unit Un_1;

interface

uses
  Windows, Messages, SysUtils, Classes, Graphics, Controls, Forms, Dialogs,
  StdCtrls, ExtCtrls, math, Spin, Menus, ComCtrls;

type
  TForm1 = class(TForm)
    Image1: TImage;
    Button1: TButton;
    Label1: TLabel;
    Label2: TLabel;
    Label3: TLabel;
    Label4: TLabel;
    Label5: TLabel;
    SaveDialog1: TSaveDialog;
    Button2: TButton;
    Button3: TButton;
    SpinEdit1: TSpinEdit;
    SpinEdit2: TSpinEdit;
    SpinEdit3: TSpinEdit;
    SpinEdit4: TSpinEdit;
    SpinEdit5: TSpinEdit;
    SpinEdit6: TSpinEdit;
    Label6: TLabel;
    Label8: TLabel;
    Image3: TImage;
    Label9: TLabel;
    MainMenu1: TMainMenu;
    N1: TMenuItem;
    N2: TMenuItem;
    N3: TMenuItem;
    N4: TMenuItem;
    N5: TMenuItem;
    N6: TMenuItem;
    N7: TMenuItem;
    N9: TMenuItem;
    Image2: TImage;
    N10: TMenuItem;
    Image4: TImage;
    Button4: TButton;
    TrackBar1: TTrackBar;
    Label10: TLabel;
    Label7: TLabel;
    Label11: TLabel;
    procedure Button1Click(Sender: TObject);
    procedure Button2Click(Sender: TObject);
    procedure Button3Click(Sender: TObject);
    procedure FormCreate(Sender: TObject);
    procedure Image1MouseMove(Sender: TObject; Shift: TShiftState; X,
      Y: Integer);
    procedure N7Click(Sender: TObject);
    procedure N2Click(Sender: TObject);
    procedure N3Click(Sender: TObject);
    procedure N4Click(Sender: TObject);
    procedure N9Click(Sender: TObject);
    procedure N5Click(Sender: TObject);
    procedure N10Click(Sender: TObject);
    procedure Image4Click(Sender: TObject);
    procedure Button4Click(Sender: TObject);
  private
    { Private declarations }
  public
    { Public declarations }
  end;

var Form1: TForm1;

implementation

{$R *.DFM}

procedure TForm1.Button1Click(Sender: TObject);
Const t=0.05;
Var   Vx0,Vy0,Vx,Vy,Vc,Vs,x,y,x1,y1,xx,yy,xx1,yy1,z1,z2,a0,b0,K,Cs,Sn:real;
                                                          a,b,c,d,i,p:integer;
Begin

Image1.Canvas.Brush.Color:=ClWhite;
Image1.Canvas.Rectangle(-10,-10,810,610);
Image1.Canvas.Pen.Width:=1;
Image1.Canvas.Pen.Color:=clBlack;
Image1.Canvas.MoveTo(400,0);
Image1.Canvas.LineTo(400,600);
Image1.Canvas.MoveTo(0,300);
Image1.Canvas.LineTo(800,300);

a:=abs(Round(spinedit1.value));
b:=abs(Round(spinedit2.value));
d:=abs(Round(spinedit5.value));

Vx0:=spinedit3.value;
Vy0:=spinedit4.value;
if ((Vx0=0) and (Vy0=0))
 then
  begin
    Vx0:=4;
    Vy0:=3;
    spinedit1.value:=4;
    spinedit1.value:=3;
  end;
Vc:=-Vx0/sqrt(sqr(Vx0)+sqr(Vy0));
Vs:=Vy0/sqrt(sqr(Vx0)+sqr(Vy0));

