Функция построения графика

Рассчитаем синусоидальную кривую в интервале -2Pi..+2Pi, с разрешением 4Pi/144, как ряд точек, которые будут соединены ломаной линией.

График масштабируется под размер области рисования графика.

Началом системы координат является центр области графика.

При этом учитываем, что система координат Windows по умолчанию инвертирована, ось Y направлена вниз!

private
   FPoints: array [0..144] of TPoint;

 {...}

 procedure TForm1.CalculateGraph;
 var
   xRangePixels, yRangePixels: Integer;
   origin: TPoint;
   radian, interval: Double;
   i: Integer;
 begin
   { 
    We calculate the sinus curve in the interval -2Pi..+2Pi, 
    with a resolution of 4Pi/144, as a series of points that 
    will be connected by a polyline. The graph is scaled to fit into 
    the paintbox. The origin of the coordinate system is the center 
    of the paintbox. The default windows coordinate system is inverted, 
    the Y axis points downward! 
  }
   xRangePixels := (paintbox1.Width - 2) div 4; { pixels in Pi }
   yRangePixels := (paintbox1.Height - 2) div 2; { pixels in 1 }
   origin       := Point(paintbox1.Width div 2, paintbox1.Height div 2);
   radian       := -2.0 * Pi;
   interval     := 4.0 * Pi / 144.0;
   for i := 0 to High(FPoints) do
    begin
     FPoints[i].X := origin.x + Round(radian * xRangePixels / Pi);
     FPoints[i].Y := origin.y - Round(sin(radian) * yRangePixels);
     radian       := radian + interval;
   end;
 end;

 procedure TForm1.PaintBox1Paint(Sender: TObject);
 var
   origin: TPoint;
   xRangePixels, yRangePixels: Integer;
 begin
   with PaintBox1.Canvas do
    begin
     { Fill background in white }
     Brush.Color := clBtnFace;
     Brush.Style := bsSolid;
     Fillrect(paintbox1.BoundsRect);

     { Paint a coordinate cross }
     origin    := Point(paintbox1.Width div 2, paintbox1.Height div 2);
     Pen.Color := clBlack;
     Pen.Style := psSolid;
     Pen.Width := 1;
     MoveTo(1, origin.Y);
     LineTo(paintbox1.Width - 1, origin.y);
     MoveTo(origin.x, 1);
     LineTo(origin.x, paintbox1.Height - 1);

     { Paint some tickmarks and label the axis }
     Font.Name    := 'Symbol';
     Font.Size    := 8;
     Font.Color   := clBlack;
     xRangePixels := (paintbox1.Width - 2) div 4; { pixels in Pi }
     yRangePixels := (paintbox1.Height - 2) div 2; { pixels in 1 }

     { X axis }
     MoveTo(origin.x - 2 * xRangePixels, origin.y - 4);
     LineTo(origin.x - 2 * xRangePixels, origin.y + 4);
     TextOut(origin.x - 2 * xRangePixels + 2, origin.y + 2, '-2p');
     MoveTo(origin.x - xRangePixels, origin.y - 4);
     LineTo(origin.x - xRangePixels, origin.y + 4);
     TextOut(origin.x - xRangePixels + 2, origin.y + 2, '-p');
     MoveTo(origin.x + xRangePixels, origin.y - 4);
     LineTo(origin.x + xRangePixels, origin.y + 4);
     TextOut(origin.x + xRangePixels - 2 - TextWidth('p'), origin.y + 2, 'p');
     MoveTo(origin.x + 2 * xRangePixels, origin.y - 4);
     LineTo(origin.x + 2 * xRangePixels, origin.y + 4);
     TextOut(origin.x + 2 * xRangePixels - 2 - TextWidth('2p'), origin.y + 2, '2p');


     { Y axis }
     MoveTo(origin.x - 4, origin.y - yRangePixels);
     LineTo(origin.x + 4, origin.y - yRangePixels);
     TextOut(origin.x + 4, origin.y - yRangePixels, '1.0');
     MoveTo(origin.x - 4, origin.y - yRangePixels div 2);
     LineTo(origin.x + 4, origin.y - yRangePixels div 2);
     TextOut(origin.x + 4, origin.y - (yRangePixels + TextHeight('1')) div 2, '0.5');
     MoveTo(origin.x - 2, origin.y + yRangePixels div 2);
     LineTo(origin.x + 2, origin.y + yRangePixels div 2);
     TextOut(origin.x + 3, origin.y + (yRangePixels - TextHeight('1')) div 2, '-0.5');
     MoveTo(origin.x - 2, origin.y + yRangePixels);
     LineTo(origin.x + 2, origin.y + yRangePixels);
     TextOut(origin.x + 3, origin.y + yRangePixels - TextHeight('1'), '-1.0');

     {Paint the graph }
     Pen.Color := clBlue;
     Polyline(FPoints);
   end;
 end;

 procedure TForm1.FormResize(Sender: TObject);
 begin
   CalculateGraph;
 end;

 procedure TForm1.FormCreate(Sender: TObject);
 begin
   CalculateGraph;
 end;