#load "Graphics.cma";;

let f=10.;;
let pi=4.*.atan 1.;;
let colors=[|0x000066;0xcccccc;0xff3300;0x99cc00;0x99cc00|];;
let secondary_colors=[|0xc1c1ff;0xeeeeee;0xffdddd;0xe8ff9f;0xe8ff9f|];;

let 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type global_vars=
{mutable ph1:float;
	mutable ph2:float;
	mutable th1:float;
	mutable th2:float;
	nb_parall:int;
	nb_merid:int;
	nb_arcs:int;
	mode:string;
	mutable c:float;
	mutable x_t:float;
	mutable y_t:float;
	mutable x_rot:float;
	mutable y_rot:float;
	mutable ecran_vide:bool;
	mutable refx:int;
	mutable refy:int;
	mutable current_color:int;
	mutable current_color_secondary:int;
	mutable interaction_type:int;
	line_width1:int;
	line_width2:int};;

let multiplie m1 m2 gv=
	[|m1.(0).(0)*.m2.(0)+.m1.(0).(1)*.m2.(1)+.m1.(0).(2)*.m2.(2)+.(gv.x_t);
	m1.(1).(0)*.m2.(0)+.m1.(1).(1)*.m2.(1)+.m1.(1).(2)*.m2.(2)+.(gv.y_t);
	m1.(2).(0)*.m2.(0)+.m1.(2).(1)*.m2.(1)+.m1.(2).(2)*.m2.(2)|];;

let rot_matrice u1 u2=
	[|[|(cos u2);0.;(sin u2)|];
	[|-1.*.(sin u1)*.(sin u2);(cos u1);(sin u1)*.(cos u2)|];
	[|-1.*.(sin u2)*.(cos u1);-1.*.(sin u1);(cos u1)*.(cos u2)|]|];;

let spherique_to_cart e=
	[|e.(0)*.(cos e.(2))*.(sin e.(1));e.(0)*.(sin e.(2));e.(0)*.(cos e.(2))*.(cos e.(1))|];;

let spherique_to_cart_light e=
	[|(cos e.(1))*.(sin e.(0));(sin e.(1));(cos e.(1))*.(cos e.(0))|];;

let polaire_to_cart e=
	[|e.(0)*.(cos e.(1));e.(0)*.(sin e.(1));0.|];;

let cart_to_cart e=
	[|e.(0);e.(1);0.|];;

let projection e gv=
	if e.(2)<0. then (Graphics.set_color gv.current_color_secondary;Graphics.set_line_width gv.line_width1)
	else (Graphics.set_color gv.current_color;Graphics.set_line_width gv.line_width2);
	((e.(0)/.(1.-.e.(2)/.f)),(e.(1)/.(1.-.e.(2)/.f)));;

let affiche e coef_rot gv=
	let r_matrice=rot_matrice (coef_rot*.(gv.x_rot)) (coef_rot*.(gv.y_rot)) in
	let rec trace_groupe l=
	match l with
		|[]->()
		|h::t->let (x,y)=projection (multiplie r_matrice h gv) gv in
		Graphics.lineto ((int_of_float (gv.c*.x))+400) ((int_of_float (gv.c*.y))+400); 
		trace_groupe t;
	in let rec itere l=
	match l with
		|[]->()
		|[]::tt->itere tt;
		|(h::t)::tt->let (x0,y0)=projection (multiplie r_matrice h gv) gv in
		Graphics.moveto ((int_of_float (gv.c*.x0))+400) ((int_of_float (gv.c*.y0))+400);
		trace_groupe t;
		itere tt;
	in itere e;;

let creer_parall gv=
	let rec un_parall i j ll=
	match j with
		|(-1)->ll
		|_->un_parall i (j-1) ([|2.*.pi*.(0.5-.(float_of_int j)/.100.);
		pi*.(0.5-.(float_of_int i)/.(float_of_int gv.nb_parall))|]::ll)
	in let rec itere i l=
	match i with
		|(-1)->l
		|_->itere (i-1) ((un_parall i 100 [])::l)
	in itere gv.nb_parall [];;