Image1.Canvas.Pen.Width:=2;
Image1.Canvas.Pen.Color:=Clblue;
Image1.Canvas.MoveTo(round(400+a*Vc),round(300-a*Vs));
For i:=-a to +a do
  begin
    x:=-i*Vc+b*sqrt(1-sqr(i/a))*Vs;
    y:=-i*Vs-b*sqrt(1-sqr(i/a))*Vc;
    Image1.Canvas.LineTo(round(400+x),round(300-y));
  end;
For i:=a downto -a do
  begin
    x:=-i*Vc-b*sqrt(1-sqr(i/a))*Vs;
    y:=-i*Vs+b*sqrt(1-sqr(i/a))*Vc;
    Image1.Canvas.LineTo(round(400+x),round(300-y));
  end;
Image1.Canvas.Pen.Color:=ClRed;

p:=round(1152/d);

If a<>b
 then
  begin
    c:=abs(sqr(a)-sqr(b));
    a0:=(1+sqr(a+b)/c)/2;
    b0:=(1-sqr(a+b)/c)/2;
    For i:=1-p to p do
      begin

        if Vx0=0
         then
          begin
            x:=d*i;
            y:=-500*Vs;
          end
         else
          if Vy0=0
           then
            begin
              x:=500*Vc;
              y:=d*i;
            end
           else
            begin
              x:=-d*i*abs(Vx0)/Vx0+500*Vc;
              y:=d*i*abs(Vy0)/Vy0-500*Vs;
            end;

        while ((x>-800) and (x<800) and (y>-800) and (y<800)) do
          begin
            yy:=2*x*y;
            xx:=sqr(x)-sqr(y)-c;
            K:=sqrt(sqr(xx)+sqr(yy));

            if y<0 then Sn:=-sqrt((1-xx/k)/2)
                   else Sn:=sqrt((1-xx/k)/2);
            if x<0 then Cs:=-sqrt((1+xx/k)/2)
                   else Cs:=sqrt((1+xx/k)/2);

            K:=sqrt(K);
            z1:=(x*Cs+y*Sn)/K;
            z2:=(y*Cs-x*Sn)/K;
            Vx:=Vx0*a0+Vx0*b0*z1+Vy0*a0*z2;
            Vy:=Vy0*b0+Vy0*a0*z1-Vx0*b0*z2;
            x1:=x+Vx*t;
            y1:=y+Vy*t;

            xx:=-x*Vc+y*Vs;
            yy:=-x*Vs-y*Vc;
            xx1:=-x1*Vc+y1*Vs;
            yy1:=-x1*Vs-y1*Vc;

             if ((xx>-400) and (xx<400) and (yy>-300) and (yy<300))
             then
              begin
                Image1.Canvas.MoveTo(round(400+xx),round(300-yy));
                Image1.Canvas.LineTo(round(400+xx1),round(300-yy1));
              end;

            x:=x1;
            y:=y1;

            if sqr(x/a)+sqr(y/b)<=1 then x:=801;

            if sqr(Vx)+sqr(Vy)<1E-5 then x:=801;
          end;
      end;
  end
 else
  For i:=1-p to p do
    begin
      if Vx0<0 then x:=799
               else x:=-799;
      y:=18-i*d;
      if Vx0<0 then Vx0:=-sqrt(sqr(Vx0)+sqr(Vy0))
               else Vx0:=sqrt(sqr(Vx0)+sqr(Vy0));
      Vy0:=0;

      while ((x>-800) and (x<800) and (y>-800) and (y<800)) do
        begin
          yy:=2*x*y;
          xx:=sqr(x)-sqr(y);
          K:=(sqr(xx)+sqr(yy));
          Vx:=Vx0-a*a*Vx0*xx/K-a*a*Vy0*yy/K;
          Vy:=Vy0-a*a*Vx0*yy/K+a*a*Vy0*xx/K;

          x1:=x+Vx*t;
          y1:=y+Vy*t;

          if ((x>-400) and (x<400) and (y>-300) and (y<300))
           then
            begin
              Image1.Canvas.MoveTo(round(400+x),round(300-y));
              Image1.Canvas.LineTo(round(400+x1),round(300-y1));
            end;

          x:=x1;
          y:=y1;

          if sqr(x/a)+sqr(y/a)<=1
           then
            x:=801;

          if sqr(Vx)+sqr(Vy)<1E-5 then x:=801;
        end;
    end;

