unit Unit1;

interface

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, StdCtrls, ComCtrls, Buttons, ExtCtrls,Math,Delau,Types;

type
  TForma = class(TForm)
    Image1: TImage;
    Edit1: TEdit;
    Label1: TLabel;
    Point: TSpeedButton;
    Ligne: TSpeedButton;
    PLigne: TSpeedButton;
    Polygone: TSpeedButton;
    Button1: TButton;
    Memo1: TMemo;
    BitBtn1: TBitBtn;
    BitBtn2: TBitBtn;
    Timer1: TTimer;
    BitBtn3: TBitBtn;
    Memo2: TMemo;
    Memo3: TMemo;
    SpeedButton1: TSpeedButton;
    SpeedButton2: TSpeedButton;
    SpeedButton3: TSpeedButton;
    SpeedButton5: TSpeedButton;
    LabeledEdit1: TLabeledEdit;
    Label2: TLabel;
    Button2: TButton;
    Button3: TButton;
    SpeedButton4: TSpeedButton;
    SpeedButton6: TSpeedButton;
    SpeedButton7: TSpeedButton;
    SpeedButton9: TSpeedButton;
    Memo4: TMemo;
    SpeedButton10: TSpeedButton;
    Memo5: TMemo;
    Button4: TButton;
    SpeedButton11: TSpeedButton;
    Button5: TButton;
    Label3: TLabel;
    SpeedButton8: TSpeedButton;
    BitBtn4: TBitBtn;
    Memo6: TMemo;
    Button6: TButton;
    procedure Edit1Change(Sender: TObject);
    procedure Image1MouseDown(Sender: TObject; Button: TMouseButton;
      Shift: TShiftState; X, Y: Integer);
    procedure Image1DblClick(Sender: TObject);
    procedure PointClick(Sender: TObject);
    procedure LigneClick(Sender: TObject);
    procedure PLigneClick(Sender: TObject);
    procedure PolygoneClick(Sender: TObject);
    procedure FormCreate(Sender: TObject);
    procedure Button1Click(Sender: TObject);
    procedure BitBtn1Click(Sender: TObject);
    procedure BitBtn2Click(Sender: TObject);
    procedure BitBtn3Click(Sender: TObject);
    procedure Timer1Timer(Sender: TObject);
    procedure SpeedButton5Click(Sender: TObject);
    procedure SpeedButton2Click(Sender: TObject);
    procedure SpeedButton3Click(Sender: TObject);
    procedure Image1MouseMove(Sender: TObject; Shift: TShiftState; X,
      Y: Integer);
    procedure SpeedButton1Click(Sender: TObject);
    procedure Button2Click(Sender: TObject);
    procedure Button3Click(Sender: TObject);
    procedure SpeedButton4Click(Sender: TObject);
    procedure SpeedButton6Click(Sender: TObject);
    procedure SpeedButton7Click(Sender: TObject);
    procedure SpeedButton9Click(Sender: TObject);
    procedure SpeedButton10Click(Sender: TObject);
    procedure Button4Click(Sender: TObject);
    procedure SpeedButton11Click(Sender: TObject);
    procedure Button5Click(Sender: TObject);
    procedure SpeedButton8Click(Sender: TObject);
    procedure BitBtn4Click(Sender: TObject);
    procedure Button6Click(Sender: TObject);
  private
    { Déclarations privées }
  public

    { Déclarations publiques }
  end;
Type TPoint=Record
      X,Y:integer;
      end;
Type Objet=Record
     Nature : String;
     ListePoint:array of Unit1.TPoint;
     end;
Type PointR=Record
     X,Y:real;
     end;
Type ObjetR=Record
     Nature : String;
     ListePoint:array of PointR;
     end;
Type Chemin=Record
      TA,TP:ptriangle;
      LesP:array of tpoint;
      EstFerme,EstSupprime:boolean;
      end;
Type TabPoints=array of unit1.tpoint;
var
  Forma: TForma;
  ListeObjets:array of Objet;
  ListeObjetsR:array of ObjetR;
  NouvelObjet:String;
  Sweep:integer;
  clique:integer;
  MaxX,MaxY,MinX,MinY:Integer;
  Enveloppe:array of TPoint;
  ptanglobant:types.tpoint;
  Chemins:array of Chemin;
  function DistPoint(P1,P2:tpoint):real;
  function DistSegment(P,P1,P2:tPoint;M:tmemo):real;
  function homothetie(T:array of unit1.tpoint;f:real):TabPoints;
  function DansPolygone(p,pinfini:ppoint):boolean;
  procedure RectangleAnglobant(o:objet;out minx,miny,maxx,maxy:integer);
implementation
function TriangleAnglobant(o:objet):TabPoints;
var b1,b2:real;
    x1,x2,x3,y1,y2,y3,i,X,Y:integer;
    p,pp,ppp:ppoint;
    ListPP: array of ppoint;
    T:TabPoints;
    mnx,mny,mxx,mxy,ymx,ymn:integer;
begin
RectangleAnglobant(o,mnx,mny,mxx,mxy);
ymx:=500-mny;ymn:=500-mxy;
b1:=ymx-mnx;
b2:=ymx+mxx;
x1:=trunc((b2-b1)/2);y1:=trunc(x1+b1);
x2:=trunc(ymn-b1);y2:=ymn;
x3:=trunc(-ymn+b2);y3:=ymn;
setlength(T,3);T[0].X:=x1;T[0].Y:=500-y1;T[1].X:=x2;T[1].Y:=500-y2;T[2].X:=x3;T[2].Y:=500-y3;
T:=homothetie(T,2);
{just pour le besoin de supptriangles}ptanglobant.x:=T[0].x;ptanglobant.Y:=T[0].Y;
setlength(Delau.ListePoint,0);
setlength(Delau.Listetriangle,0);
Delau.maxPoint:=0;
Delau.maxTriangle:=0;
p:=Delau.AddPoint(T[0].X,T[0].Y);pp:=Delau.AddPoint(T[1].X,T[1].Y);ppp:=Delau.AddPoint(T[2].X,T[2].Y);
Delau.AddTriangle(Delau.CreateTriangle(p,pp,ppp));
TriangleAnglobant:=t;
end;


procedure RectangleAnglobant(o:objet;out minx,miny,maxx,maxy:integer);
var i,N:Integer;
MxX,MxY,MnX,MnY:integer;
begin
MxX:=o.ListePoint[0].X;MxY:=o.ListePoint[0].Y;MnX:=o.ListePoint[0].X;MnY:=o.ListePoint[0].Y;//Initialisation
N:=length(o.ListePoint);
for i:=1 to N-1 do
    begin
    if MxX<o.ListePoint[i].X then MxX:=o.ListePoint[i].X;
    if MxY<o.ListePoint[i].Y then MxY:=o.ListePoint[i].Y;
    if MnX>o.ListePoint[i].X then MnX:=o.ListePoint[i].X;
    if MnY>o.ListePoint[i].Y then MnY:=o.ListePoint[i].Y;
    end;
minx:=mnx;miny:=mny;maxx:=mxx;maxy:=mxy;
end;

