inital commit: geht, bis auf Drucken ...HEADmaster

11 files changed, 2181 insertions, 0 deletions

diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..3baa84a
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,7 @@
+*.bak
+*.ppu
+*.o
+*.tar.gz
+*~
+weihnachtsstern
+lib
diff --git a/unit1.lfm b/unit1.lfm
new file mode 100644
index 0000000..a5e7184
--- /dev/null
+++ b/unit1.lfm
@@ -0,0 +1,165 @@
+object Form1: TForm1
+  Left = 93
+  Height = 551
+  Top = 315
+  Width = 1225
+  Caption = 'Form1'
+  ClientHeight = 551
+  ClientWidth = 1225
+  Color = clBtnFace
+  DesignTimePPI = 107
+  Font.Color = clWindowText
+  Font.Height = -12
+  Font.Name = 'MS Sans Serif'
+  OnActivate = FormActivate
+  OnCreate = FormCreate
+  OnDestroy = FormDestroy
+  OnResize = FormResize
+  LCLVersion = '2.0.12.0'
+  object Image1: TImage
+    Left = 276
+    Height = 438
+    Top = 45
+    Width = 465
+  end
+  object Image2: TImage
+    Left = 740
+    Height = 438
+    Top = 45
+    Width = 465
+  end
+  object Label1: TLabel
+    Left = 9
+    Height = 13
+    Top = 7
+    Width = 48
+    Caption = 'Drehen:'
+    Font.Color = clWindowText
+    Font.Height = -12
+    Font.Name = 'MS Sans Serif'
+    ParentColor = False
+    ParentFont = False
+  end
+  object Image3: TImage
+    Tag = -1
+    Left = 0
+    Height = 331
+    Top = 152
+    Width = 278
+    OnMouseDown = Image3MouseDown
+    OnMouseMove = Image3MouseMove
+    OnMouseUp = Image3MouseUp
+  end
+  object RadioGroup1: TRadioGroup
+    Left = 0
+    Height = 55
+    Top = 36
+    Width = 206
+    AutoFill = True
+    Caption = 'Körper'
+    ChildSizing.LeftRightSpacing = 6
+    ChildSizing.EnlargeHorizontal = crsHomogenousChildResize
+    ChildSizing.EnlargeVertical = crsHomogenousChildResize
+    ChildSizing.ShrinkHorizontal = crsScaleChilds
+    ChildSizing.ShrinkVertical = crsScaleChilds
+    ChildSizing.Layout = cclLeftToRightThenTopToBottom
+    ChildSizing.ControlsPerLine = 1
+    ClientHeight = 38
+    ClientWidth = 202
+    Font.Color = clWindowText
+    Font.Height = -12
+    Font.Name = 'MS Sans Serif'
+    ItemIndex = 0
+    Items.Strings = (
+      'Deltoidalhexakontaederstern'
+      'Pentagonhexakontaederstern'
+    )
+    OnClick = RadioGroup1Click
+    ParentFont = False
+    TabOrder = 0
+  end
+  object CheckBox1: TCheckBox
+    Left = 62
+    Height = 21
+    Top = 6
+    Width = 98
+    Caption = 'automatisch'
+    Font.Color = clWindowText
+    Font.Height = -12
+    Font.Name = 'MS Sans Serif'
+    OnClick = CheckBox1Click
+    ParentFont = False
+    TabOrder = 1
+  end
+  object Button1: TButton
+    Left = 9
+    Height = 28
+    Top = 107
+    Width = 84
+    Caption = 'Spitze'
+    Font.Color = clWindowText
+    Font.Height = -12
+    Font.Name = 'MS Sans Serif'
+    OnClick = Button1Click
+    ParentFont = False
+    TabOrder = 2
+  end
+  object Button2: TButton
+    Left = 98
+    Height = 28
+    Top = 107
+    Width = 99
+    Caption = 'Determinante'
+    Font.Color = clWindowText
+    Font.Height = -12
+    Font.Name = 'MS Sans Serif'
+    OnClick = Button2Click
+    ParentFont = False
+    TabOrder = 3
+  end
+  object Button3: TButton
+    Left = 169
+    Height = 28
+    Top = 0
+    Width = 126
+    Caption = 'Spitzen entfernen'
+    Font.Color = clWindowText
+    Font.Height = -12
+    Font.Name = 'MS Sans Serif'
+    OnClick = Button3Click
+    ParentFont = False
+    TabOrder = 4
+  end
+  object ProgressBar1: TProgressBar
+    Left = 303
+    Height = 18
+    Top = 4
+    Width = 233
+    Font.Color = clWindowText
+    Font.Height = -12
+    Font.Name = 'MS Sans Serif'
+    ParentFont = False
+    Smooth = True
+    TabOrder = 5
+    Visible = False
+  end
+  object Button4: TButton
+    Left = 205
+    Height = 28
+    Top = 107
+    Width = 64
+    Caption = 'Test'
+    Font.Color = clWindowText
+    Font.Height = -12
+    Font.Name = 'MS Sans Serif'
+    OnClick = Button4Click
+    ParentFont = False
+    TabOrder = 6
+  end
+  object ZeichenTimer: TTimer
+    Enabled = False
+    Interval = 50
+    OnTimer = ZeichenTimerTimer
+    Top = 27
+  end
+end
diff --git a/unit1.pas b/unit1.pas
new file mode 100644
index 0000000..f098124
--- /dev/null
+++ b/unit1.pas
@@ -0,0 +1,1125 @@
+unit Unit1;
+
+{$mode objfpc}{$H+}
+
+interface
+
+uses