End;



procedure TForm1.Button2Click(Sender: TObject);
var c,a0,b0,Q,K,V0x,Vx,Vy,x1,y1,x,y,t,z1,z2:real;
a,b,i,i1,a10,a1:integer;
begin
Image1.Canvas.Pen.Width:=2;
button2.Enabled:=false;
spinedit6.Enabled:=false;
a1:=spinedit6.Value;

for i1:=1 to trunc(0.4*a1) do begin
image1.Canvas.Rectangle(-1,-1,1000,1000);
a:=-(a1-5)+i1;
b:=trunc(a1*(a1-5)/abs(a));

c:=a*a-b*b;
a0:=a/(a-b);
b0:=b/(b-a);
image1.Canvas.Pen.Color:=clblue;
image1.Canvas.Ellipse(400-a,300-b,400+a,300+b);

for i:=1 to 16 do begin
a10:=0;V0x:=-40;t:=0.1;x:=-399;y:=340-i*40;

while ((x1>-400) and (x1<400) and (y1>-300) and (y1<300) and (a10=0)) do begin
if x>0 then a10:=1;
Q:=1/2*arctan2(2*x*y,x*x-y*y-c);
K:=sqrt(sqrt(sqr(sqr(x)-sqr(y)-c)+4*x*x*y*y));
z1:=(x*cos(Q)+y*sin(Q))/K;
z2:=(y*cos(Q)-x*sin(Q))/K;
Vx:=V0x*a0+V0x*b0*z1;
Vy:=-V0x*b0*z2;
x1:=x+Vx*t;
y1:=y+Vy*t;

Image1.Canvas.Pen.Color:=clred;

image1.Canvas.MoveTo(400-trunc(x),300-trunc(y));
image1.Canvas.LineTo(400-trunc(x1),300-trunc(y1));

image1.Canvas.MoveTo(399+trunc(x),300-trunc(y));
image1.Canvas.LineTo(399+trunc(x1),300-trunc(y1));

y:=y1;x:=x1;
end;
x1:=0;y1:=0;
end;
application.ProcessMessages;
end;
button2.Enabled:=true;
spinedit6.Enabled:=true;
end;

procedure TForm1.Button3Click(Sender: TObject);
var a0,b0,c,Q,K,V0x,Vx,Vy,x1,y1,x,y,t,z1,z2:real;
x11,a1,b1,i,i1,a10,j,a,b:integer;
begin
Image1.Canvas.Pen.Width:=2;
b1:=spinedit6.value;
a1:=b1-5;

button3.Enabled:=false;
spinedit6.Enabled:=false;

x11:=-trunc(400-b1);i1:=0;

for j:=1 to 800+b1 do begin

if trunc(j/24)=j/24 then i1:=i1+1;
x11:=x11+1;
image1.Canvas.Rectangle(-1,-1,1000,1000);
a:=-trunc(a1*b1/abs(b));
b:=a1-i1;

c:=abs(a*a-b*b);
a0:=a/(a-b);
b0:=b/(b-a);
image1.Canvas.Pen.Color:=clblue;
image1.Canvas.Ellipse(x11+400-a,300-b,x11+400+a,300+b);

for i:=1 to 16 do begin
a10:=0;
V0x:=20;t:=1.01;x:=-399;y:=340-i*40;

while ((x1>-400) and (x1<400) and (y1>-300) and (y1<300) and (a10=0)) do begin
if x>0 then a10:=1;
Q:=1/2*arctan2(2*x*y,x*x-y*y-c);
K:=sqrt(sqrt(sqr(sqr(x)-sqr(y)-c)+4*x*x*y*y));
z1:=(x*cos(Q)+y*sin(Q))/K;
z2:=(y*cos(Q)-x*sin(Q))/K;
Vx:=V0x*a0+V0x*b0*z1;
Vy:=-V0x*b0*z2;
x1:=x+Vx*t;
y1:=y+Vy*t;

image1.Canvas.Pen.Color:=clred;
if i>1 then begin
image1.Canvas.MoveTo(801,300-trunc(340-i*40));
image1.Canvas.lineto(801+trunc(x11)-2,300-trunc(340-i*40));  // pravii linii