function DansPolygone(p,pinfini:ppoint):boolean;
var i,x,y,compteur,n:integer;
    p1,p2:pPoint;
    d1,d2:tDroite;
begin
new(p1);new(p2);
//Premiere droite
forma.image1.Canvas.Pen.Color:=clred;forma.image1.Canvas.Ellipse(p.X-2,p.Y-2,p.X+2,p.Y+2);
d1.a:=(p.y-pinfini.y);  d1.b:=-(p.x-pinfini.x);  d1.c:=-(d1.a*p.x+d1.b*p.y);
forma.image1.Canvas.Pen.Color:=clblue;
for x:=0 to 500 do for y:=0 to 500 do if abs(((d1.a*x)+(d1.b*y)+d1.c))<=2 then forma.image1.Canvas.Ellipse(X-2,Y-2,X+1,Y+1);
compteur:=0;n:=length(ListeObjets[0].listepoint);
for i:=0 to n-1 do
    begin
    p1.X:=ListeObjets[0].listepoint[i].X;p1.Y:=ListeObjets[0].listepoint[i].Y;
    p2.X:=ListeObjets[0].listepoint[(i+1) mod n].X;p2.Y:=ListeObjets[0].listepoint[(i+1) mod n].Y;
    //Deuxieme droite
    d2.a:=(p1.y-p2.y);  d2.b:=-(p1.x-p2.x);  d2.c:=-(d2.a*p1.x+d2.b*p1.y);
    forma.image1.Canvas.Pen.Color:=clred;
    for x:=0 to 500 do for y:=0 to 500 do if abs(((d2.a*x)+(d2.b*y)+d2.c))<=2 then forma.image1.Canvas.Ellipse(X-2,Y-2,X+1,Y+1);
    if (not ptsMemeCotedeD(p,pinfini,d2))and(not ptsMemeCotedeD(p1,p2,D1)) then inc(compteur);
    end;
if compteur mod 2 <>0 then DansPolygone:=true else DansPolygone:=false;
//showmessage(inttostr(compteur));
end;

function homothetie(T:array of unit1.tpoint;f:real):TabPoints;
var i,N:integer;
    TT:TabPoints;
    X,Y:real;
begin
//*************Centre de Gravité X,Y
N:=length(T);
For i:=0 to N-1 do
    begin
    X:=X+T[i].X;
    Y:=Y+T[i].Y;
    end;
X:=X/N;Y:=Y/N;
//**************Homotetie
setlength(TT,N);
For i:=0 to N-1 do
    Begin
    TT[i].X:=trunc(F*T[i].X+X*(1-F));
    TT[i].Y:=trunc(F*T[i].Y+Y*(1-F));
    End;
homothetie:=TT;
end;

 function DistPoint(P1,P2:tpoint):real;
 begin
 DistPoint:=sqrt(sqr(P2.X-P1.X)+sqr(P2.Y-P1.Y));
 end;

 function DistSegment(P,P1,P2:tPoint;M:tmemo):Real;
 Var Angle:double;
 begin
 DistSegment:=abs(((P1.Y-P2.Y)*P.X+
      (P2.X-P1.X)*P.Y+
      (P1.X*P2.Y-P2.X*P1.Y))/
       sqrt(sqr(P2.X-P1.X)+sqr(P2.Y-P1.Y)));
 if DistPoint(P1,P)*DistPoint(P,P2)=0 then DistSegment:=0
 else begin
 Angle:=(((P1.X-P.X)*(P1.X-P2.X))+((P1.Y-P.Y)*(P1.Y-P2.Y)))/(DistPoint(P1,P)*DistPoint(P1,P2)); //L'angle 1
 //M.Lines.Add(FloatToStr(Angle));
 //M.Lines.SaveToFile('d:\bbbb');
 //If ABS(angle)=1 then angle:=0.99*Angle;
 if angle>1 then angle:=1;
 if angle<-1 then angle:=-1;
 Angle:=radtodeg(arccos(Angle));

 if Angle>90 then DistSegment:=DistPoint(P1,P);
 Angle:=round((((P2.X-P.X)*(P2.X-P1.X))+((P2.Y-P.Y)*(P2.Y-P1.Y)))/(DistPoint(P2,P)*DistPoint(P2,P1))); //L'angle 2
 //if abs(angle)>1 then showmessage(floattostr(angle))else
 if angle>1 then angle:=1;
 if angle<-1 then angle:=-1;
 Angle:=radtodeg(arccos(Angle));
 if Angle>90 then DistSegment:=DistPoint(P2,P);
      end;
 end;
{$R *.dfm}

procedure TForma.Edit1Change(Sender: TObject);
var B:TColor;
begin
B:=Image1.Canvas.Brush.Color;
Image1.Canvas.Brush.Color:=86186240;
Sweep:=strtoint(Edit1.Text);
Image1.Canvas.MoveTo(0,Sweep);
Image1.Canvas.LineTo(Image1.Width,Sweep);
end;

procedure TForma.Image1MouseDown(Sender: TObject; Button: TMouseButton;
  Shift: TShiftState; X, Y: Integer);

begin
if Point.Flat then begin
                          Point.Flat:=false;
                          SetLength(ListeObjets,length(ListeObjets)+1);
                          ListeObjets[length(ListeObjets)-1].Nature:='P';
                          SetLength(ListeObjets[length(ListeObjets)-1].ListePoint,1);
                          ListeObjets[length(ListeObjets)-1].ListePoint[0].X:=X;
                          ListeObjets[length(ListeObjets)-1].ListePoint[0].Y:=Y;
                          Image1.Canvas.Ellipse(X,Y,X+4,Y+4);
                          end;

if Ligne.Flat then begin
                          inc(clique);
                          if clique=1 then begin
                                                SetLength(ListeObjets,length(ListeObjets)+1);
                                                ListeObjets[length(ListeObjets)-1].Nature:='L';
                                                Image1.Canvas.MoveTo(X,Y);
                                                end;
                          SetLength(ListeObjets[length(ListeObjets)-1].ListePoint,clique);
                          ListeObjets[length(ListeObjets)-1].ListePoint[clique-1].X:=X;
                          ListeObjets[length(ListeObjets)-1].ListePoint[clique-1].Y:=Y;
                          if clique=2 then begin Ligne.Flat:=false;clique:=0;Image1.Canvas.LineTo(X,Y);end;
                          end;

if PLigne.Flat then begin
                         inc(clique);
                          if clique=1 then begin
                                                SetLength(ListeObjets,length(ListeObjets)+1);
                                                ListeObjets[length(ListeObjets)-1].Nature:='PL';
                                                Image1.Canvas.MoveTo(X,Y);
                                                end;
                          SetLength(ListeObjets[length(ListeObjets)-1].ListePoint,clique);
                          ListeObjets[length(ListeObjets)-1].ListePoint[clique-1].X:=X;
                          ListeObjets[length(ListeObjets)-1].ListePoint[clique-1].Y:=Y;
                          Image1.Canvas.LineTo(X,Y);
                          end;

if Polygone.Flat then begin
                          inc(clique);
                          if clique=1 then begin
                                                SetLength(ListeObjets,length(ListeObjets)+1);
                                                ListeObjets[length(ListeObjets)-1].Nature:='PG';
                                                Image1.Canvas.MoveTo(X,Y);
                                                end;
                          SetLength(ListeObjets[length(ListeObjets)-1].ListePoint,clique);
                          ListeObjets[length(ListeObjets)-1].ListePoint[clique-1].X:=X;
                          ListeObjets[length(ListeObjets)-1].ListePoint[clique-1].Y:=Y;
                          Image1.Canvas.LineTo(X,Y);
                          end;
end;

