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 unit Unit1;
 
 interface
 
 uses
   Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
   Dialogs, StdCtrls, ExtCtrls;
 const PointsCount = 25;
       rPoint      = 3;
 type
   // Ñòðóêòóðà îïèñûâàþùàÿ òî÷êó â ïðîñòðàíñòâå
 
   TPoint3D = record
     X: Real;
     Y: Real;
     Z: Real;
   end;
 
 type
   TForm1 = class(TForm)
     Image1: TImage;
     Button1: TButton;
     Timer1: TTimer;
     Button2: TButton;
     procedure Button1Click(Sender: TObject);
     procedure FormCreate(Sender: TObject);
     procedure FormClose(Sender: TObject; var Action: TCloseAction);
     procedure Timer1Timer(Sender: TObject);
     procedure Button2Click(Sender: TObject);
  { Private declarations }
   private
     // Êîîðäèíàòû öåíòðà ýêðàíà
     oX: Integer;
     oY: Integer;
 
     ScaleX,ScaleY:real;
     DrawBuffer:  TBitMap;    // Áóôåð äëÿ ðèñîâàíèÿ
     BufferColor: TColor;     // Öâåò áóôåðà
     X0,Y0,Xn,Yn,dX,dY : Real;
     zMin, zMax: real;
     Alpha: Real;
     AlphaP: Real;
     Points3D: array[0..PointsCount,0..PointsCount] of TPoint3D; // Ìàññèâ òðåõìåðíûõ òî÷åê
     Points2D: array[0..PointsCount,0..PointsCount] of TPoint;
     subAxis3D_X: array[0..13] of TPoint3D;
     subAxis3D_Y: array[0..13] of TPoint3D;
     subAxis3D_Z: array[0..13] of TPoint3D;
     subAxis2D_X: array[0..13] of TPoint;
     subAxis2D_Y: array[0..13] of TPoint;
     subAxis2D_Z: array[0..13] of TPoint;
     Axis3D: array[0..8] of  TPoint3D;
     Axis2D: array[0..8] of  TPoint;
     procedure ClearBuffer;  // Î÷èñòêà áóôåðà ðèñîâàíèÿ
     procedure DrawPoints;   // Ïðîöåäóðà ðèñîâàíèÿ òî÷åê
   public
     { Public declarations }
   end;
 
 var
   Form1: TForm1;
 
 implementation
 
 {$R *.dfm}
 
 procedure TForm1.Button1Click(Sender: TObject);
 var i,j : integer;
 begin
     X0:=-3.14; Xn:=3.14;
     Y0:=-3.14; Yn:=3.14;
     dX:= (Xn-X0)/PointsCount;
     dY:= (Yn-Y0)/PointsCount;
     Axis3d[0].X:=0;
     Axis3d[0].Y:=0;
     Axis3d[0].Z:=0;
 
     Axis3d[1].X:=-4;
     Axis3d[1].Y:=0;
     Axis3d[1].Z:=0;
     Axis3d[2].X:=4;
     Axis3d[2].Y:=0;
     Axis3d[2].Z:=0;
 
     Axis3d[3].X:=0;
     Axis3d[3].Y:=-4;
     Axis3d[3].Z:=0;
 
     Axis3d[4].X:=0;
     Axis3d[4].Y:=4;
     Axis3d[4].Z:=0;
 
     Axis3d[5].X:=0;
     Axis3d[5].Y:=0;
     Axis3d[5].Z:=-4;
 
     Axis3d[6].X:=0;
     Axis3d[6].Y:=0;
     Axis3d[6].Z:=4;
   for i:=0 to 6 do
   begin
    subAxis3D_X[2*i].X:=Trunc(X0)+i;
    subAxis3D_X[2*i].Y:=-0.2;
    subAxis3D_X[2*i].Z:=0;
    subAxis3D_X[2*i+1].X:=Trunc(X0)+i;
    subAxis3D_X[2*i+1].Y:=0.2;
    subAxis3D_X[2*i+1].Z:=0;
   end;
   for i:=0 to 6 do
   begin
    subAxis3D_Y[2*i].X:=-0.2;
    subAxis3D_Y[2*i].Y:=Trunc(Y0)+i;
    subAxis3D_Y[2*i].Z:=0;
    subAxis3D_Y[2*i+1].X:=0.2;
    subAxis3D_Y[2*i+1].Y:=Trunc(Y0)+i;
    subAxis3D_Y[2*i+1].Z:=0;
   end;
   for i:=0 to 6 do
   begin
    subAxis3D_Z[2*i].X:=0;
    subAxis3D_Z[2*i].Y:=-0.2;
    subAxis3D_Z[2*i].Z:=-3+i;
    subAxis3D_Z[2*i+1].X:=0;
    subAxis3D_Z[2*i+1].Y:=0.2;
    subAxis3D_Z[2*i+1].Z:=-3+i;
   end;
 