image1.Canvas.MoveTo(-1,300-trunc(340-i*40));                 // levii linii
image1.Canvas.lineto(-1+trunc(x11)+2,300-trunc(340-i*40));
end;

image1.Canvas.MoveTo(x11+400+trunc(x),300-trunc(y));
image1.Canvas.lineTo(x11+400+trunc(x1),300-trunc(y1));

image1.Canvas.MoveTo(x11+401-trunc(x),300-trunc(y));
image1.Canvas.lineTo(x11+401-trunc(x1),300-trunc(y1));

y:=y1;x:=x1;
end;
x1:=0;y1:=0;
end;
application.ProcessMessages;
end;

button3.Enabled:=true;
spinedit6.Enabled:=true;
end;

procedure TForm1.FormCreate(Sender: TObject);
begin
image1.Canvas.Rectangle(-1,-1,1000,1000);
image3.Canvas.Rectangle(-1,-1,106,106);
n5.Enabled:=false;
n6.Enabled:=false;
end;

procedure speed(x,y:real;var Vxx,Vyy:real);
var a,b:integer;Vx,Vy,z1,z2,Sn,Cs,K,c,a0,b0,Vx0,Vy0,Vs,Vc:real;
begin
a:=abs(Round(form1.spinedit1.value));
b:=abs(Round(form1.spinedit2.value));
Vx0:=form1.spinedit3.value;
Vy0:=form1.spinedit4.value;
Vc:=-Vx0/sqrt(sqr(Vx0)+sqr(Vy0));
Vs:=Vy0/sqrt(sqr(Vx0)+sqr(Vy0));
c:=abs(sqr(a)-sqr(b));
a0:=(1+sqr(a+b)/c)/2;
b0:=(1-sqr(a+b)/c)/2;

K:=sqrt(sqr(sqr(x)-sqr(y)-c)+sqr(2*x*y));

if y<0 then Sn:=-sqrt((1-(sqr(x)-sqr(y)-c)/k)/2)
            else Sn:=sqrt((1-(sqr(x)-sqr(y)-c)/k)/2);
if x<0 then Cs:=-sqrt((1+(sqr(x)-sqr(y)-c)/k)/2)
            else Cs:=sqrt((1+(sqr(x)-sqr(y)-c)/k)/2);
K:=sqrt(K);
z1:=(x*Cs+y*Sn)/K;
z2:=(y*Cs-x*Sn)/K;
Vx:=Vx0*a0+Vx0*b0*z1+Vy0*a0*z2;
Vy:=Vy0*b0+Vy0*a0*z1-Vx0*b0*z2;

Vxx:=-Vx*Vc+Vy*Vs;
Vyy:=-Vx*Vs-Vy*Vc;
end;

procedure TForm1.Image1MouseMove(Sender: TObject; Shift: TShiftState; X,Y: Integer);
var Vxx,Vyy:real;
begin

if n5.Checked=true then
if image1.Canvas.Pixels[x,y]=clred then begin

x:=x-400;y:=300-y;
speed(x,y,Vxx,Vyy);

Vxx:=abs(Vxx);

Image3.Canvas.Brush.Color:=Clwhite;
Image3.Canvas.Rectangle(-1,-1,106,106);
Image3.Canvas.Brush.Color:=Clgreen;
image3.Canvas.MoveTo(3,52);
image3.Canvas.LineTo(3+trunc(7*Vxx),52);

image3.Canvas.MoveTo(3,52);
image3.Canvas.LineTo(3,52-trunc(7*Vyy));

image3.Canvas.MoveTo(3,52);
image3.Canvas.LineTo(3+trunc(7*Vxx),52-trunc(7*Vyy));

label7.Caption:='Vx = '+floattostr(Vxx);
label8.Caption:='Vy = '+floattostr(Vyy);
end;
end;

procedure TForm1.N7Click(Sender: TObject);
begin
showmessage('Test build v 0.94.01 - RiaSoft (C) 29.04.2007');
end;