procedure TForma.Image1DblClick(Sender: TObject);
begin
if PLigne.Flat then begin
                          PLigne.Flat:=false;
                          clique:=0;
                          end;

if Polygone.Flat then begin
                          Polygone.Flat:=false;
                          Image1.Canvas.LineTo(ListeObjets[length(ListeObjets)-1].ListePoint[0].X,ListeObjets[length(ListeObjets)-1].ListePoint[0].Y);
                          clique:=0;
                          end;
end;

procedure TForma.PointClick(Sender: TObject);
begin
Point.Flat:=true;
end;

procedure TForma.LigneClick(Sender: TObject);
begin
Ligne.Flat:=true;
end;

procedure TForma.PLigneClick(Sender: TObject);
begin
PLigne.Flat:=true;
end;

procedure TForma.PolygoneClick(Sender: TObject);
begin
Polygone.Flat:=true;
end;

procedure TForma.FormCreate(Sender: TObject);
begin
Image1.Canvas.Create;
clique:=0;
end;

procedure TForma.Button1Click(Sender: TObject);
var i:integer;
begin
for i:=0 to length(ListeObjets)-1 do
Memo1.Lines.Add(ListeObjets[i].nature);
end;

procedure TForma.BitBtn1Click(Sender: TObject);
var Taille,i,j,k,w:integer;
    DistSweep,Dist:real;
    Pix:tPoint;
begin
for   i:= 1 to Image1.Width   do    //X
  for j:= 1 to Sweep-1 do           //Y , la veritable formule est < sweep mais comme c'est des pix de ce fait discontinue c'est exactement sweep-1, de toute façon c pas comme ça pour le continu
    for k:= 0 to Length(ListeObjets)-1 do
      begin
      DistSweep:=ABS(Sweep-J);
      Pix.X:=i;
      Pix.Y:=j;
      Dist:=-1;
      if ListeObjets[k].Nature='P' then Dist:=Round(DistPoint(ListeObjets[k].ListePoint[0],Pix));
      if ListeObjets[k].Nature='L' then Dist:=Round(DistSegment(Pix,ListeObjets[k].ListePoint[0],ListeObjets[k].ListePoint[1],memo2));
      if DistSweep=Dist then Image1.Canvas.Ellipse(I,J,I+2,J+2);
      if ListeObjets[k].Nature='PL'then for w:=0 to length(ListeObjets[k].ListePoint)-2 do
                                            begin
                                            Dist:=round(DistSegment(Pix,ListeObjets[k].ListePoint[w],ListeObjets[k].ListePoint[w+1],memo2));
                                            if DistSweep=Dist then Image1.Canvas.Ellipse(I,J,I+2,J+2);
                                            end;
      if ListeObjets[k].Nature='PG'then for w:=0 to length(ListeObjets[k].ListePoint)-1 do
                                            begin
                                            Dist:=round(DistSegment(Pix,ListeObjets[k].ListePoint[w],ListeObjets[k].ListePoint[(w+1)mod length(ListeObjets[k].ListePoint)],memo2));
                                            if DistSweep=Dist then Image1.Canvas.Ellipse(I,J,I+2,J+2);
                                            end;
      end;



end;

procedure TForma.BitBtn2Click(Sender: TObject);
var H,W:integer;
begin
H:=Image1.Height;
W:=Image1.Width;
Image1.Canvas.Brush.Color:=clWhite;
Image1.Canvas.Rectangle(0,0,W,H);
//setlength(ListeObjets,0);
end;

procedure TForma.BitBtn3Click(Sender: TObject);
begin
Timer1.Enabled:=not Timer1.Enabled;
end;

procedure TForma.Timer1Timer(Sender: TObject);
var H,W,I:integer;
begin
inc(Sweep);
Edit1.Text:=inttostr(Sweep);
H:=Image1.Height;
W:=Image1.Width;
Image1.Canvas.Brush.Color:=clWhite;
Image1.Canvas.Rectangle(0,0,W,H);
Image1.Canvas.MoveTo(0,Sweep);
Image1.Canvas.LineTo(Image1.Width,Sweep);
for i:=0 to length(ListeObjets)-1do
  if ListeObjets[i].Nature='P' then Image1.Canvas.Ellipse(ListeObjets[i].ListePoint[0].X,ListeObjets[i].ListePoint[0].Y,ListeObjets[i].ListePoint[0].X+3,ListeObjets[i].ListePoint[0].Y+3)
  else if ListeObjets[i].Nature='L' then begin Image1.Canvas.MoveTo(ListeObjets[i].ListePoint[0].X,ListeObjets[i].ListePoint[0].Y); Image1.Canvas.LineTo(ListeObjets[i].ListePoint[1].X,ListeObjets[i].ListePoint[1].Y);end
  else if ListeObjets[i].Nature='PL' then for w:=0 to length(ListeObjets[i].ListePoint)-2 do begin
                                                                                             Image1.Canvas.MoveTo(ListeObjets[i].ListePoint[w].X,ListeObjets[i].ListePoint[w].Y);
                                                                                             Image1.Canvas.LineTo(ListeObjets[i].ListePoint[w+1].X,ListeObjets[i].ListePoint[w+1].Y);
                                                                                             end
  else if ListeObjets[i].Nature='PG' then for w:=0 to length(ListeObjets[i].ListePoint)-1 do begin
                                                                                             Image1.Canvas.MoveTo(ListeObjets[i].ListePoint[w].X,ListeObjets[i].ListePoint[w].Y);
                                                                                             Image1.Canvas.LineTo(ListeObjets[i].ListePoint[(w+1)mod length(ListeObjets[i].ListePoint)].X,ListeObjets[i].ListePoint[(w+1)mod length(ListeObjets[i].ListePoint)].Y);
                                                                                             end;
BitBtn1.Click;
end;

procedure TForma.SpeedButton5Click(Sender: TObject);
var i,N:integer;
    T,G:array of Unit1.TPoint;
    X,Y,F:real;
begin
F:=strtofloat(LabeledEdit1.Text);
//*************Centre de Gravité X,Y
N:=length(ListeObjets[0].ListePoint);
For i:=0 to N-1 do
    begin
    X:=X+ListeObjets[0].ListePoint[i].X;
    Y:=Y+ListeObjets[0].ListePoint[i].Y;
    end;
X:=X/N;Y:=Y/N;
//**************Homotetie
setlength(G,N);
For i:=0 to N-1 do
    Begin
    G[i].X:=trunc(F*ListeObjets[0].ListePoint[i].X+X*(1-F)); 
    G[i].Y:=trunc(F*ListeObjets[0].ListePoint[i].Y+Y*(1-F));
    End;
//*************Affichage
For i:=1 to N do
    begin
    Image1.Canvas.MoveTo(G[i-1].X,G[i-1].Y);
    Image1.Canvas.LineTo(G[i mod (n)].X,G[i mod (n)].Y);
    end;
{on a pas toujours une homotetie autour de l'objet d'origine,
c'est à cause du centre de gravité, MP'=k*MP, les segments ne sont peut etre pas proportionnels}
end;