+  Classes, SysUtils, Forms, Controls, Graphics, Dialogs, ExtCtrls, StdCtrls,
+  ComCtrls, vecMath, Math;
+
+type
+
+  { TForm1 }
+
+  TForm1 = class(TForm)
+    Button1: TButton;
+    Button2: TButton;
+    Button3: TButton;
+    Button4: TButton;
+    CheckBox1: TCheckBox;
+    Image1: TImage;
+    Image2: TImage;
+    Image3: TImage;
+    Label1: TLabel;
+    ProgressBar1: TProgressBar;
+    RadioGroup1: TRadioGroup;
+    ZeichenTimer: TTimer;
+    procedure FormActivate(Sender: TObject);
+    procedure FormDestroy(Sender: TObject);
+    procedure FormCreate(Sender: TObject);
+    procedure ZeichenTimerTimer(Sender: TObject);
+    procedure CheckBox1Click(Sender: TObject);
+    procedure CheckBox2Click(Sender: TObject);
+    procedure Image3MouseDown(Sender: TObject; Button: TMouseButton;
+      Shift: TShiftState; X, Y: Integer);
+    procedure Image3MouseUp(Sender: TObject; Button: TMouseButton;
+      Shift: TShiftState; X, Y: Integer);
+    procedure Image3MouseMove(Sender: TObject; Shift: TShiftState; X,
+      Y: Integer);
+    procedure FormResize(Sender: TObject);
+    procedure RadioGroup1Click(Sender: TObject);
+    procedure Button1Click(Sender: TObject);
+    procedure Button2Click(Sender: TObject);
+    procedure Button3Click(Sender: TObject);
+    procedure Button4Click(Sender: TObject);
+  private
+
+  public
+    Dim,Koerp:   Integer;
+    Kanten:      array of TPoint;
+    Ecken:       array of TMatrix;
+    ProjektionL,
+    ProjektionR,
+    Rotation,
+    Beschl,Rot:  TMatrix;
+    Zoom:        extended;
+
+    procedure Drehen;
+    procedure BeschlBelegen;
+    procedure RotationInitialisieren;
+    procedure ProjektionenBelegen;
+    procedure KoerperErzeugen;
+    procedure Zeichnen;
+    procedure KantenZeichnen(Pte: array of TPoint; PZ: array of extended; drawZ: boolean; drawTo: TCanvas);
+    procedure drawColoredLine(wo: TCanvas; X1,Y1: Integer; Z1: extended; X2,Y2: Integer; Z2: Extended);
+    function farbVerlauf(x: Extended): TColor;
+    procedure SetZoom;
+  end;
+
+var
+  Form1: TForm1;
+
+implementation
+
+{$R *.lfm}
+
+uses
+  unit2;
+
+procedure TForm1.FormActivate(Sender: TObject);
+begin
+ Dim:=3;
+ Koerp:=-1;
+ RadioGroup1.OnClick(Sender);
+end;
+
+procedure TForm1.FormDestroy(Sender: TObject);
+var i: integer;
+begin
+ for i:=0 to length(Ecken)-1 do
+  Ecken[i].destroy;
+ ProjektionL.destroy;
+ ProjektionR.destroy;
+ Rotation.destroy;
+ Rot.destroy;
+ Beschl.destroy;
+end;
+
+procedure TForm1.FormCreate(Sender: TObject);
+begin
+ setlength(Ecken,0);
+ ProjektionL:=TMatrix.create;
+ ProjektionR:=TMatrix.create;
+ Rotation:=TMatrix.create;
+ Rot:=TMatrix.create;
+ Beschl:=TMatrix.create;
+end;
+
+procedure TForm1.ZeichenTimerTimer(Sender: TObject);
+var i: integer;
+begin
+ Zeichnen;
+ for i:=0 to ZeichenTimer.Interval div 10 do
+  begin
+   Drehen;
+   BeschlBelegen;
+  end;
+end;
+
+procedure TForm1.ProjektionenBelegen;
+var z,s: integer;
+    tmp: TMatrix;
+const alpha = 2*pi/360 * 10;
+begin
+ ProjektionL.destroy;
+ ProjektionL:=TMatrix.create;
+ ProjektionL.xdim:=4;
+ ProjektionL.ydim:=3;
+ for z:=0 to 2 do
+  for s:=0 to 3 do
+   ProjektionL.a[z,s]:=byte(z=s);
+
+ ProjektionR.destroy;
+ ProjektionR:=TMatrix.create;
+ ProjektionR.xdim:=4;
+ ProjektionR.ydim:=4;
+ ProjektionR.assign0;
+ ProjektionR.a[0,0]:=cos(alpha);
+ ProjektionR.a[0,2]:=sin(alpha);
+ ProjektionR.a[3,0]:=-sin(alpha);
+ ProjektionR.a[3,2]:=cos(alpha);
+ ProjektionR.a[1,1]:=1;
+ ProjektionR.a[2,3]:=1;
+
+ ProjektionR._times(ProjektionL);
+
+ tmp:=TMatrix.create;
+ tmp.xdim:=dim;
+ tmp.ydim:=4;
+ for s:=0 to dim-1 do
+  for z:=0 to 3 do
+   tmp.a[z,s]:=byte(z=s);
+
+ ProjektionR.times_(tmp);
+ ProjektionL.times_(tmp);
+end;
+
+procedure TForm1.KoerperErzeugen;
+function spiegleKante(Knr,Enr: integer; N: TMatrix): integer;
+var Es:     array[boolean] of integer;
+    i:      integer;
+    M,O:    TMatrix;
+    bol,nk: boolean;
+    tmp:    extended;
+begin
+  M:=TMatrix.create;
+  O:=TMatrix.create;
+  Es[false]:=Kanten[Knr].x;
+  Es[true]:=Kanten[Knr].y;
+  for bol:=false to true do begin
+    M.assign(Ecken[Enr]);
+    M.minus(Ecken[Es[bol]]);
+    M.transp;
+    M.times_(N);
+    tmp:=M.a[0,0];
+    M.assign(N);
+    M.times(2*tmp);
+    M.plus(Ecken[Es[bol]]);
+    tmp:=1;
+    for i:=0 to length(Ecken)-1 do begin
