq xmin -> 0 et xmax -> width - 1 donc entre les points A(xmin, O) et B(xmax, width - 1) a = (width-1) / (xmax-xmin) et b = y - ax pour x = xmin et y = 0 par exemple => b = -(width-1) * xmin / (xmax-xmin) et donc y = (width-1) * (x - xmin) / (xmax - xmin) *) let coord (xmin, xmax) width x = int_of_float ( (float_of_int (width - 1)) *. (x -. xmin) /. (xmax -. xmin)) (* SORTIE : coord : float * float -> int -> float -> int = <fun> *) (* Remarque : on ajoute 0.5 au flottant trouve avant de le passer en entier pour obtenir l'arrondi et non la troncature. Exemple : float_of_int 5.8 donnerait 5, or la valeur souhaitee est 6. Si on fait > 6.3 donne bien 6. *) (* Verification *) coord (-1.0,1.0) 800 (-1.0) (* SORTIE : - : int = 0 *) coord (-1.0,1.0) (* SORTIE : - : int = 799 *) coord (-1.0,1.0) (* SORTIE : - : int = 599 *) let point x y xmin xmax ymin ymax width height = moveto (coord (xmin, xmax) (width) x) (coord (ymin, ymax) (height) y) (* SORTIE : point : float -> float -> float -> float -> float -> float -> int -> int -> unit = <fun> *)
3 let trait x y xmin xmax ymin ymax width height = lineto (coord (xmin, xmax) (width) x) (coord (ymin, ymax) (height) y) (* SORTIE : trait : float -> float -> float -> float -> float -> float -> int -> int -> unit = <fun> *) let draw_axes (xmin, ymin, xmax, ymax) = set_color black; point 0.0 ymin xmin xmax ymin ymax (size_x()) (size_y()); trait 0.0 ymax xmin xmax ymin ymax (size_x()) (size_y()); point xmin 0.0 xmin xmax ymin ymax (size_x()) (size_y()); trait xmax 0.0 xmin xmax ymin ymax (size_x()) (size_y()) (* SORTIE : draw_axes : float * float * float * float -> unit = <fun> *) (* Essai *) draw_axes (-2.0, -1.0, 1.0, 2.0) let step (xmin, xmax) n i = xmin +. (xmax -. xmin) *. (float_of_int i) /. (float_of_int (n-1)) (* SORTIE : step : float * float -> int -> int -> float = <fun> *) (* Essai *) step (-1.0, 1.0) (* SORTIE : - : float = -0.5 *) let trace (xmin, ymin, xmax, ymax) f n = draw_axes (xmin, ymin, xmax, ymax); point xmin (f xmin) xmin xmax ymin ymax (size_x()) (size_y()); for i = 1 to n-1 do let x = step (xmin, xmax) n i in trait x (f x) xmin xmax ymin ymax (size_x()) (size_y()); (* SORTIE : trace : float * float * float * float -> (float -> float) -> int -> unit = <fun> *) trace (-6.0, -1.5, 6.0, 1.5) sin 500
4 (***************************** Exercice 3 *****************************) let trace_pol ro xmin xmax ymin ymax pas tmax = draw_axes (xmin, ymin, xmax, ymax); let t = ref 0. and r = ro 0. in point (r *. (cos!t)) (r *. sin!t) xmin xmax ymin ymax (size_x()) (size_y()); while!t < tmax do let r = ro!t in trait (r*.(cos!t)) (r*.sin!t) xmin xmax ymin ymax (size_x()) (size_y()); t :=!t +. pas (* SORTIE : trace_pol : (float -> float) -> float -> float -> float -> float -> float -> float -> unit = <fun> *) let rec puiss x n = if n = 0 then 1. else x *. (puiss x (n - 1)) (* SORTIE : puiss : float -> int -> float = <fun> *) (* Le papillon *) trace_pol (fun t -> exp (cos (2. *. t)) -. 2.*.(cos (4. *. t)) +. (puiss (sin (t /. 12.)) 5) ) (-3.) 3. (-3.) (* La torpille *) trace_pol (fun t -> exp (cos (2.*.t)) -. 2.*.(cos (3. *. t)) +. (puiss (sin (t /. 20.)) 5) ) (-5.) 3. (-3.) (***************************** Exercice 4 *****************************) let famille f xmin xmax ymin ymax mmin mmax n pas = draw_axes (xmin, xmax, ymin, ymax); let m = ref mmin in while!m <= mmax do set_color (rgb ((int_of_float (!m) * 20) mod ) ((int_of_float (!m) * 30) mod 255) ((int_of_float (!m) * 40) mod )); point xmin (f xmin!m) xmin xmax ymin ymax (size_x()) (size_y());