procedure TForma.SpeedButton2Click(Sender: TObject);
var i,N:Integer;
begin
MaxX:=ListeObjets[0].ListePoint[0].X;MaxY:=ListeObjets[0].ListePoint[0].Y;MinX:=ListeObjets[0].ListePoint[0].X;MinY:=ListeObjets[0].ListePoint[0].Y;//Initialisation
N:=length(ListeObjets[0].ListePoint);
for i:=1 to N-1 do
    begin
    if MaxX<ListeObjets[0].ListePoint[i].X then MaxX:=ListeObjets[0].ListePoint[i].X;
    if MaxY<ListeObjets[0].ListePoint[i].Y then MaxY:=ListeObjets[0].ListePoint[i].Y;
    if MinX>ListeObjets[0].ListePoint[i].X then MinX:=ListeObjets[0].ListePoint[i].X;
    if MinY>ListeObjets[0].ListePoint[i].Y then MinY:=ListeObjets[0].ListePoint[i].Y;
    end;
Image1.Canvas.Brush.Style:= BsClear;
Image1.Canvas.Rectangle(MaxX,MaxY,MinX,MinY);
end;

procedure TForma.SpeedButton3Click(Sender: TObject);
var MaX,MiX,MaY,MiY,LongX,LongY,i,s1,s2,dx,dy:integer;
begin
LongX:=MaxX-MinX;
LongY:=MaxY-MinY;
S2:=LongX*LongY; //Rectangle Englobant
s1:=0;
for i:=0 to length(ListeObjets[0].ListePoint)-1 do
    begin
    S1:=S1+((ListeObjets[0].ListePoint[i].X*ListeObjets[0].ListePoint[(i+1) mod length(ListeObjets[0].ListePoint)].Y));
    S1:=S1-((ListeObjets[0].ListePoint[i].Y*ListeObjets[0].ListePoint[(i+1) mod length(ListeObjets[0].ListePoint)].X));
    end;
S1:=trunc(abs(S1)/2);            //Objet
Dx:=trunc(((1-(S1/S2))*LongX)/2);
Dy:=trunc(((1-(S1/S2))*LongY)/2);
MaX:=MaxX-Dx;MiX:=MinX+Dx; 
MaY:=MaxY-Dy;MiY:=MinY+Dy;
Image1.Canvas.Brush.Style:= BsClear;
Image1.Canvas.Rectangle(MaX,MaY,MiX,MiY);
end;

procedure TForma.Image1MouseMove(Sender: TObject; Shift: TShiftState; X,
  Y: Integer);
begin
Label2.Caption:=inttostr(X)+'   '+inttostr(Y);
end;

procedure TForma.SpeedButton1Click(Sender: TObject);
var i:integer;
    Amax,A:Real;
    P,PminY,Pred,PAmax:TPoint;
begin
PminY.Y:=ListeObjets[0].ListePoint[0].Y;
For i :=1 to length(ListeObjets[0].ListePoint)-1 do
    if ListeObjets[0].ListePoint[i].Y<PminY.Y then PminY:=ListeObjets[0].ListePoint[i];
    //***
Pred.X:=PminY.X+10; Pred.Y:=PminY.Y;
P:=PminY;
repeat
      SetLength(Enveloppe,length(enveloppe)+1);
      Enveloppe[length(enveloppe)-1]:=P;
      Amax:=0;
      for i:=0 to length(ListeObjets[0].ListePoint)-1 do
          begin
               if (ListeObjets[0].ListePoint[i].X<>P.X)and(ListeObjets[0].ListePoint[i].Y<>P.Y) then
                begin
             A:=(((P.X-Pred.X)*(P.X-ListeObjets[0].ListePoint[i].X))+((P.Y-Pred.Y)*(P.Y-ListeObjets[0].ListePoint[i].Y)))/(DistPoint(P,Pred)*DistPoint(P,ListeObjets[0].ListePoint[i])); //Pred P  i  ***P P1 P2
                A:=abs(radtodeg(arccos(A)));
                if A>Amax then begin Amax:=A; PAmax:=ListeObjets[0].ListePoint[i];end;
                end;
          end;
          Pred:=P;
          P:=PAmax;
until (P.X=PMinY.X)and(P.Y=PMinY.Y);
end;

procedure TForma.Button2Click(Sender: TObject);
var i:integer;
begin
For i:=1 to length(Enveloppe) do
    begin
    Image1.Canvas.MoveTo(Enveloppe[i-1].X,Enveloppe[i-1].Y);
    Image1.Canvas.LineTo(Enveloppe[i mod (length(Enveloppe))].X,Enveloppe[i mod (length(Enveloppe))].Y);
    Image1.Canvas.TextOut(Enveloppe[i-1].X,Enveloppe[i-1].Y,inttostr(i-1));
    end;
end;

procedure TForma.Button3Click(Sender: TObject);
var i:integer;
begin
image1.Canvas.pen.color:=clred;
//image1.Canvas.brush.color:=clwhite;
For i:=1 to length(ListeObjets[0].ListePoint) do
    begin
    Image1.Canvas.MoveTo(ListeObjets[0].ListePoint[i-1].X,ListeObjets[0].ListePoint[i-1].Y);
    Image1.Canvas.LineTo(ListeObjets[0].ListePoint[i mod (length(ListeObjets[0].ListePoint))].X,ListeObjets[0].ListePoint[i mod (length(ListeObjets[0].ListePoint))].Y);
    Image1.Canvas.TextOut(ListeObjets[0].ListePoint[i-1].X,ListeObjets[0].ListePoint[i-1].Y,inttostr(i-1));
    end;
end;

procedure TForma.SpeedButton4Click(Sender: TObject);
var b1,b2:real;
    x1,x2,x3,y1,y2,y3,ymax,ymin,i,X,Y:integer;
    p,pp,ppp:ppoint;
    ListPP: array of ppoint;
    T:TabPoints;
begin
ymax:=500-miny;ymin:=500-maxy;
b1:=ymax-minx;
b2:=ymax+maxx;
x1:=trunc((b2-b1)/2);y1:=trunc(x1+b1);
x2:=trunc(ymin-b1);y2:=ymin;
x3:=trunc(-ymin+b2);y3:=ymin;
Image1.Canvas.MoveTo(x1,500-y1);
Image1.Canvas.LineTo(x3,500-y3);
Image1.Canvas.LineTo(x2,500-y2);
Image1.Canvas.LineTo(x1,500-y1);
setlength(T,3);T[0].X:=x1;T[0].Y:=500-y1;T[1].X:=x2;T[1].Y:=500-y2;T[2].X:=x3;T[2].Y:=500-y3;
T:=homothetie(T,2);
{just pour le besoin de supptriangles}ptanglobant.x:=T[0].x;ptanglobant.Y:=T[0].Y;
Image1.Canvas.MoveTo(T[0].x,T[0].y);
Image1.Canvas.LineTo(T[1].x,T[1].y);
Image1.Canvas.LineTo(T[2].x,T[2].y);
Image1.Canvas.LineTo(T[0].x,T[0].y);
//**********afficher les etiquettes des points
Image1.Canvas.TextOut(x1,500-y1,'P1');Image1.Canvas.TextOut(x2,500-y2,'P2');Image1.Canvas.TextOut(x3,500-y3,'P3');
//************
setlength(Delau.ListePoint,0);
setlength(Delau.Listetriangle,0);
//Delau.ListePoint:=ListePoint;
Delau.maxPoint:=0;
Delau.maxTriangle:=0;
//Delau.Listetriangle:=0;
p:=Delau.AddPoint(T[0].X,T[0].Y);pp:=Delau.AddPoint(T[1].X,T[1].Y);ppp:=Delau.AddPoint(T[2].X,T[2].Y);
//for i:=0 to length(Delau.ListePoint)-1 do showmessage(inttostr(listepoint[i].X)+'  '+inttostr(listepoint[i].Y));
// cre les deux triangles initiaux
Delau.AddTriangle(Delau.CreateTriangle(p,pp,ppp));
end;