+      O.assign(M);
+      O.minus(Ecken[i]);
+      tmp:=min(tmp,O.len);
+    end;
+    if tmp>1e-6 then begin
+      Es[bol]:=length(Ecken);
+      setlength(Ecken,length(Ecken)+1);
+      Ecken[Es[bol]]:=TMatrix.create;
+      Ecken[Es[bol]].assign(M);
+    end
+    else begin
+      for i:=0 to length(Ecken)-1 do begin
+        O.assign(M);
+        O.minus(Ecken[i]);
+        if O.len <=1.1e-6 then begin
+          Es[bol]:=i;
+          break;
+        end;
+      end;
+    end;
+  end;
+  result:=-1;
+  nk:=true;
+  for i:=0 to length(kanten)-1 do
+    nk:=nk and ((Kanten[i].x<>Es[false]) or (Kanten[i].y<>Es[true]))
+           and ((Kanten[i].y<>Es[false]) or (Kanten[i].x<>Es[true]));
+  if nk then begin
+    setlength(Kanten,length(Kanten)+1);
+    Kanten[length(Kanten)-1].x:=Es[false];
+    Kanten[length(Kanten)-1].y:=Es[true];
+    result:=length(Kanten)-1;
+  end
+  else
+  for i:=0 to length(kanten)-1 do begin
+    if (Kanten[i].x=Es[false]) and (Kanten[i].y=Es[true]) then result:=i;
+    if (Kanten[i].y=Es[false]) and (Kanten[i].x=Es[true]) then result:=i;
+  end;
+  M.destroy;
+  O.destroy;
+end;
+
+var ral:         array of array[boolean] of TMatrix;
+
+procedure rotierePunkt(Quelle: TMatrix; Achse: integer; umNull: boolean; var Ziel: TMatrix);
+var tang,otang: TMatrix;
+    tmp:        extended;
+begin
+  Ziel.assign(Quelle);
+  if ral[Achse,true].len<1e-6 then exit;
+  if not umNull then Ziel.minus(ral[Achse,false]);
+  tang:=TMatrix.create;
+  otang:=TMatrix.create;
+  tang.assign(Ziel);
+  Ziel.transp;
+  Ziel.times_(ral[Achse,true]);
+  tmp:=Ziel.a[0,0];
+  Ziel.assign(ral[Achse,true]);
+  Ziel.times(tmp/sqr(ral[Achse,true].len));
+  tang.minus(Ziel);
+  if tang.len<1e-6 then begin
+    if not umNull then Ziel.plus(ral[Achse,false]);
+    tang.destroy;
+    otang.destroy;
+    exit;
+  end;
+  otang.assign(ral[Achse,true]);
+  otang.cross(tang);
+  otang.times(tang.len/otang.len*sin(ral[Achse,true].len));
+  tang.times(cos(ral[Achse,true].len));
+  Ziel.plus(tang);
+  Ziel.plus(otang);
+  if not umNull then Ziel.plus(ral[Achse,false]);
+  tang.destroy;
+  otang.destroy;
+end;
+
+procedure rotiereKante(Kante,Achse: integer);
+var M,N:     TMatrix;
+    Es:      array[boolean] of integer;
+    bol,gef: boolean;
+    i:       integer;
+begin
+  M:=TMatrix.create;
+  N:=TMatrix.create;
+  Es[false]:=Kanten[Kante].x;
+  Es[true]:=Kanten[Kante].y;
+  for bol:=false to true do begin
+    rotierePunkt(Ecken[Es[bol]],Achse,false,M);
+    gef:=false;
+    for i:=0 to length(Ecken)-1 do begin
+      N.assign(M);
+      N.minus(Ecken[i]);
+      if N.len<1e-6 then begin
+        gef:=true;
+        Es[bol]:=i;
+        break;
+      end;
+    end;
+    if not gef then begin
+      setlength(Ecken,length(Ecken)+1);
+      Ecken[length(Ecken)-1]:=TMatrix.create;
+      Ecken[length(Ecken)-1].assign(M);
+      Es[bol]:=length(Ecken)-1;
+    end;
+  end;
+  gef:=false;
+  for i:=0 to length(Kanten)-1 do
+    gef:=gef or ((Kanten[i].x=Es[false]) and (Kanten[i].y=Es[true])) or
+                ((Kanten[i].y=Es[false]) and (Kanten[i].x=Es[true]));
+  if not gef then begin
+    setlength(Kanten,length(Kanten)+1);
+    Kanten[length(Kanten)-1].x:=Es[false];
+    Kanten[length(Kanten)-1].y:=Es[true];
+  end;
+
+  M.destroy;
+  N.destroy;
+end;
+
+var skl:             array of TPoint;
+    i,j,k:           integer;
+    M,N:             TMatrix;
+    nsa,bol:         boolean;
+    b,d,f,t,phi,tmp: extended;
+begin
+ case Koerp of
+  0:
+   begin
+    if dim<>3 then exit;
+//    b:=3/22*(7-sqrt(5));               // kurze Seite      (lange Seite=1)
+    d:=3*sqrt((5-sqrt(5))/20);         // kurze Diagonale
+    f:=1/11*sqrt((470+156*sqrt(5))/5); // lange Diagonale
+
+    Setlength(Ecken,16);
+    for i:=0 to length(Ecken)-1 do begin
+      Ecken[i]:=TMatrix.create;
+      Ecken[i].xdim:=1;
+      Ecken[i].ydim:=dim;
+    end;
+    Setlength(Kanten,35);
+    for i:=0 to length(Kanten)-1 do
+      Kanten[i].x:=-1;
+    Ecken[0].a[0,0]:=0;
+    Ecken[0].a[1,0]:=0;
+    Ecken[0].a[2,0]:=sqrt(1-sqr(d*cos(pi/5)/sin(2*pi/5)));  // die berechnete Höhe
+    for i:=0 to 4 do begin
+      Ecken[i+1].a[0,0]:=cos(2*pi/5*i)*d*cos(pi/5)/sin(2*pi/5);
+      Ecken[i+1].a[1,0]:=sin(2*pi/5*i)*d*cos(pi/5)/sin(2*pi/5);
+      Ecken[i+1].a[2,0]:=0;
