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Код

var
 cx,cy:integer;
 dX,dY:real;

function TfrmGraph.X1(b,alpha:real):real;
begin
 X1:=b*(cos(alpha/4)*cos(alpha/4)*cos(alpha/4));
end;

function TfrmGraph.Y1(b,alpha:real):real;
begin
 Y1:=b*(sin(alpha/4)*sin(alpha/4)*sin(alpha/4));
end;

procedure TfrmGraph.Astroid;
const Step = 0.01;
var XX,YY,x,y:real;
 a,b:real;
 alpha:real;
 k:real;
begin
 a:=0;
 b:=1440/180*pi;
 alpha:=a;
 XX:=Abs(X1(k,a));
 YY := Abs(Y1(k,a));
 alpha:=a;
 repeat
 if YY < Abs(Y1(k,alpha)) then YY := Abs(Y1(k,alpha));
 alpha:=alpha+0.01;
 until alpha>=b;
 dX := imgGraph.Height/2.2 / XX;
 dY := imgGraph.Width/2.2 / YY;
 alpha:=a;
 y := Y1(k,alpha);
 x := X1(k,alpha);
 imgGraph.Canvas.MoveTo(cx + Round(dX * x ),cy - Round(dY * y ));
 alpha:=a+0.01;
 imgGraph.Canvas.Pen.Color:=clGreen;
 imgGraph.Canvas.Pen.Width:=3;
 Repeat
 y := Y1(k,alpha);
 x := X1(k,alpha);
 imgGraph.Canvas.Lineto(Round(cx + (dX * x )), Round(cy - (dY * y )));
 alpha := alpha + 0.01;
 Until alpha > b;
end;

procedure TfrmGraph.CoordGrid;
begin
 imgGraph.Canvas.Pen.Width:=1;
 imgGraph.Canvas.Pen.Color:=clRed;
 imgGraph.Canvas.MoveTo(0,cx);
 imgGraph.Canvas.LineTo(imgGraph.Width,cx);
 imgGraph.Canvas.MoveTo(cy,0);
 imgGraph.Canvas.LineTo(cy,imgGraph.Height);
 imgGraph.Canvas.Font.Size:=8;
 imgGraph.Canvas.Font.Style:=[fsBold];
 imgGraph.Canvas.Brush.Color:=clWhite;
 imgGraph.Canvas.TextOut(485,cy-30,'X');
 imgGraph.Canvas.TextOut(cx-25,5,'Y');
 imgGraph.Canvas.Brush.Color:=clBlack;
end;

procedure TfrmGraph.FormCreate(Sender: TObject);
begin
 cx:=round(imgGraph.Width/2);
 cy:=round(imgGraph.Height/2);
 Astroid;
 CoordGrid;
end;
end.