procedure TForma.SpeedButton6Click(Sender: TObject);
var i:integer;
    p:tpoint;
begin
{ PROBLEMME AVEC LES POINTS ALA ISTIKAMA WAHIDA , ET PROBLEMME DE SUPPERPOSITION DES TRIANGLES A L4INTERIEUR}
for i:=0 to length(ListeObjets[0].ListePoint)-1 do
    begin
    p:=ListeObjets[0].ListePoint[i];
    Delau.Algorythm_Delaunay(p.X,p.Y);
    //ShowMessage(inttostr(i));
    end
end;

procedure TForma.SpeedButton7Click(Sender: TObject);
var i,x,y:integer;
    points:array[0..2] of Types.tpoint;
    p:ppoint;
begin
image1.Canvas.Brush.Style:=bssolid;
image1.Canvas.Brush.color:=clwhite;
image1.Canvas.FillRect(image1.ClientRect);
for i:=0 to Delau.maxTriangle-1 do
    begin
    p:=Delau.listetriangle[i].p1;
    points[0].X:=p.X; points[0].Y:=p.Y;
    p:=Delau.listetriangle[i].p2;
    points[1].X:=p.X; points[1].Y:=p.Y;
    p:=Delau.listetriangle[i].p3;
    points[2].X:=p.X; points[2].Y:=p.Y;
    image1.Canvas.pen.color:=clblack;
    image1.Canvas.brush.color:=clwhite;
    image1.Canvas.Polygon(points);
    end;
end;

procedure TForma.SpeedButton9Click(Sender: TObject);
var d1,d2:tDroite;
    pt1,pt2,pt3,pcg,pinf:pPoint;
    p:types.tpoint;
    i,N:integer;
begin
{RAJOUTER AUSSI L4INTERSECTION}
SpeedButton2.Click;
SpeedButton4.Click;
SpeedButton6.Click;
new(pt1);new(pt2);new(pt3);new(pinf);pinf^:=ptanglobant;new(pcg);
N:=length(Listetriangle); i:=0;
while(i<=n-1) do
    begin
    pt1.X:=Listetriangle[i].p1.X;pt1.Y:=Listetriangle[i].p1.Y;
    pt2.X:=Listetriangle[i].p2.X;pt2.Y:=Listetriangle[i].p2.Y;
    pt3.X:=Listetriangle[i].p3.X;pt3.Y:=Listetriangle[i].p3.Y;
    p.x:=(pt1.x+pt2.x+pt3.x)div 3;p.y:=(pt1.y+pt2.y+pt3.y)div 3;
    pcg.X:=p.X; pcg.Y:=p.Y;
    if not(DansPolygone(pcg,pinf))then Delau.DelTriangle(Listetriangle[i]) else inc(i);
    N:=length(Listetriangle);
    end;
BitBtn2.Click;
SpeedButton7.Click;
end;

procedure TForma.SpeedButton10Click(Sender: TObject);
var i,n,ncf,ncs,nv,v,v1,v2,w,ctr,x,y,it,it2:integer;//ncf nombre de chemins fermés
    T,pr,sv:ptriangle;
    M,C,pd,pf:tpoint;
begin
// le premier chemin, chercher le premier triangle
pd.X:=ListeObjets[0].ListePoint[0].x;pd.Y:=ListeObjets[0].ListePoint[0].y;
pf.X:=ListeObjets[0].ListePoint[length(ListeObjets[0].ListePoint)-1].x;pf.Y:=ListeObjets[0].ListePoint[length(ListeObjets[0].ListePoint)-1].y;
setlength(chemins,1);
Chemins[0].TP:=nil;Chemins[0].EstFerme:=false;Chemins[0].EstSupprime:=false;
setlength(Chemins[0].LesP,1); Chemins[0].LesP[0].X:=(pd.X+pf.X)div 2;Chemins[0].LesP[0].Y:=(pd.Y+pf.Y)div 2;
for i:=0 to length(listetriangle)-1 do
    begin
    t:=listetriangle[i];
    ctr:=0;
    if ((listetriangle[i].p1.X=pd.X)and(listetriangle[i].p1.Y=pd.Y))or((listetriangle[i].p1.X=pf.X)and(listetriangle[i].p1.Y=pf.Y)) then inc(ctr);
    if ((listetriangle[i].p2.X=pd.X)and(listetriangle[i].p2.Y=pd.Y))or((listetriangle[i].p2.X=pf.X)and(listetriangle[i].p2.Y=pf.Y)) then inc(ctr);
    if ((listetriangle[i].p3.X=pd.X)and(listetriangle[i].p3.Y=pd.Y))or((listetriangle[i].p3.X=pf.X)and(listetriangle[i].p3.Y=pf.Y)) then inc(ctr);
    if ctr>1 then Chemins[0].TA:=t;
    end;
Image1.Canvas.Ellipse(Chemins[0].LesP[0].X-3,Chemins[0].LesP[0].Y-3,Chemins[0].LesP[0].X+3,Chemins[0].LesP[0].Y+3);

ncf:=0;ncs:=0;n:=1;it:=0;
while (ncf+ncs<length(Chemins)) do
      begin
      inc(it); showmessage('iteration : '+inttostr(it));it2:=0;
      n:=length(Chemins);
      //SpeedButton11.Click;
      for i:=0 to n-1 do  // Pour tous chemin
          begin
          if(not Chemins[i].EstFerme)and(not Chemins[i].EstSupprime) then
                 begin
                 //inc(it2); showmessage('iteration 2 : '+inttostr(it2));
                 x:=(t.p1.X+t.p2.X+t.p3.X)div 3;y:=(t.p1.y+t.p2.y+t.p3.y)div 3;
                 image1.Canvas.Brush.Color:=clred;
                 image1.Canvas.pen.color:=clred;
                 Image1.Canvas.Ellipse(x-3,y-3,x+3,y+3);
                 //if t<> nil then Image1.Canvas.Ellipse(t.c.X-3,t.c.Y-3,t.c.X+3,t.c.Y+3); // si t pas nil
                 T:=Chemins[i].TA;// aficher les infor du triangle et du chemin
                 // Compter les voisins de TA
                 nv:=0;
                 if t<> nil then if T.t1<>nil then inc(nv);if T.t2<>nil then inc(nv);if T.t3<>nil then inc(nv);   //nv nombre de voisins
                 if T.t1=Chemins[i].TP then pr:=T.t1;if T.t2=Chemins[i].TP then pr:=T.t2;if T.t3=Chemins[i].TP then pr:=T.t3;// TP triangle precedent
                 // si un voisin c'est donc le precedent alors fermer le chemin, ajouter je ne sais pas quoid

                 if (nv=1)and(it<>1) then begin Chemins[i].EstFerme:=true;inc(ncf);end; // sil a un voisin seulement ou si c'est le premier triangle et qu'il a un seul voisin
                 // si deux voisins