+    end;
+    M:=TMatrix.create;
+    M.xdim:=1;
+    M.ydim:=dim;
+    N:=TMatrix.create;
+    N.xdim:=1;
+    N.ydim:=dim;
+    for i:=0 to 4 do begin
+      Ecken[i+6].assign(Ecken[i+1]);
+      Ecken[i+6].plus(Ecken[(i+1) mod 5 +1]);
+      Ecken[i+6].times(-1/2);
+      Ecken[i+6].plus(Ecken[0]);
+      Ecken[i+6].times(-f/Ecken[i+6].len);
+      Ecken[i+6].plus(Ecken[0]);
+      Ecken[i+11].assign(Ecken[0]);
+      M.assign(Ecken[i+6]);
+      Ecken[i+11].times(0.5);
+      M.times(0.5);
+      Ecken[i+11].plus(M);
+      M.assign(Ecken[i+1]);
+      M.minus(Ecken[0]);
+      N.assign(Ecken[(i+1) mod 5+1]);
+      N.minus(Ecken[0]);
+      M.cross(N);
+      M.times(3/M.len);
+      Ecken[i+11].plus(M);
+    end;
+    for i:=0 to 4 do begin
+      Kanten[i].x:=0;
+      Kanten[i].y:=i+1;
+      Kanten[i+5].x:=i+1;
+      Kanten[i+5].y:=i+6;
+      Kanten[i+10].x:=i+6;
+      Kanten[i+10].y:=(i+1) mod 5 +1;
+      Kanten[i+15].x:=i+11;
+      Kanten[i+15].y:=0;
+      Kanten[i+20].x:=i+11;
+      Kanten[i+20].y:=i+1;
+      Kanten[i+25].x:=i+11;
+      Kanten[i+25].y:=i+6;
+      Kanten[i+30].x:=i+11;
+      Kanten[i+30].y:=(i+1) mod 5 +1;
+    end;
+
+    setlength(skl,5);
+    for i:=0 to 4 do begin
+      skl[i].x:=i+5;
+      skl[i].y:=(i+4) mod 5+10;
+    end;
+
+    repeat
+      nsa:=false;
+      i:=length(skl)-1;
+      while i>=0 do begin
+        M.assign(Ecken[Kanten[skl[i].x].x]);
+        M.minus(Ecken[Kanten[skl[i].x].y]);
+        N.assign(Ecken[Kanten[skl[i].y].x]);
+        N.minus(Ecken[Kanten[skl[i].y].y]);
+        N.cross(M);
+        N.times(1/N.len);
+        j:=length(skl)-1;
+        while j>=0 do begin
+          setlength(skl,length(skl)+1);
+          skl[length(skl)-1].x:=spiegleKante(skl[j].x,Kanten[skl[i].x].x,N);
+          skl[length(skl)-1].y:=spiegleKante(skl[j].y,Kanten[skl[i].x].x,N);
+          bol:=false;
+          for k:=0 to length(skl)-2 do
+            bol:=bol or ((skl[length(skl)-1].x=skl[k].x) and
+                         (skl[length(skl)-1].y=skl[k].y)) or
+                        ((skl[length(skl)-1].y=skl[k].x) and
+                         (skl[length(skl)-1].x=skl[k].y));
+          if bol then setlength(skl,length(skl)-1)
+          else nsa:=true;
+          dec(j);
+        end;
+        dec(i);
+      end;
+    until not nsa;
+
+    for i:=0 to length(skl)-1 do begin
+      M.assign(Ecken[Kanten[skl[i].x].x]);
+      M.minus(Ecken[Kanten[skl[i].x].y]);
+      N.assign(Ecken[Kanten[skl[i].y].x]);
+      N.minus(Ecken[Kanten[skl[i].y].y]);
+      N.cross(M);
+      N.times(1/N.len);
+      j:=length(Kanten)-1;
+      while j>=0 do begin
+        spiegleKante(j,Kanten[skl[i].x].x,N);
+        dec(j);
+      end;
+    end;
+    M.destroy;
+    N.destroy;
+   end;
+  1:
+   begin
+    if dim<>3 then exit;
+    phi:=(sqrt(5)+1)/2;
+    t:=1/12*(power(44+12*phi*(9+sqrt(81*phi-15)),1/3)+power(44+12*phi*(9-sqrt(81*phi-15)),1/3)-4);
+    b:=2*(1-2*sqr(t))/(1+2*t);         // kurze Seite      (lange Seite=1)
+    d:=2*(1-2*sqr(t));                 // Diagonale
+    f:=sqrt(b*(b+d));                  // (ganz) kurze Diagonale
+
+    Setlength(Ecken,21);
+    for i:=0 to length(Ecken)-1 do begin
+      Ecken[i]:=TMatrix.create;
+      Ecken[i].xdim:=1;
+      Ecken[i].ydim:=dim;
+    end;
+    Setlength(Kanten,45);
+    for i:=0 to length(Kanten)-1 do
+      Kanten[i].x:=-1;
+    Ecken[0].a[0,0]:=0;
+    Ecken[0].a[1,0]:=0;
+    Ecken[0].a[2,0]:=sqrt(1-sqr(d*cos(pi/5)/sin(2*pi/5)));  // die berechnete Höhe
+    for i:=0 to 4 do begin
+      Ecken[i+1].a[0,0]:=cos(2*pi/5*i)*d*cos(pi/5)/sin(2*pi/5);
+      Ecken[i+1].a[1,0]:=sin(2*pi/5*i)*d*cos(pi/5)/sin(2*pi/5);
+      Ecken[i+1].a[2,0]:=0;
+    end;
+    M:=TMatrix.create;
+    M.xdim:=1;
+    M.ydim:=dim;
+    N:=TMatrix.create;
+    N.xdim:=1;
+    N.ydim:=dim;
+    for i:=0 to 4 do begin
+      Ecken[i+6].assign(Ecken[i+1]);
+      Ecken[i+6].plus(Ecken[(i+1) mod 5 +1]);
+      Ecken[i+6].times(1/2);
+      Ecken[i+6].minus(Ecken[0]);
+      Ecken[i+6].times(sqrt(sqr(b)-sqr((d-b)/2))/Ecken[i+6].len);
+      N.assign(Ecken[(i+1) mod 5 +1]);
+      N.minus(Ecken[i+1]);
+      N.times((d-b)/2/N.len);
+      Ecken[i+6].plus(N);
+      Ecken[i+6].plus(Ecken[i+1]);
+      N.times(b/N.len);
+      Ecken[i+11].assign(Ecken[i+6]);
