[Rat]

Я бы так сделал:

Код:

unit Unit1;

interface

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

type
  TForm1 = class(TForm)
    PaintBox1: TPaintBox;
    SpinEdit1: TSpinEdit;
    Label1: TLabel;
    Button1: TButton;
    procedure Button1Click(Sender: TObject);
  private
    procedure DrawDot(x, y: Integer);
    { Private declarations }
  public
    { Public declarations }
  end;

var
  Form1: TForm1;
  ax: array[1..30] of Integer;
  ay: array[1..30] of Integer;

implementation

{$R *.dfm}

procedure TForm1.DrawDot(x, y : Integer);
begin
  // Ðèñóåì òî÷êó ñ ïåðåâîäîì îòñ÷åòà íóëåâîé òî÷êè
  PaintBox1.Canvas.MoveTo(40 - x, 40 - y);
  PaintBox1.Canvas.LineTo(40 - (x + 1), 40 - y);
end;

procedure TForm1.Button1Click(Sender: TObject);
var
  i : Integer;
  tx1, ty1, tx2, ty2, tx3, ty3 : Integer;
  rect : TRect;
begin
  // Î÷èùàåì îáëàñòü ðèñîâàíèÿ
  rect.Left := 0;
  rect.Top  := 0;
  rect.Bottom := 41;
  rect.Right  := 41;
  PaintBox1.Canvas.Brush.Color := clBtnFace;

  if SpinEdit1.Value > 30 then SpinEdit1.Value := 30;
  PaintBox1.Canvas.FillRect(rect);
// Ãåíåðèðóåì è ðèñóåì òî÷êè
  Randomize;
  for i:= 1 to SpinEdit1.Value do
  begin
    ax[i] := random(40);
    ay[i] := random(40);
    DrawDot(ax[i], ay[i]);
  end;

// Èùåì ñàìóþ âûñøóþ òî÷êó
  tx1 := 0;
  ty1 := 0;
  for i:= 1 to SpinEdit1.Value do
  begin
    if ay[i] > ty1 then
      begin
        ty1 := ay[i];
        tx1 := ax[i];
      end;
  end;

// Èùåì ñàìóþ ëåâóþ òî÷êó
  tx2 := 40;
  ty2 := 0;
  for i:= 1 to SpinEdit1.Value do
  begin
    if ax[i] < tx2 then
      begin
        ty2 := ay[i];
        tx2 := ax[i];
      end;
  end;

// Èùåì ñàìóþ ïðàâóþ òî÷êó
  tx3 := 0;
  ty3 := 0;
  for i:= 1 to SpinEdit1.Value do
  begin
    if ax[i] > tx3 then
      begin
        ty3 := ay[i];
        tx3 := ax[i];
      end;
  end;

// Ñòðîèì ïî íàéäåííûì òî÷êàì òðåóãîëüíèê

  PaintBox1.Canvas.MoveTo(40 - tx1, 40 - ty1);
  PaintBox1.Canvas.LineTo(40 - tx2, 40 - ty2);
  PaintBox1.Canvas.LineTo(40 - tx3, 40 - ty3);
  PaintBox1.Canvas.LineTo(40 - tx1, 40 - ty1);

end;

end.