                 if (nv=2)or((nv=1) and (it=1)) then
                    begin
                    if (T.t1<>nil)and(T.t1<>pr) then begin M.x:=(T.p2.x+T.p3.x)div 2;M.y:=(T.p2.y+T.p3.y)div 2; sv:=T.t1; Image1.Canvas.TextOut(M.X,M.Y,'V1'); end;
                    if (T.t2<>nil)and(T.t2<>pr) then begin M.x:=(T.p1.x+T.p3.x)div 2;M.y:=(T.p1.y+T.p3.y)div 2; sv:=T.t2;Image1.Canvas.TextOut(M.X,M.Y,'V2');end;
                    if (T.t3<>nil)and(T.t3<>pr) then begin M.x:=(T.p2.x+T.p1.x)div 2;M.y:=(T.p2.y+T.p1.y)div 2; sv:=T.t3;Image1.Canvas.TextOut(M.X,M.Y,'V3');end;
                    setlength(chemins[i].LesP,length(chemins[i].LesP)+1);    chemins[i].LesP[length(chemins[i].LesP)-1].X:=M.X;    chemins[i].LesP[length(chemins[i].LesP)-1].Y:=M.Y;
                    chemins[i].TA:=sv;chemins[i].TP:=T;
                    end;
                 // si trois voisins
                 if (nv=3) or ((nv=2)and(it=1)) then
                    begin
                    chemins[i].EstSupprime:=true;// supprimer le chemin qui va se bifurquer
                    inc(ncs);
                    c.X:=(t.p1.X+t.p2.X+t.p3.X)div 3;c.Y:=(t.p1.y+t.p2.y+t.p3.Y)div 3;// meme s'il y a t.c et quil marche quand je change le code il peut ne pas marcher
                    setlength(chemins[i].LesP,length(chemins[i].LesP)+1); chemins[i].LesP[length(chemins[i].LesP)-1].X:=C.X; chemins[i].LesP[length(chemins[i].LesP)-1].Y:=C.Y;// ajout du centre de gravité
                   //premier voisin
                    if T.t1<>pr then
                       begin
                       M.x:=(T.p2.x+T.p3.x)div 2;M.y:=(T.p2.y+T.p3.y)div 2;
                       setlength(chemins,length(chemins)+1);
                       chemins[length(chemins)-1].TA:=T.t1;chemins[length(chemins)-1].TP:=T;chemins[length(chemins)-1].EstFerme:=false;chemins[length(chemins)-1].EstSupprime:=false;
                       setlength(chemins[length(chemins)-1].LesP,length(chemins[i].LesP)+1);
                       for w:=0 to length(chemins[i].LesP)-1 do begin chemins[length(chemins)-1].LesP[w].X:=chemins[i].LesP[w].x; chemins[length(chemins)-1].LesP[w].Y:=chemins[i].LesP[w].y; end;
                       chemins[length(chemins)-1].LesP[w].X:=M.X;chemins[length(chemins)-1].LesP[w].Y:=M.Y;
                       end;
                    // deuxieme voisin
                    if T.t2<>pr then
                       begin
                       M.x:=(T.p1.x+T.p3.x)div 2;M.y:=(T.p1.y+T.p3.y)div 2;
                       setlength(chemins,length(chemins)+1);
                       chemins[length(chemins)-1].TA:=T.t2;chemins[length(chemins)-1].TP:=T;chemins[length(chemins)-1].EstFerme:=false;chemins[length(chemins)-1].EstSupprime:=false;
                       setlength(chemins[length(chemins)-1].LesP,length(chemins[i].LesP)+1);
                       for w:=0 to length(chemins[i].LesP)-1 do begin chemins[length(chemins)-1].LesP[w].X:=chemins[i].LesP[w].x; chemins[length(chemins)-1].LesP[w].Y:=chemins[i].LesP[w].y; end;
                       chemins[length(chemins)-1].LesP[w].X:=M.X;chemins[length(chemins)-1].LesP[w].Y:=M.Y;
                       end;
                    // troisieme voisin
                    if T.t3<>pr then
                       begin
                       M.x:=(T.p2.x+T.p1.x)div 2;M.y:=(T.p2.y+T.p1.y)div 2;
                       setlength(chemins,length(chemins)+1);
                       chemins[length(chemins)-1].TA:=T.t3;chemins[length(chemins)-1].TP:=T;chemins[length(chemins)-1].EstFerme:=false;chemins[length(chemins)-1].EstSupprime:=false;
                       setlength(chemins[length(chemins)-1].LesP,length(chemins[i].LesP)+1);
                       for w:=0 to length(chemins[i].LesP)-1 do begin chemins[length(chemins)-1].LesP[w].X:=chemins[i].LesP[w].x; chemins[length(chemins)-1].LesP[w].Y:=chemins[i].LesP[w].y; end;
                       chemins[length(chemins)-1].LesP[w].X:=M.X;chemins[length(chemins)-1].LesP[w].Y:=M.Y;
                       end;

                    end;
                 end;
          end;
      end;

end;

procedure TForma.Button4Click(Sender: TObject);
var i,p : integer ;
    t:ptriangle;
    S:string;
begin
for i:=0 to length(listetriangle)-1 do
    begin
    t:=listetriangle[i];
     S:=inttostr(i)+'    '+
    'p1 '+inttostr(t.p1.x)+'  '+inttostr(t.p1.y)+'  '+
    'p2 '+inttostr(t.p2.x)+'  '+inttostr(t.p2.y)+'  '+
    'p3 '+inttostr(t.p3.x)+'  '+inttostr(t.p3.y)+'  ';
    if t.t1=nil then s:=s+'v1p1 nil' else s:=s+'v1p1 '+inttostr(t.t1.p1.x)+'  '+inttostr(t.t1.p1.y)+'v1p2  '+inttostr(t.t1.p2.x)+'  '+inttostr(t.t1.p2.y)+'v1p3  '+inttostr(t.t1.p3.x)+'  '+inttostr(t.t1.p3.y);
    if t.t2=nil then s:=s+'v2p1 nil' else s:=s+'v2p1 '+inttostr(t.t2.p1.x)+'  '+inttostr(t.t2.p1.y)+'v2p2  '+inttostr(t.t2.p2.x)+'  '+inttostr(t.t2.p2.y)+'v2p3  '+inttostr(t.t2.p3.x)+'  '+inttostr(t.t2.p3.y);
    if t.t3=nil then s:=s+'v3p1 nil' else s:=s+'v3p1 '+inttostr(t.t3.p1.x)+'  '+inttostr(t.t3.p1.y)+'v3p2  '+inttostr(t.t3.p2.x)+'  '+inttostr(t.t3.p2.y)+'v3p3  '+inttostr(t.t3.p3.x)+'  '+inttostr(t.t3.p3.y);
    Memo5.Lines.Add(S);
    end;
end;

procedure TForma.SpeedButton11Click(Sender: TObject);
var i,k:integer;
    s:string;
begin
label3.Caption:='chemins '+inttostr(length(Chemins))+'  points '+inttostr(length(Chemins[0].LesP));
for i:=0 to length(Chemins)-1 do
    begin
    s:=inttostr(length(Chemins[i].LesP));if Chemins[i].estsupprime then s:=s+'  Supp';if Chemins[i].EstFerme then s:=s+'   Ferm'; Memo5.Lines.Add(s);
    for k:=1 to length(Chemins[i].LesP)-1 do
        begin
        image1.Canvas.pen.color:=clblack;
        Image1.Canvas.MoveTo(Chemins[i].LesP[k-1].X,Chemins[i].LesP[k-1].Y);
        Image1.Canvas.LineTo(Chemins[i].LesP[k].X,Chemins[i].LesP[k].Y);
        end;
    end;
end;