+      Ecken[i+11].plus(N);
+      M.assign(Ecken[i+6]);
+      M.plus(Ecken[i+11]);
+      M.times(0.3);
+      Ecken[i+16].assign(Ecken[0]);
+      Ecken[i+16].times(0.7);
+      Ecken[i+16].plus(M);
+      M.assign(Ecken[i+1]);
+      M.minus(Ecken[0]);
+      N.assign(Ecken[(i+1) mod 5 +1]);
+      N.minus(Ecken[0]);
+      M.cross(N);
+      M.times(3/M.len);
+      Ecken[i+16].Plus(M);
+    end;
+    for i:=0 to 4 do begin
+      Kanten[i].x:=0;
+      Kanten[i].y:=i+1;
+      Kanten[i+5].x:=i+1;
+      Kanten[i+5].y:=i+6;
+      Kanten[i+10].x:=i+6;
+      Kanten[i+10].y:=i+11;
+      Kanten[i+15].x:=i+11;
+      Kanten[i+15].y:=(i+1) mod 5 +1;
+      Kanten[i+20].x:=0;
+      Kanten[i+20].y:=i+16;
+      Kanten[i+25].x:=i+1;
+      Kanten[i+25].y:=i+16;
+      Kanten[i+30].x:=i+6;
+      Kanten[i+30].y:=i+16;
+      Kanten[i+35].x:=i+11;
+      Kanten[i+35].y:=i+16;
+      Kanten[i+40].x:=(i+1) mod 5 +6;
+      Kanten[i+40].y:=i+16;
+    end;
+
+    setlength(ral,2);
+    for i:=0 to 3 do
+      ral[i div 2,odd(i)]:=TMatrix.create;
+    ral[0,false].assign(Ecken[0]);             // die 5er-Symmetrieachse
+    ral[0,true].assign(Ecken[0]);
+    ral[0,true].times(2*pi/5/ral[0,true].len);
+
+    ral[1,false].assign(Ecken[6]);             // die 3er-Symmetrieachse
+    tmp:=arccos((sqrt(3)/6*f)/sqrt(sqr(b)-sqr(f/2))); // Kippwinkel der Rotationsachse gegenüber Flächennormale
+    ral[1,true].assign(Ecken[1]);
+    ral[1,true].plus(Ecken[11]);
+    ral[1,true].times(-1/2);
+    ral[1,true].plus(Ecken[6]);
+    ral[1,true].times(1/ral[1,true].len);
+    N.assign(Ecken[1]);
+    N.minus(Ecken[11]);
+    N.cross(ral[1,true]);
+    N.times(1/N.len);
+    ral[1,true].times(sin(tmp));
+    N.times(cos(tmp));
+    ral[1,true].plus(N);
+    ral[1,true].times(2*pi/3/ral[1,true].len);
+
+    repeat
+      nsa:=false;
+      i:=length(ral)-1;
+      while i>=0 do begin
+        j:=length(ral)-1;
+        while j>=0 do begin
+          setlength(ral,length(ral)+1);
+          for bol:=false to true do begin
+            ral[length(ral)-1,bol]:=TMatrix.create;
+            rotierePunkt(ral[j,bol],i,bol,ral[length(ral)-1,bol]);
+          end;
+          bol:=false;
+          for k:=0 to length(ral)-2 do begin
+            M.assign(ral[k,false]);
+            M.minus(ral[length(ral)-1,false]);
+            if M.len<1e-6 then begin
+              M.assign(ral[k,true]);
+              M.minus(ral[length(ral)-1,true]);
+              if M.len<1e-6 then begin
+                bol:=true;
+                break;
+              end;
+            end;
+          end;
+          if bol then begin
+            ral[length(ral)-1,false].destroy;
+            ral[length(ral)-1,true].destroy;
+            setlength(ral,length(ral)-1);
+          end
+          else nsa:=true;
+          dec(j);
+        end;
+        dec(i);
+      end;
+    until not nsa;
+
+    for i:=0 to length(ral)-1 do begin
+      j:=length(Kanten)-1;
+      while j>=0 do begin
+        rotiereKante(j,i);
+        dec(j);
+      end;
+    end;
+
+    for i:=0 to 2*length(ral)-1 do
+      ral[i div 2,odd(i)].destroy;
+    setlength(ral,0);
+
+
+    M.destroy;
+    N.destroy;
+   end;
+ end{of Case};
+ M:=TMatrix.create;
+ M.assign0;
+ for i:=0 to length(Ecken)-1 do
+   M.plus(Ecken[i]);
+ M.times(-1/length(Ecken));
+ for i:=0 to length(Ecken)-1 do
+   Ecken[i].plus(M);
+ b:=0;
+ for i:=0 to length(Ecken)-1 do
+   b:=max(b,Ecken[i].len);
+ for i:=0 to length(Ecken)-1 do
+   Ecken[i].times(1/2/b);
+ M.Destroy;
+
+ for i:=0 to length(Kanten)-1 do
+   if Kanten[i].x>Kanten[i].y then begin
+     j:=Kanten[i].x;
+     Kanten[i].x:=Kanten[i].y;
+     Kanten[i].y:=j;
+   end;
+
+ for i:=0 to length(Kanten)-2 do begin
+   j:=i;
+   for k:=i+1 to length(Kanten)-1 do
+     if  (Kanten[k].x<Kanten[j].x) or
+        ((Kanten[k].x=Kanten[j].x) and
+         (Kanten[k].y<Kanten[j].y)) then
+       j:=k;
+   if j>i then begin
+     k:=Kanten[j].x;
+     Kanten[j].x:=Kanten[i].x;
+     Kanten[i].x:=k;
+     k:=Kanten[j].y;
+     Kanten[j].y:=Kanten[i].y;
+     Kanten[i].y:=k;
+   end;
+ end;
+
+ SetZoom;
+end;
+
+procedure TForm1.CheckBox1Click(Sender: TObject);
+begin
+ ZeichenTimer.Enabled:=Checkbox1.Checked;
+ Image3.Visible:=not Checkbox1.Checked;
+end;
+
+procedure TForm1.CheckBox2Click(Sender: TObject);