5 for i = 1 to n do let x = step (xmin, xmax) n i in trait x (f x!m) xmin xmax ymin ymax (size_x()) (size_y()); m :=!m +. pas; (* SORTIE : famille : (float -> float -> float) -> float -> float -> float -> float -> float -> float -> int -> float -> unit = <fun> *) famille (fun x m -> exp (-.x +. m *. log (abs_float x))) (-1.5) (-2.) famille (fun x m -> exp (-. m*. x *. x)) (-4.) famille (fun x m -> 1. /. (1. +. power (x *. x) m)) (-4.) (* Les courbes y = 1 / (1 + x^2m) montrent une convergence non uniforme de cette suite de fonctions vers une fonction discontinue *) (***************************** Exercice 5 *****************************) let dead = rgb (* gris clair *) (* SORTIE : dead : color = *) let baby = green (* SORTIE : baby : color = *) let age x = if x = dead x = white then white else if x <= 0 then black else x - (rgb ) (* SORTIE : age : color -> color = <fun> *) let xmin = ref 0 (* SORTIE : xmin : int ref = ref 0 *) let ymin = ref 0 (* SORTIE : ymin : int ref = ref 0 *) let xmax = ref 0
6 (* SORTIE : xmax : int ref = ref 0 *) let ymax = ref 0 (* SORTIE : ymax : int ref = ref 0 *) (* Attention : les cellules ont une taille de 5x5 *) let cellule x y = let c = point_color (5 * x) (5 * y) in c <> white && c <> baby (* SORTIE : cellule : int -> int -> bool = <fun> *) let dessine_point x y c = set_color c; fill_rect (5 * x) (5 * y) 5 5 (* SORTIE : dessine_point : int -> int -> color -> unit = <fun> *) let pass1 () = for x =!xmin - 1 to!xmax + 1 do for y =!ymin - 1 to!ymax + 1 do let nb_voisins = ref 0 in if cellule (x - 1) (y - 1) then incr nb_voisins; if cellule (x + 1) (y - 1) then incr nb_voisins; if cellule (x - 1) (y + 1) then incr nb_voisins; if cellule (x + 1) (y + 1) then incr nb_voisins; if cellule (x) (y + 1) then incr nb_voisins; if cellule (x + 1) (y) then incr nb_voisins; if cellule (x - 1) (y) then incr nb_voisins; if cellule (x) (y - 1) then incr nb_voisins; if!nb_voisins = 3 && not(cellule x y) then begin dessine_point x y baby; if x <!xmin then xmin := x; if y <!ymin then ymin := y; if x >!xmax then xmax := x; if y >!ymax then ymax := y; end; if (!nb_voisins < 2!nb_voisins > 3) && cellule x y then dessine_point x y dead; done (* SORTIE : pass1 : unit -> unit = <fun> *) let pass2 () = for x =!xmin - 1 to!xmax + 1 do for y =!ymin - 1 to!ymax + 1 do dessine_point x y (age (point_color (5 * x) (5 * y))); done
7 (* SORTIE : pass2 : unit -> unit = <fun> *) let init () = xmin := ; ymin := ; xmax := 0; ymax := 0; let continue = ref true in while!continue do let st = wait_next_event [Button_down; Key_pressed] in if st.keypressed then continue := false else begin let (x, y) = (st.mouse_x / 5,st.mouse_y / 5) and c = point_color st.mouse_x st.mouse_y in if c = baby then dessine_point x y white else dessine_point x y baby; if x >!xmax then xmax := x; if y >!ymax then ymax := y; if x <!xmin then xmin := x; if y <!ymin then ymin := y; end; done (* SORTIE : init : unit -> unit = <fun> *) let main () = init (); let cont = ref true and pass = ref true in while!cont do if!pass then pass2() else pass1(); pass := not (!pass); let st = wait_next_event [Button_down; Key_pressed] in if st.keypressed then cont := false; (* SORTIE : main : unit -> unit = <fun> *) main () let evolution_rapide () = for i = 1 to 500 do
8 dessine_point (30 + random int 100) (30 + random int 60) baby xmin := 30; ymin := 30; xmax := 130; ymax := 90; while not key_pressed() do pass2(); pass1(); (* SORTIE : evolution_rapide : unit -> unit = <fun> *) evolution_rapide() let croix n = clear_graph(); for li = 10 to 110 do dessine_point 80 li baby for co = 30 to 130 do dessine_point co 60 baby xmin := 30; ymin := 10; xmax := 130; ymax := 110; for i = 1 to n do pass2(); pass1(); done (* SORTIE : croix : int -> unit = <fun> *) croix 112 croix 1000
(************************ Instructions de base ************************) #open "graphics";; open_graph " 800x ";; (* SORTIE : - : unit = () *)
(**********************************************************************) (* Corrige du TD 4 *) (**********************************************************************) (************************ Instructions
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