procedure TForm1.N2Click(Sender: TObject);
begin
image1.Canvas.Rectangle(-1,-1,1000,1000);
n2.Checked:=true;
n3.Checked:=false;
n4.Checked:=false;
button1.Visible:=true;
button2.Visible:=false;
button3.Visible:=false;
//////////////////
button4.Visible:=true;
////////////
n5.Enabled:=true;
/////////////
spinedit1.Enabled:=true;
spinedit2.Enabled:=true;
spinedit3.Enabled:=true;
spinedit4.Enabled:=true;
spinedit5.Enabled:=true;
spinedit6.Enabled:=false;

end;

procedure TForm1.N3Click(Sender: TObject);
begin
label11.Visible:=false;
image1.Visible:=true;
image4.Visible:=false;

spinedit6.MaxValue:=200;

image1.Canvas.Rectangle(-1,-1,1000,1000);
n2.Checked:=false;
n3.Checked:=true;
n4.Checked:=false;
button1.Visible:=false;
button2.Visible:=true;
button3.Visible:=false;

n5.Checked:=false;
n5.Enabled:=false;
/////////////
button4.Visible:=false;
trackbar1.Visible:=false;
//////////////
label7.Visible:=false;
label8.Visible:=false;
label9.Visible:=false;
image3.Visible:=false;
///////////////
spinedit1.Enabled:=false;
spinedit2.Enabled:=false;
spinedit3.Enabled:=false;
spinedit4.Enabled:=false;
spinedit5.Enabled:=false;
spinedit6.Enabled:=true;
end;

procedure TForm1.N4Click(Sender: TObject);
begin
label11.Visible:=false;
image1.Visible:=true;
image4.Visible:=false;

spinedit6.MaxValue:=150;

image1.Canvas.Rectangle(-1,-1,1000,1000);
n2.Checked:=false;
n3.Checked:=false;
n4.Checked:=true;
button1.Visible:=false;
button2.Visible:=false;
button3.Visible:=true;

n5.Checked:=false;
n5.Enabled:=false;
//////////////////
button4.Visible:=false;
trackbar1.Visible:=false;
////////////////////
label7.Visible:=false;
label8.Visible:=false;
label9.Visible:=false;
image3.Visible:=false;
///////////////////
spinedit1.Enabled:=false;
spinedit2.Enabled:=false;
spinedit3.Enabled:=false;
spinedit4.Enabled:=false;
spinedit5.Enabled:=false;
spinedit6.Enabled:=true;
end;

procedure TForm1.N9Click(Sender: TObject);
begin
Savedialog1.Filter := 'Bitmap files (*.bmp)|*.bmp';
if image1.Visible=true then if SaveDialog1.Execute=true then image1.Picture.SaveToFile(savedialog1.FileName+'.bmp');
if image4.Visible=true then if SaveDialog1.Execute=true then image4.Picture.SaveToFile(savedialog1.FileName+'.bmp');

end;

procedure TForm1.N5Click(Sender: TObject);
begin
n5.Checked:=not(n5.Checked);
if n5.Checked=true then begin
label7.Visible:=true;
label8.Visible:=true;
label9.Visible:=true;
image3.Visible:=true;
end;
if n5.Checked=false then begin
label7.Visible:=false;
label8.Visible:=false;
label9.Visible:=false;
image3.Visible:=false;
end;

end;

procedure TForm1.N10Click(Sender: TObject);
begin
form1.Close;
end;


procedure TForm1.Image4Click(Sender: TObject);
var a,b,i,c:integer;P,Vx0,Vy0,Vc,Vs,x,y,Vxx,Vyy,vy,vx,zzz:real;
begin
trackbar1.Enabled:=false;
Image4.Canvas.Brush.Color:=Clwhite;
Image4.Canvas.Rectangle(-1,-1,1060,1060);
Image4.Canvas.Pen.Width:=1;
Image4.Canvas.Pen.Color:=clBlack;
Image4.Canvas.MoveTo(400,0);
Image4.Canvas.LineTo(400,600);
Image4.Canvas.MoveTo(0,300);
Image4.Canvas.LineTo(800,300);

a:=abs(Round(form1.spinedit1.value));b:=abs(Round(form1.spinedit2.value));
Vx0:=form1.spinedit3.value;Vy0:=form1.spinedit4.value;
Vc:=-Vx0/sqrt(sqr(Vx0)+sqr(Vy0));Vs:=Vy0/sqrt(sqr(Vx0)+sqr(Vy0));