+begin
+ ZeichenTimer.Interval:=30;
+end;
+
+procedure TForm1.KantenZeichnen(Pte: array of TPoint; PZ: array of extended; drawZ: boolean; drawTo: TCanvas);
+var i: integer;
+begin
+ if drawZ then
+  begin
+   for i:=0 to length(Kanten)-1 do
+    drawColoredLine(drawto,Pte[Kanten[i].X].X,Pte[Kanten[i].X].Y,PZ[Kanten[i].X],
+                           Pte[Kanten[i].Y].X,Pte[Kanten[i].Y].Y,PZ[Kanten[i].Y]);
+  end
+   else
+  begin
+   for i:=0 to length(Kanten)-1 do
+    begin
+     drawto.MoveTo(Pte[Kanten[i].X].X,Pte[Kanten[i].X].Y);
+     drawto.LineTo(Pte[Kanten[i].Y].X,Pte[Kanten[i].Y].Y);
+    end;
+  end;
+end;
+
+procedure TForm1.drawColoredLine(wo: TCanvas; X1,Y1: Integer; Z1: extended; X2,Y2: Integer; Z2: Extended);
+var i:         integer;
+    a,b,az,bz: extended;
+begin
+ if abs(X2-X1)>abs(Y1-Y2) then
+  begin
+   a:=(Y1-Y2)/(X1-X2);
+   b:=Y1-X1*a;
+   az:=(Z1-Z2)/(X1-X2);
+   bz:=Z1-X1*az;
+   if X1<X2 then
+    begin
+     for I:=X1 to X2 do
+      wo.Pixels[I,round(I*a + b)]:=farbVerlauf(I*az + bz);
+    end
+     else
+    begin
+     for I:=X2 to X1 do
+      wo.Pixels[I,round(I*a + b)]:=farbVerlauf(I*az + bz);
+    end;
+  end
+   else
+  begin
+   if Y1=Y2 then exit;
+   a:=(X1-X2)/(Y1-Y2);
+   b:=X1-Y1*a;
+   az:=(Z1-Z2)/(Y1-Y2);
+   bz:=Z1-Y1*az;
+   if Y1<Y2 then
+    begin
+     for I:=Y1 to Y2 do
+      wo.Pixels[round(I*a + b),I]:=farbVerlauf(I*az + bz);
+    end
+     else
+    begin
+     for I:=Y2 to Y1 do
+      wo.Pixels[round(I*a + b),I]:=farbVerlauf(I*az + bz);
+    end
+  end;
+end;
+
+function TForm1.farbVerlauf(x: Extended): TColor;
+begin
+ x:=5*x;
+ if x<1 then
+  begin
+   result:=min($FF,max($0,round($FF*x))) shl 16;
+   exit;
+  end;
+ x:=x-1;
+ if x<1 then
+  begin
+   result:=(min($FF,max($0,round($FF*(1-x)))) shl 16) or
+           (min($FF,max($0,round($FF*x))) shl 8);
+   exit;
+  end;
+ x:=x-1;
+ if x<1 then
+  begin
+   result:=$00FF00 or
+           min($FF,max($0,round($FF*x)));
+   exit;
+  end;
+ x:=x-1;
+ if x<1 then
+  begin
+   result:=$0000FF or
+           (min($FF,max($0,round($FF*(1-x)))) shl 8);
+   exit;
+  end;
+ x:=x-1;
+ result:=$0000FF or
+         (min($FF,max($0,round($FF*x))) shl 16);
+end;
+
+procedure TForm1.RotationInitialisieren;
+var z,s: integer;
+begin
+ Rot.xdim:=dim;
+ Rot.ydim:=dim;
+ repeat
+  for z:=0 to dim-1 do
+   for s:=0 to dim-1 do
+    Rot.a[z,s]:=0.01*random;
+  Rotation.assignId(dim);
+  Rotation.plus(Rot);
+ until Rotation.det>0;
+end;
+
+procedure TForm1.BeschlBelegen;
+var z,s: integer;
+    M:   TMatrix;
+begin
+ M:=TMatrix.create;
+ M.xdim:=dim;
+ M.ydim:=dim;
+ repeat
+  for z:=0 to dim-1 do
+   for s:=0 to dim-1 do
+    M.a[z,s]:=0.02*random;
+  Beschl.assignId(dim);
+  Beschl.plus(M);
+ until Beschl.det>0;
+ Beschl.orthogonalize(true);
+ M.destroy;
+end;
+
+procedure TForm1.Drehen;
+begin
+ Rotation.assignId(dim);
+ Rotation.plus(Rot);
+ Rotation.orthogonalize(true);
+ Rot.times_(Beschl);
+ ProjektionL.times_(Rotation);
+ ProjektionR.times_(Rotation);
+end;
+
+procedure TForm1.Image3MouseDown(Sender: TObject; Button: TMouseButton;
+  Shift: TShiftState; X, Y: Integer);
+begin
+ Image3.Tag:=floor(Y*dim*(dim-1)/2/Image3.Height)+
+             X*((dim*(dim-1)) div 2);
+end;
+
+procedure TForm1.Image3MouseUp(Sender: TObject; Button: TMouseButton;
+  Shift: TShiftState; X, Y: Integer);
+begin
+ Image3.Tag:=-1;
+end;
+
+procedure TForm1.Image3MouseMove(Sender: TObject; Shift: TShiftState; X,
+  Y: Integer);
+var M:     TMatrix;
+    a1,a2: integer;
+const alpha = 2*pi/360 * 1;
+begin
+ if not(ssLeft in Shift) then exit;
+ Y:=Image3.Tag mod ((dim*(dim-1)) div 2);
+ X:=X - (Image3.Tag div ((dim*(dim-1)) div 2));
+ Image3.Tag:=Image3.Tag + X*((dim*(dim-1)) div 2);
+ M:=TMatrix.create;
+ M.assignId(dim);
+ a1:=0;
+ while Y>=0 do
+  begin
+   inc(a1);
+   Y:=Y-dim+a1;
+  end;
+ a2:=Y+dim;
+ dec(a1);
+ M.a[a1,a1]:=cos(alpha*X);
+ M.a[a1,a2]:=sin(alpha*X);
+ M.a[a2,a1]:=-sin(alpha*X);
+ M.a[a2,a2]:=cos(alpha*X);
+ ProjektionR.times_(M);
+ ProjektionL.times_(M);
+ M.destroy;
+ Zeichnen;
+end;
+
+procedure TForm1.Zeichnen;
+var Pkt:   TMatrix;
+    Pkte:  array[boolean] of array of TPoint;
+    PZ:    array of extended;
+    i:     integer;
+    b:     boolean;
+    mi,ma: extended;
+begin
+ if length(Ecken)=0 then
+  exit;