procedure TForma.Button5Click(Sender: TObject);
var i,x,y:integer;
    p:ptriangle;
begin
for i:=0 to length(Delau.listetriangle)-1 do
    begin
    p:=Delau.listetriangle[i];
    x:=(p.p1.X+p.p2.X+p.p3.X)div 3;y:=(p.p1.y+p.p2.y+p.p3.y)div 3;
    image1.Canvas.Brush.Color:=clgreen;
    image1.Canvas.pen.color:=clgreen;
    Image1.Canvas.Ellipse(x-3,y-3,x+3,y+3);
    end;
end;

procedure TForma.SpeedButton8Click(Sender: TObject);
var i,k,Sqlt:integer;
    LM,L:real;
begin
for i :=1 to length(chemins)-1 do
    begin
    LM:=-1; L:=0;
    for k:=1 to length(Chemins[i].LesP)-1 do
        begin
        L:=L+DistPoint(Chemins[i].LesP[i-1],Chemins[i].LesP[i]);
        end;
    if L>LM then begin LM:=L; Sqlt:=i;end;
    end;
//Affichage du squellette
for k:=1 to length(Chemins[Sqlt].LesP)-1 do
        begin
        image1.Canvas.pen.color:=clblack;
        Image1.Canvas.MoveTo(Chemins[Sqlt].LesP[k-1].X,Chemins[Sqlt].LesP[k-1].Y);
        Image1.Canvas.LineTo(Chemins[Sqlt].LesP[k].X,Chemins[Sqlt].LesP[k].Y);
        end;
end;

procedure TForma.BitBtn4Click(Sender: TObject);
var i,N:Integer; tt:TabPoints;
p:tpoint;
d1,d2:tDroite;pt1,pt2,pt3,pcg,pinf:pPoint;
ncf,ncs,nv,v,v1,v2,w,ctr,x,y,it,it2:integer;{ncf nombre de chemins fermés } T,pr,sv:ptriangle;    M,C,pd,pf:tpoint;
k,Sqlt:integer;LM,L:real;
begin
//1111111111 rectangle anglobant
RectangleAnglobant(listeobjets[0],minx,miny,maxx,maxy);
Image1.Canvas.Brush.Style:= BsClear;
Image1.Canvas.Rectangle(MaxX,MaxY,MinX,MinY);
//2222222222 Triangle anglobant
tT:=TriangleAnglobant(listeobjets[0]);
Image1.Canvas.MoveTo(tT[0].x,Tt[0].y);
Image1.Canvas.LineTo(tT[1].x,Tt[1].y);
Image1.Canvas.LineTo(tT[2].x,Tt[2].y);
Image1.Canvas.LineTo(tT[0].x,Tt[0].y);
//3333333333 Dalau
for i:=0 to length(ListeObjets[0].ListePoint)-1 do
    begin
    p:=ListeObjets[0].ListePoint[i];
    Delau.Algorythm_Delaunay(p.X,p.Y);
    end;
//44444444 Baricentre
new(pt1);new(pt2);new(pt3);new(pinf);pinf^:=ptanglobant;new(pcg);
N:=length(Listetriangle); i:=0;
while(i<=n-1) do
    begin
    pt1.X:=Listetriangle[i].p1.X;pt1.Y:=Listetriangle[i].p1.Y;
    pt2.X:=Listetriangle[i].p2.X;pt2.Y:=Listetriangle[i].p2.Y;
    pt3.X:=Listetriangle[i].p3.X;pt3.Y:=Listetriangle[i].p3.Y;
    p.x:=(pt1.x+pt2.x+pt3.x)div 3;p.y:=(pt1.y+pt2.y+pt3.y)div 3;
    pcg.X:=p.X; pcg.Y:=p.Y;
    if not(DansPolygone(pcg,pinf))then Delau.DelTriangle(Listetriangle[i]) else inc(i);
    N:=length(Listetriangle);
    end;
BitBtn2.Click;
SpeedButton7.Click;
//555555555 Squellette
// le premier chemin, chercher le premier triangle
pd.X:=ListeObjets[0].ListePoint[0].x;pd.Y:=ListeObjets[0].ListePoint[0].y;
pf.X:=ListeObjets[0].ListePoint[length(ListeObjets[0].ListePoint)-1].x;pf.Y:=ListeObjets[0].ListePoint[length(ListeObjets[0].ListePoint)-1].y;
setlength(chemins,1);
Chemins[0].TP:=nil;Chemins[0].EstFerme:=false;Chemins[0].EstSupprime:=false;
setlength(Chemins[0].LesP,1); Chemins[0].LesP[0].X:=(pd.X+pf.X)div 2;Chemins[0].LesP[0].Y:=(pd.Y+pf.Y)div 2;
for i:=0 to length(listetriangle)-1 do
    begin
    t:=listetriangle[i];
    ctr:=0;
    if ((listetriangle[i].p1.X=pd.X)and(listetriangle[i].p1.Y=pd.Y))or((listetriangle[i].p1.X=pf.X)and(listetriangle[i].p1.Y=pf.Y)) then inc(ctr);
    if ((listetriangle[i].p2.X=pd.X)and(listetriangle[i].p2.Y=pd.Y))or((listetriangle[i].p2.X=pf.X)and(listetriangle[i].p2.Y=pf.Y)) then inc(ctr);
    if ((listetriangle[i].p3.X=pd.X)and(listetriangle[i].p3.Y=pd.Y))or((listetriangle[i].p3.X=pf.X)and(listetriangle[i].p3.Y=pf.Y)) then inc(ctr);
    if ctr>1 then Chemins[0].TA:=t;
    end;
Image1.Canvas.Ellipse(Chemins[0].LesP[0].X-3,Chemins[0].LesP[0].Y-3,Chemins[0].LesP[0].X+3,Chemins[0].LesP[0].Y+3);

ncf:=0;ncs:=0;n:=1;it:=0;
while (ncf+ncs<length(Chemins)) do
      begin
      inc(it); showmessage('iteration : '+inttostr(it));it2:=0;
      n:=length(Chemins);
      //SpeedButton11.Click;
      for i:=0 to n-1 do  // Pour tous chemin
          begin
          if(not Chemins[i].EstFerme)and(not Chemins[i].EstSupprime) then
                 begin
                 //inc(it2); showmessage('iteration 2 : '+inttostr(it2));
                 x:=(t.p1.X+t.p2.X+t.p3.X)div 3;y:=(t.p1.y+t.p2.y+t.p3.y)div 3;
                 image1.Canvas.Brush.Color:=clred;
                 image1.Canvas.pen.color:=clred;
                 Image1.Canvas.Ellipse(x-3,y-3,x+3,y+3);
                 //if t<> nil then Image1.Canvas.Ellipse(t.c.X-3,t.c.Y-3,t.c.X+3,t.c.Y+3); // si t pas nil
                 T:=Chemins[i].TA;// aficher les infor du triangle et du chemin
                 // Compter les voisins de TA
                 nv:=0;
                 if t<> nil then if T.t1<>nil then inc(nv);if T.t2<>nil then inc(nv);if T.t3<>nil then inc(nv);   //nv nombre de voisins
                 if T.t1=Chemins[i].TP then pr:=T.t1;if T.t2=Chemins[i].TP then pr:=T.t2;if T.t3=Chemins[i].TP then pr:=T.t3;// TP triangle precedent
                 // si un voisin c'est donc le precedent alors fermer le chemin, ajouter je ne sais pas quoid