let creer_merid gv=
	let rec un_merid i j ll=
	match j with
		|(-1)->ll
		|_->un_merid i (j-1) ([|(2.*.pi*.(0.5-.(float_of_int i)/.(float_of_int gv.nb_merid)));
		(pi*.(0.5-.(float_of_int j)/.100.))|]::ll)
	in let rec itere i l=
	match i with
		|(-1)->l
		|_->itere (i-1) ((un_merid i 100 [])::l)
	in itere gv.nb_merid [];;

let spherique_to_stereo e=
	let ph=e.(0) in let th=e.(1) in
	[|(tan (pi/.4.-.th/.2.));ph|];;

let spherique_to_mercator e=
	let ph=e.(0) in let th=e.(1) in
	[|ph;tan th|];;

let spherique_to_lambert e=
	let ph=e.(0) in let th=e.(1) in
	[|ph;sin th|];;

let stereo_to_spherique r t=
	[|t;pi/.2.-.2.*.atan(r/.2.)|];;

let spherique_to_stereo2 e=
	let ph=e.(0) in let th=e.(1) in
	(2.*.(tan (pi/.4.-.th/.2.)),ph);;

let creer_loxo gv=
	let (r1,t1)=(spherique_to_stereo2 [|gv.ph1;gv.th1|])
	and (r2,t2)=(spherique_to_stereo2 [|gv.ph2;gv.th2|]) in
	let coef_a=(log (r1/.r2))/.(t1-.t2) in let coef_b=r1/.(exp (coef_a*.t1)) in
	let rec itere n l=match n with
		|(-1)->l
		|_->
		let t=(float_of_int (n-1000))*.0.01 in let r=coef_b*.exp(coef_a*.t) in
		itere (n-1) ((stereo_to_spherique r t)::l);
	in itere 2000 [];;

let creer_loxo_light gv=
	let (r1,t1)=(spherique_to_stereo2 [|gv.ph1;gv.th1|])
	and (r2,t2)=(spherique_to_stereo2 [|gv.ph2;gv.th2|]) in
	let coef_a=(log (r1/.r2))/.(t1-.t2) in let coef_b=r1/.(exp (coef_a*.t1)) in
	let rec itere n l=match n with
		|(-1)->l
		|_->
		let t=gv.ph1+.((float_of_int n)/.200.)*.(gv.ph2-.gv.ph1)
		in let r=coef_b*.exp(coef_a*.t) in
		itere (n-1) ((stereo_to_spherique r t)::l);
	in itere 200 [];;

let creer_ortho gv=
	let (a1,a2,b1,b2,c1,c2)=((sin gv.th1),(sin gv.th2),((cos gv.th1)*.(cos gv.ph1)),
	((cos gv.th2)*.(cos gv.ph2)),(-1.*.(cos gv.th1)*.(sin gv.ph1)),(-1.*.(cos gv.th2)*.(sin gv.ph2)))
	in let coef_d=(c2-.c1*.a2/.a1)/.(b2-.b1*.a2/.a1)
	in let coef_c=c1/.a1-.coef_d*.b1/.a1 in
	let rec itere n l=match n with
		|(-1)->l
		|_->
		let ph=2.*.pi*.float_of_int(n)/.1000.
		in let th=(-1.)*.(atan ((coef_d*.(cos ph)+.(sin ph))/.coef_c)) in
		itere (n-1) ([|ph;th|]::l);
in itere 1000 [];;

let creer_ortho_light gv=
	let (a1,a2,b1,b2,c1,c2)=((sin gv.th1),(sin gv.th2),((cos gv.th1)*.(cos gv.ph1)),
	((cos gv.th2)*.(cos gv.ph2)),(-1.*.(cos gv.th1)*.(sin gv.ph1)),(-1.*.(cos gv.th2)*.(sin gv.ph2)))
	in let coef_d=(c2-.c1*.a2/.a1)/.(b2-.b1*.a2/.a1)
	in let coef_c=c1/.a1-.coef_d*.b1/.a1 in
	let rec itere n l=match n with
		|(-1)->l
		|_->
		let ph=gv.ph1+.(float_of_int(n)/.100.)*.(gv.ph2-.gv.ph1)
		in let th=(-1.)*.(atan ((coef_d*.(cos ph)+.(sin ph))/.coef_c))
		in itere (n-1) ([|ph;th|]::l);
	in itere 100 [];;