+ setlength(Pkte[false],length(Ecken));
+ setlength(Pkte[true],length(Ecken));
+ setlength(PZ,length(Ecken));
+ for i:=0 to length(Pkte[false])-1 do
+  for b:=false to true do
+   begin
+    Pkt:=Ecken[i].duplicate;
+    if B then Pkt._times(ProjektionR)
+         else Pkt._times(ProjektionL);
+    PZ[i]:=Pkt.a[2,0];
+    Pkte[b,i]:=Pkt.asPoint(Zoom);
+    Pkte[b,i].x:=Pkte[b,i].x + Image1.Width div 2;
+    Pkte[b,i].y:=Pkte[b,i].y + Image1.Height div 2;
+    Pkt.destroy;
+   end;
+ mi:=PZ[0];
+ ma:=PZ[0];
+ for i:=0 to length(PZ)-1 do
+  begin
+   mi:=min(mi,PZ[i]);
+   ma:=max(ma,PZ[i]);
+  end;
+ ma:=max(ma,mi+0.00001);
+ for i:=0 to length(PZ)-1 do
+  PZ[i]:=(PZ[i]-mi)/(ma-mi);
+ Image1.Canvas.Rectangle(-10,-10,Image1.Width+10,Image1.Height+10);
+ KantenZeichnen(Pkte[true],PZ,false,Image1.Canvas);
+ Image2.Canvas.Rectangle(-10,-10,Image2.Width+10,Image2.Height+10);
+ KantenZeichnen(Pkte[false],PZ,false,Image2.Canvas);
+end;
+
+procedure TForm1.FormResize(Sender: TObject);
+var L,T: integer;
+begin
+ L:=Image1.Left;
+ T:=Image1.Top;
+ Image1.Free;
+ Image2.Free;
+ Image1:=TImage.Create(Form1);
+ Image2:=TImage.Create(Form1);
+ Image1.Parent:=Form1;
+ Image2.Parent:=Form1;
+ Image1.Left:=L;
+ Image1.Top:=T;
+ Image2.Top:=T;
+ Image1.Width:=min(Form1.ClientHeight-Image1.Top,(Form1.ClientWidth-Image1.Left) div 2);
+ Image1.Height:=Image1.Width;
+ Image2.Width:=Image1.Width;
+ Image2.Height:=Image2.Width;
+ Image2.Left:=Image1.Left+Image1.Width;
+ Progressbar1.Width:=Form1.Clientwidth-Progressbar1.Left;
+ SetZoom;
+ Zeichnen;
+end;
+
+procedure TForm1.SetZoom;
+begin
+ case Koerp of
+  0: Zoom:=min(Image1.Width,Image1.Height)*0.9;
+  1: Zoom:=min(Image1.Width,Image1.Height)*0.9;
+ end{of Case};
+end;
+
+procedure TForm1.RadioGroup1Click(Sender: TObject);
+var i: integer;
+begin
+ if Koerp = Radiogroup1.ItemIndex then exit;
+ Koerp:=RadioGroup1.ItemIndex;
+
+ for i:=0 to length(Ecken)-1 do
+  Ecken[i].destroy;
+ ProjektionenBelegen;
+ RotationInitialisieren;
+ BeschlBelegen;
+ KoerperErzeugen;
+ Image3.Canvas.Brush.Color:=Form1.Color;
+ Image3.Canvas.Rectangle(-10,-10,Image3.Width+10,Image3.Height+10);
+ For i:=1 to (dim*(dim-1)) div 2 do
+  begin
+   Image3.Canvas.MoveTo(10,round((I-0.5)*(Image3.Height*2/(dim*(dim-1)))));
+   Image3.Canvas.LineTo(Image3.Width-10,round((I-0.5)*(Image3.Height*2/(dim*(dim-1)))));
+  end;
+// Drehen;
+// BeschlBelegen;
+ Zeichnen;
+end;
+
+procedure TForm1.Button1Click(Sender: TObject);
+begin
+ Form2.Showmodal;
+end;
+
+procedure TForm1.Button2Click(Sender: TObject);
+var M:         TMatrix;
+    I,J,K,L,N: Longint;
+    B:         Boolean;
+    Memo1:     TMemo;
+    s:         String;
+    x:         extended;
+    fcs:       array of Longint;
+begin
+  M:=TMatrix.create;
+  M.xdim:=length(Kanten)-3;
+  for I:=0 to length(Kanten)-1 do begin
+    B:=Kanten[I].x=Kanten[I].y;
+    for J:=0 to I-1 do
+      B:=B or ((Kanten[I].X=Kanten[J].X) and (Kanten[I].Y=Kanten[J].Y))
+           or ((Kanten[I].X=Kanten[J].Y) and (Kanten[I].Y=Kanten[J].X));
+    if B then M.xdim:=M.xdim-1;
+  end;
+  M.ydim:=3*length(Ecken)-9;
+  if M.xdim<>M.ydim then begin
+    if MessageDlg(
+      'Die Anzahl der Randbedingungen ('
+       +inttostr(M.xdim)+
+      ') unterscheidet sich von der Anzahl der Freiheitsgrade ('
+      +inttostr(M.ydim)+
+      ')! Genauere Erklärung gewünscht?',mterror,[mbYes,mbNo],0) = mrYes then begin
+      Memo1:=TMemo.Create(Form1);
+      Memo1.Parent:=Form1;
+      Memo1.Left:=Image1.Left;
+      Memo1.Top:=Image1.Top;
+      Memo1.Width:=Form1.ClientWidth-Memo1.Left;
+      Memo1.Height:=Form1.ClientHeight-Memo1.Top;
+      Memo1.Lines.Clear;
+      x:=0;
+      for I:=0 to length(Ecken)-1 do
+        x:=max(x,Ecken[I].len);
+      s:='';
+      for I:=0 to length(Kanten)-1 do
+        s:=s+' '+inttostr(Kanten[I].x)+'-'+inttostr(Kanten[I].y);
+      delete(s,1,1);
+      Memo1.Lines.Add(s);
+      Memo1.Lines.Add('');
+      s:='';
+      for I:=0 to length(Ecken)-1 do
+        if Ecken[I].len>=0.98*x then
+          s:=s+' '+inttostr(I);
+      delete(s,1,1);
+      Memo1.Lines.Add(s);
+      Memo1.Lines.Add('');
+      s:='';
+      for I:=0 to length(Kanten)-1 do
+        if (Ecken[Kanten[I].x].len>=0.98*x) or
+           (Ecken[Kanten[I].y].len>=0.98*x) then