   for i:=0 to PointsCount do
    for j:=0 to PointsCount do
     begin
       Points3D[i][j].X:=X0+i*dX;
       Points3D[i][j].Y:=Y0+j*dY;
       Points3D[i][j].Z:=cos(Points3D[i][j].X+sin(Points3D[i][j].Y));
     end;
 
    zMin:=Points3D[0][0].Z;
    zMax:=zMin;
    for i:=0 to PointsCount do
     for j:=0 to PointsCount do
     begin
       if (zMin>Points3D[i][j].Z) then
       zMin:= Points3D[i][j].Z;
       if (zMax<Points3D[i][j].Z) then
       zMax:= Points3D[i][j].Z;
     end;
   ScaleX:=50;//(Xn-X0);
   ScaleY:=100;//(zMax-zMin);
   //ScaleY:=100;
   DrawPoints;
 end;
 
 procedure TForm1.FormCreate(Sender: TObject);
 begin
   // Âû÷èñëÿåì öåíòð ýêðàíà
   oX := Image1.Width div 2;
   oY := Image1.Height div 2;
 
   Alpha:=0;
   AlphAP:=ArcTan(1)/4;
 
 //  ScaleX:=50;
 //  ScaleY:=25;
   // Óñòàíàâëèâàåì öâåò ôîíà (áóôôåðà ðèñîâàíèÿ)
 
   BufferColor       := clWhite;
 
   // Ñîçäàåì áóôôåðà ðèñîâàíèÿ
 
   DrawBuffer        := TBitMap.Create;
   DrawBuffer.Width  := Image1.Width;
   DrawBuffer.Height := Image1.Height;
 
   // Î÷èùàåì áóôôåð
 
   ClearBuffer;
 end;
 
 procedure TForm1.DrawPoints;
 var
   tX:  Real;
   tY:  Real;
   i,j: Integer;
 
 begin
   if DrawBuffer <> nil then
   begin
     ClearBuffer;
     for i:=0 to 6 do
      begin
         tX:=(Axis3D[i].X+Axis3D[i].Y*cos(AlphaP))*ScaleX;
         tY:=(Axis3D[i].Z+Axis3D[i].Y*sin(AlphaP))*ScaleY;
         Axis2D[i].X:=ROUND(oX+tX);
         Axis2D[i].Y:=ROUND(oY-tY);
      end;
 
      for i:=0 to 13 do
      begin
         tX:=(subAxis3D_X[i].X+subAxis3D_X[i].Y*cos(AlphaP))*ScaleX;
         tY:=(subAxis3D_X[i].Z+subAxis3D_X[i].Y*sin(AlphaP))*ScaleY;
         subAxis2D_X[i].X:=ROUND(oX+tX);
         subAxis2D_X[i].Y:=ROUND(oY-tY);
 
         tX:=(subAxis3D_Y[i].X+subAxis3D_Y[i].Y*cos(AlphaP))*ScaleX;
         tY:=(subAxis3D_Y[i].Z+subAxis3D_Y[i].Y*sin(AlphaP))*ScaleY;
         subAxis2D_Y[i].X:=ROUND(oX+tX);
         subAxis2D_Y[i].Y:=ROUND(oY-tY);
 
         tX:=(subAxis3D_Z[i].X+subAxis3D_Z[i].Y*cos(AlphaP))*ScaleX;
         tY:=(subAxis3D_Z[i].Z+subAxis3D_Z[i].Y*sin(AlphaP))*ScaleY;
         subAxis2D_Z[i].X:=ROUND(oX+tX);
         subAxis2D_Z[i].Y:=ROUND(oY-tY);
      end;
 
     for i := 0 to PointsCount do
       for j := 0 to PointsCount do
       begin
           tX:=(Points3D[i][j].X+Points3D[i][j].Y*cos(AlphaP))*ScaleX;
           tY:=(Points3D[i][j].Z+Points3D[i][j].Y*sin(AlphaP))*ScaleY;
           Points2D[i][j].X:=ROUND(oX+tX);
           Points2D[i][j].Y:=ROUND(oY-tY);
       end;
 
 
     DrawBuffer.Canvas.Pen.Width:=3;
     DrawBuffer.Canvas.Pen.Color   := clBlue;
     DrawBuffer.Canvas.Brush.Color := clGreen;
 