Image4.Canvas.Pen.Width:=1;Image4.Canvas.Pen.Color:=Clgreen;
speed(-400,0,vx,vy);

For i:=-a to a do begin
    ///////////////////verh
    x:=-i*Vc+b*sqrt(1-sqr(i/a))*Vs;
    y:=-i*Vs-b*sqrt(1-sqr(i/a))*Vc;
    Speed(x,y,Vxx,Vyy);
    P:=-0.5*(trackbar1.Position+0.5*(vx*vx+vy*vy-Vxx*Vxx-Vyy*Vyy));

    Image4.Canvas.pixels[round(400+x),round(300-y)]:=clblue;

    //image4.Canvas.MoveTo(trunc(400+x),300);
    //image4.Canvas.lineTo(trunc(400+x),300-trunc(p*10));

    {image4.Canvas.MoveTo(400,300);
    Image4.Canvas.Pen.Width:=1;Image4.Canvas.Pen.Color:=Clgreen;
    image4.Canvas.LineTo( 400+ trunc(100*x*p/(sqrt(x*x+y*y)*10)) ,300-trunc(100*y*p/(sqrt(x*x+y*y)*10)) ); }

    image4.Canvas.MoveTo(400+trunc(x),300-trunc(y));
    //image4.Canvas.LineTo( 400+ trunc(100*i*p/(a*10)) ,300-trunc(100*sqrt(a*a-i*i)*p/(a*10)) );
    if 1-x*x/(a*a)<>0 then if x<>0 then begin
    if p>0 then zzz:=arctan(-b*x/(sqrt(1-x*x/(a*a))*a*a))+pi/2;
    if p<0 then zzz:=arctan(-b*x/(sqrt(1-x*x/(a*a))*a*a))-pi/2;
    end;
    p:=abs(p);

    c:=c+1;if c/3=trunc(c/3) then image4.Canvas.LineTo( 400+trunc(x+5*p*cos(zzz)) ,300+trunc(-y-5*p*sin(zzz)) );

    {if c/3=trunc(c/3) then begin image4.Canvas.MoveTo(400,300);
    image4.Canvas.lineTo(trunc(400+x),300-trunc(y));end;   }

    application.ProcessMessages;

    /////////////////// niz
    x:=-i*Vc-b*sqrt(1-sqr(-i/a))*Vs;
    y:=-i*Vs+b*sqrt(1-sqr(-i/a))*Vc;
    Speed(x,y,Vxx,Vyy);
    P:=-0.5*(trackbar1.Position+0.5*(vx*vx+vy*vy-Vxx*Vxx-Vyy*Vyy));
    Image4.Canvas.pixels[round(400+x),round(300-y)]:=clblue;

    image4.Canvas.MoveTo(400+trunc(x),300-trunc(y));
    if 1-x*x/(a*a)<>0 then if x<>0 then begin
    if p>0 then zzz:=arctan(-b*x/(sqrt(1-x*x/(a*a))*a*a))+pi/2;
    if p<0 then zzz:=arctan(-b*x/(sqrt(1-x*x/(a*a))*a*a))-pi/2;
    end;

    p:=abs(p);

    c:=c+1;if c/3=trunc(c/3) then image4.Canvas.LineTo( 400+trunc(x+5*p*cos(zzz)) ,300-trunc(y-5*p*sin(zzz)) );
end;

trackbar1.Enabled:=true;
end;

procedure TForm1.Button4Click(Sender: TObject);
begin
image1.Visible:=not image1.Visible;
image4.Visible:=not image4.Visible;
label11.Visible:=image4.Visible;
trackbar1.Visible:=image4.Visible;
end;

end.