Plot y = sin(x) on a PaintBox component

// draw a coordinate cross and plot the function y = sin(x)
// the Windows form is taken up by a PaintBox Component 440x688 pixels
// in the left upper corner is a Button titled "Plot sin(x)"
// Delphi 3.0    (vegaseat)

unit PlotFunctionz;

interface

uses
  Windows, Messages, SysUtils, Classes, Graphics, Controls, Forms, Dialogs,
  StdCtrls, ExtCtrls;

type
  TForm1 = class(TForm)
    Button1: TButton;
    PaintBox1: TPaintBox;
    procedure CalculateGraph;
    procedure PaintBox1Paint(Sender: TObject);
    procedure Button1Click(Sender: TObject);
    procedure FormResize(Sender: TObject);
  private
    { Private declarations }

  public
    { Public declarations }
  end;

var
  Form1: TForm1;
  FPoints: array [0..144] of TPoint;
  
implementation

{$R *.DFM}


procedure TForm1.CalculateGraph;
var 
  xRangePixels, yRangePixels: Integer;
  origin: TPoint; 
  radian, interval: Double;
  i: Integer; 
begin 
  { 
    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.Button1Click(Sender: TObject);
begin
  CalculateGraph;
end;

// need this to get plot going
procedure TForm1.FormResize(Sender: TObject);
begin
  CalculateGraph;
end;

end.