 
     DrawBuffer.Canvas.MoveTo(Axis2D[1].X,Axis2D[1].Y);
     DrawBuffer.Canvas.LineTo(Axis2D[2].X,Axis2D[2].Y);
 
     DrawBuffer.Canvas.MoveTo(Axis2D[3].X,Axis2D[3].Y);
     DrawBuffer.Canvas.LineTo(Axis2D[4].X,Axis2D[4].Y);
 
     DrawBuffer.Canvas.MoveTo(Axis2D[5].X,Axis2D[5].Y);
     DrawBuffer.Canvas.LineTo(Axis2D[6].X,Axis2D[6].Y);
 
 
     DrawBuffer.Canvas.Pen.Width   :=2;
     DrawBuffer.Canvas.Pen.Color   := clBlue;
 
     for i:=0 to 6 do
     begin
       DrawBuffer.Canvas.MoveTo(subAxis2D_X[2*i].X, subAxis2D_X[2*i].Y);
       DrawBuffer.Canvas.LineTo(subAxis2D_X[2*i+1].X, subAxis2D_X[2*i+1].Y);
       DrawBuffer.Canvas.MoveTo(subAxis2D_Y[2*i].X, subAxis2D_Y[2*i].Y);
       DrawBuffer.Canvas.LineTo(subAxis2D_Y[2*i+1].X, subAxis2D_Y[2*i+1].Y);
       DrawBuffer.Canvas.MoveTo(subAxis2D_Z[2*i].X, subAxis2D_Z[2*i].Y);
       DrawBuffer.Canvas.LineTo(subAxis2D_Z[2*i+1].X, subAxis2D_Z[2*i+1].Y);
     end;
     // Ðèñóåì íàø ïîëèãîí.
 
     DrawBuffer.Canvas.Pen.Width   :=1;
     DrawBuffer.Canvas.Pen.Color   := clBlack;
     DrawBuffer.Canvas.Brush.Color := clGreen;
     for i := 0 to PointsCount do
       begin
            DrawBuffer.Canvas.MoveTo(Points2D[i][0].X, Points2D[i][0].Y);
            for j := 1 to PointsCount do
                DrawBuffer.Canvas.LineTo(Points2D[i][j].X, Points2D[i][j].Y);
       end;
 
     for i := 0 to PointsCount do
       begin
            DrawBuffer.Canvas.MoveTo(Points2D[0][i].X, Points2D[0][i].Y);
            for j := 1 to PointsCount do
                DrawBuffer.Canvas.LineTo(Points2D[j][i].X, Points2D[j][i].Y);
       end;
 
     //DrawBuffer.Canvas.Polygon(Points2D);
     Image1.Canvas.Draw(0, 0, DrawBuffer);
     end;
 end;
 
 procedure TForm1.ClearBuffer;
 begin
   DrawBuffer.Canvas.Pen.Color   := BufferColor;
   DrawBuffer.Canvas.Brush.Color := BufferColor;
   DrawBuffer.Canvas.Rectangle(0, 0, Image1.Width, Image1.Height);
 end;
 
 procedure TForm1.FormClose(Sender: TObject; var Action: TCloseAction);
 begin
  if DrawBuffer <> nil then
   begin
     DrawBuffer.Free;
     DrawBuffer := nil;
   end;
 end;
 
 procedure TForm1.Timer1Timer(Sender: TObject);
 var i,j:integer;
 begin
   //https://ru.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D1%80%D0%B8%D1%86%D0%B0_%D0%BF%D0%BE%D0%B2%D0%BE%D1%80%D0%BE%D1%82%D0%B0
   Alpha:=Alpha+0.05;
   X0:=-3.14; Xn:=3.14;
   Y0:=-3.14; Yn:=3.14;
   dX:= (Xn-X0)/PointsCount;
   dY:= (Yn-Y0)/PointsCount;
   for i:=0 to PointsCount do
    for j:=0 to PointsCount do
     begin
       Points3D[i][j].X:=(X0+i*dX)*cos(Alpha)-(Y0+j*dY)*sin(Alpha);
       Points3D[i][j].Y:=(X0+i*dX)*sin(Alpha)+(Y0+j*dY)*cos(Alpha);
       Points3D[i][j].Z:=Points3D[i][j].Z*1;
     end;
   DrawPoints;
 end;
 
 procedure TForm1.Button2Click(Sender: TObject);
 begin
   Timer1.Enabled:= not Timer1.Enabled;
 end;
 
 end.