                 if (nv=1)and(it<>1) then begin Chemins[i].EstFerme:=true;inc(ncf);end; // sil a un voisin seulement ou si c'est le premier triangle et qu'il a un seul voisin
                 // si deux voisins

                 if (nv=2)or((nv=1) and (it=1)) then
                    begin
                    if (T.t1<>nil)and(T.t1<>pr) then begin M.x:=(T.p2.x+T.p3.x)div 2;M.y:=(T.p2.y+T.p3.y)div 2; sv:=T.t1; Image1.Canvas.TextOut(M.X,M.Y,'V1'); end;
                    if (T.t2<>nil)and(T.t2<>pr) then begin M.x:=(T.p1.x+T.p3.x)div 2;M.y:=(T.p1.y+T.p3.y)div 2; sv:=T.t2;Image1.Canvas.TextOut(M.X,M.Y,'V2');end;
                    if (T.t3<>nil)and(T.t3<>pr) then begin M.x:=(T.p2.x+T.p1.x)div 2;M.y:=(T.p2.y+T.p1.y)div 2; sv:=T.t3;Image1.Canvas.TextOut(M.X,M.Y,'V3');end;
                    setlength(chemins[i].LesP,length(chemins[i].LesP)+1);    chemins[i].LesP[length(chemins[i].LesP)-1].X:=M.X;    chemins[i].LesP[length(chemins[i].LesP)-1].Y:=M.Y;
                    chemins[i].TA:=sv;chemins[i].TP:=T;
                    end;
                 // si trois voisins
                 if (nv=3) or ((nv=2)and(it=1)) then
                    begin
                    chemins[i].EstSupprime:=true;// supprimer le chemin qui va se bifurquer
                    inc(ncs);
                    c.X:=(t.p1.X+t.p2.X+t.p3.X)div 3;c.Y:=(t.p1.y+t.p2.y+t.p3.Y)div 3;// meme s'il y a t.c et quil marche quand je change le code il peut ne pas marcher
                    setlength(chemins[i].LesP,length(chemins[i].LesP)+1); chemins[i].LesP[length(chemins[i].LesP)-1].X:=C.X; chemins[i].LesP[length(chemins[i].LesP)-1].Y:=C.Y;// ajout du centre de gravité
                   //premier voisin
                    if T.t1<>pr then
                       begin
                       M.x:=(T.p2.x+T.p3.x)div 2;M.y:=(T.p2.y+T.p3.y)div 2;
                       setlength(chemins,length(chemins)+1);
                       chemins[length(chemins)-1].TA:=T.t1;chemins[length(chemins)-1].TP:=T;chemins[length(chemins)-1].EstFerme:=false;chemins[length(chemins)-1].EstSupprime:=false;
                       setlength(chemins[length(chemins)-1].LesP,length(chemins[i].LesP)+1);
                       for w:=0 to length(chemins[i].LesP)-1 do begin chemins[length(chemins)-1].LesP[w].X:=chemins[i].LesP[w].x; chemins[length(chemins)-1].LesP[w].Y:=chemins[i].LesP[w].y; end;
                       chemins[length(chemins)-1].LesP[w].X:=M.X;chemins[length(chemins)-1].LesP[w].Y:=M.Y;
                       end;
                    // deuxieme voisin
                    if T.t2<>pr then
                       begin
                       M.x:=(T.p1.x+T.p3.x)div 2;M.y:=(T.p1.y+T.p3.y)div 2;
                       setlength(chemins,length(chemins)+1);
                       chemins[length(chemins)-1].TA:=T.t2;chemins[length(chemins)-1].TP:=T;chemins[length(chemins)-1].EstFerme:=false;chemins[length(chemins)-1].EstSupprime:=false;
                       setlength(chemins[length(chemins)-1].LesP,length(chemins[i].LesP)+1);
                       for w:=0 to length(chemins[i].LesP)-1 do begin chemins[length(chemins)-1].LesP[w].X:=chemins[i].LesP[w].x; chemins[length(chemins)-1].LesP[w].Y:=chemins[i].LesP[w].y; end;
                       chemins[length(chemins)-1].LesP[w].X:=M.X;chemins[length(chemins)-1].LesP[w].Y:=M.Y;
                       end;
                    // troisieme voisin
                    if T.t3<>pr then
                       begin
                       M.x:=(T.p2.x+T.p1.x)div 2;M.y:=(T.p2.y+T.p1.y)div 2;
                       setlength(chemins,length(chemins)+1);
                       chemins[length(chemins)-1].TA:=T.t3;chemins[length(chemins)-1].TP:=T;chemins[length(chemins)-1].EstFerme:=false;chemins[length(chemins)-1].EstSupprime:=false;
                       setlength(chemins[length(chemins)-1].LesP,length(chemins[i].LesP)+1);
                       for w:=0 to length(chemins[i].LesP)-1 do begin chemins[length(chemins)-1].LesP[w].X:=chemins[i].LesP[w].x; chemins[length(chemins)-1].LesP[w].Y:=chemins[i].LesP[w].y; end;
                       chemins[length(chemins)-1].LesP[w].X:=M.X;chemins[length(chemins)-1].LesP[w].Y:=M.Y;
                       end;

                    end;
                 end;
          end;
      end;

//6666666666666 Chemin le plus long
for i :=1 to length(chemins)-1 do
    begin
    LM:=-1; L:=0;
    for k:=1 to length(Chemins[i].LesP)-1 do
        begin
        L:=L+DistPoint(Chemins[i].LesP[i-1],Chemins[i].LesP[i]);
        end;
    if L>LM then begin LM:=L; Sqlt:=i;end;
    end;
//Affichage du squellette
for k:=1 to length(Chemins[Sqlt].LesP)-1 do
        begin
        image1.Canvas.pen.color:=clblack;
        Image1.Canvas.MoveTo(Chemins[Sqlt].LesP[k-1].X,Chemins[Sqlt].LesP[k-1].Y);
        Image1.Canvas.LineTo(Chemins[Sqlt].LesP[k].X,Chemins[Sqlt].LesP[k].Y);
        end;
end;

procedure TForma.Button6Click(Sender: TObject);
var k,i,j:integer; XY:char;
begin
//Memo6.Lines.Clear;
i:=-1;XY:='X';
setlength(ListeObjetsR,0);
for k:=0 to Memo6.Lines.Count-1 do
    begin
    if (Memo6.Lines[k]='PL') or (Memo6.Lines[k]='PG') then begin
                                                           SetLength(ListeObjetsR,length(ListeObjetsR)+1);
                                                           inc(i);ListeObjetsR[i].Nature:=Memo6.Lines[k];
                                                           end
                                                      else begin
                                                          if XY='X' then begin
                                                                         SetLength(ListeObjetsR[i].ListePoint,length(ListeObjetsR[i].ListePoint)+1);
                                                                         ListeObjetsR[i].ListePoint[length(ListeObjetsR[i].ListePoint)-1].X:=strtofloat(Memo6.Lines[k]);
                                                                         XY:='Y';
                                                                         end
                                                                    else begin
                                                                         ListeObjetsR[i].ListePoint[length(ListeObjetsR[i].ListePoint)-1].Y:=strtofloat(Memo6.Lines[k]);
                                                                         XY:='X';
                                                                         end;
                                                           end;
    end;

end;

end.