let bouger n gv=match n with
	|1->let (x,y)=Graphics.mouse_pos() in
		Graphics.clear_graph();
		gv.ecran_vide<-true;
		gv.x_t<-gv.x_t+.(float_of_int (x-(gv.refx))/.(gv.c));
		gv.y_t<-gv.y_t+.(float_of_int (y-(gv.refy))/.(gv.c));
		gv.refx<-x;gv.refy<-y
	|2->let (x,y)=Graphics.mouse_pos() in 
		Graphics.clear_graph();
		gv.ecran_vide<-true;
		gv.y_rot<-gv.y_rot+.((float_of_int (x-(gv.refx))/.100.));
		gv.x_rot<-gv.x_rot+.((float_of_int (y-(gv.refy))/.100.));
		gv.refx<-x;gv.refy<-y
	|3->let (x,y)=Graphics.mouse_pos() in 
		Graphics.clear_graph();
		gv.ecran_vide<-true;
		gv.c<-gv.c+.((float_of_int (y-(gv.refy)))*.2.);
		gv.refx<-x;gv.refy<-y
	|0->let (x,y)=Graphics.mouse_pos() in gv.refx<-x;gv.refy<-y;
	|_->();;

let rec dessiner l gv=match l with
	|[]->gv.ecran_vide<-false
	|h::t->let (coef_rot,couleur,e)=h
	in gv.current_color<-colors.(couleur);
	gv.current_color_secondary<-secondary_colors.(couleur);
	affiche e coef_rot gv;
	dessiner t gv;;

let rec interaction n l gv=
	bouger n gv;
	if gv.ecran_vide then dessiner l gv else ();
	match Graphics.read_key() with
		|'a'-> interaction 1 l gv
		|'z'-> interaction 2 l gv
		|'e'-> interaction 3 l gv
		|'q'-> ()
		| _ -> interaction 0 l gv;;

let lancer gv=
	let parall=creer_parall gv in
	let merid=creer_merid gv in
	let orth=[creer_ortho_light gv] in
	let lox=[creer_loxo_light gv] in
	let trans f1 f2 target=
		List.map (List.map f1) (f2 target);
	in let creer_liste_graphique f1 f2=
		(1.,1,(trans f1 f2 parall))::
		(1.,1,(trans f1 f2 merid))::
		(1.,0,(trans f1 f2 terre))::
		(1.,2,(trans f1 f2 orth))::
		(1.,3,(trans f1 f2 lox))::[]
	in let liste_graphique=(match gv.mode with
		|"3d"->creer_liste_graphique spherique_to_cart_light (fun x->x)
		|"stereo"->creer_liste_graphique polaire_to_cart (List.map (List.map spherique_to_stereo))
		|"mercator"->creer_liste_graphique cart_to_cart (List.map (List.map spherique_to_mercator))
		|"lambert"->creer_liste_graphique cart_to_cart (List.map (List.map spherique_to_lambert))
		|_->[]) in
	Graphics.open_graph "";
	interaction 0 liste_graphique gv;
	Graphics.close_graph();;

let gv0={
	ph1=0.55;
	ph2=2.46;
	th1=0.5;
	th2=0.63;
	nb_parall=10;
	nb_merid=10;
	nb_arcs=0;
	mode="lambert";
	c=200.;
	x_t=0.;
	y_t=0.;
	x_rot=0.;
	y_rot=0.;
	ecran_vide=true;
	refx=0;
	refy=0;
	current_color=0x000000;
	current_color_secondary=0xcccccc;
	interaction_type=0;
	line_width1=0;
	line_width2=2};;

lancer gv0;;