+          s:=s+' '+inttostr(Kanten[I].x)+'-'+inttostr(Kanten[I].y);
+      delete(s,1,1);
+      Memo1.Lines.Add(s);
+      Memo1.Lines.Add('');
+      s:='';
+      for i:=0 to length(Ecken)-1 do
+        if Ecken[I].len>=0.98*x then begin
+          s:=s+' '+inttostr(i)+':';
+          for j:=0 to length(Kanten)-1 do
+            if (Kanten[j].x=i) or (Kanten[j].y=i) then
+              s:=s+inttostr(Kanten[j].x+Kanten[j].y-i)+',';
+          delete(s,length(s),1);
+        end;
+      delete(s,1,1);
+      Memo1.Lines.Add(s);
+      Application.ProcessMessages;
+      MessageDlg('Memo schließen.',mtInformation,[mbOk],0);
+      Memo1.Free;
+    end;
+    exit;
+  end;
+  M.assign0;
+
+  case Radiogroup1.ItemIndex of
+    0: begin
+      // Ecken 1,6,11
+      setlength(fcs,3);
+      fcs[0]:=1;
+      fcs[1]:=6;
+      fcs[2]:=11;
+    end;
+    1: begin
+      // Ecken 0,1,16
+      setlength(fcs,3);
+      fcs[0]:=0;
+      fcs[1]:=1;
+      fcs[2]:=16;
+    end;
+  end{of case};
+
+  j:=0;
+  for i:=0 to length(Kanten)-1 do begin
+    K:=Kanten[i].x;
+    L:=Kanten[i].y;
+    for N:=length(fcs)-1 downto 0 do begin
+      if fcs[N]=K then K:=-1;
+      if fcs[N]=L then L:=-1;
+      if K>=fcs[N] then dec(K);
+      if L>=fcs[N] then dec(L);
+    end;
+    if K<>-1 then
+      for N:=0 to 2 do
+        M.a[j,3*K+N]:=
+          M.a[j,3*K+N]
+           + Ecken[Kanten[i].x].a[N,0]
+           - Ecken[Kanten[i].y].a[N,0];
+    if L<>-1 then
+      for N:=0 to 2 do
+        M.a[j,3*L+N]:=
+          M.a[j,3*L+N]
+           + Ecken[Kanten[i].y].a[N,0]
+           - Ecken[Kanten[i].x].a[N,0];
+    if (K<>-1) or (L<>-1) then inc(j);
+  end;
+
+  M.Progressbar:=Progressbar1;
+  Messagedlg('det M = '+floattostr(M.det(dmGauss)),mtInformation,[mbOk],0);
+  M.Free;
+end;
+
+procedure TForm1.Button3Click(Sender: TObject);
+var I,J,K,L: Longint;
+    x:       extended;
+begin
+  x:=0;
+  for I:=0 to length(Ecken)-1 do
+    x:=max(x,Ecken[I].len);
+  I:=length(Ecken)-1;
+  while I>=0 do begin
+    if Ecken[I].len>=0.98*x then begin
+      for J:=I+1 to length(Ecken)-1 do
+        Ecken[J-1].assign(Ecken[J]);
+      Ecken[length(Ecken)-1].Free;
+      setlength(Ecken,length(Ecken)-1);
+      J:=length(Kanten)-1;
+      L:=0;
+      while J>=0 do begin
+        if (Kanten[J].x=I) or (Kanten[J].y=I) then begin
+          inc(L);
+          for K:=J+1 to length(Kanten)-1 do
+            Kanten[K-1]:=Kanten[K];
+          setlength(Kanten,length(Kanten)-1);
+        end
+        else begin
+          if Kanten[J].x>I then dec(Kanten[J].x);
+          if Kanten[J].y>I then dec(Kanten[J].y);
+        end;
+        dec(J);
+      end;
+      if L<>4 then Form1.Caption:=Form1.Caption+' '+inttostr(L);
+    end;
+    dec(I);
+  end;
+  x:=0;
+  for I:=0 to length(Ecken)-1 do
+    x:=max(x,Ecken[I].len);
+  for i:=0 to length(Ecken)-1 do
+    Ecken[i].times(1/2/x);
+  Zeichnen;
+end;
+
+procedure TForm1.Button4Click(Sender: TObject);
+const mindim = 4;
+      maxdim = 9;
+var M:       TMatrix;
+    dm:      TDetMethode;
+    I,J,K,L: Longint;
+    ts,errs: array[mindim..maxdim,TDetMethode] of extended;
+    t1,t2:   extended;
+    s:       string;
+begin
+  M:=TMatrix.create;
+  t2:=0;
+  for I:=mindim to maxdim do begin
+    for dm:=low(dm) to high(dm) do begin
+      ts[I,dm]:=0;
+      errs[I,dm]:=0;
+    end;
+    for J:=1 to 50 do begin
+      M.assignId(I);
+      for K:=0 to I-1 do
+        for L:=0 to I-1 do
+          if random*50<=J then
+            M.a[K,L]:=M.a[K,L]+random-0.5;
+      for dm:=low(dm) to high(dm) do begin
+        ts[I,dm]:=ts[I,dm]-now;
+        t1:=M.det(dm);
+        ts[I,dm]:=ts[I,dm]+now;
+        if dm=low(dm) then t2:=t1;
+        errs[I,dm]:=sqr(t1-t2);
+      end;
+    end;
+  end;
+  M.Free;
+  s:='';
+  for i:=mindim to maxdim do begin
+    s:=s+inttostr(i)+': ';
+    for dm:=low(dm) to high(dm) do
+      s:=s+floattostr(errs[i,dm])+' '+floattostr(ts[i,dm]*24*60*60)+';';
+    delete(s,length(s),1);
+    s:=s+#13;
+  end;
+  delete(s,length(s),1);
+  Messagedlg(s,mtinformation,[mbOk],0);
+end;
+
+end.
+
diff --git a/unit2.lfm b/unit2.lfm
new file mode 100644
index 0000000..18cdc54
--- /dev/null
+++ b/unit2.lfm
@@ -0,0 +1,18 @@
+object Form2: TForm2
+  Left = 390
+  Height = 533
+  Top = 355
+  Width = 779
+  Caption = 'Form2'
+  ClientHeight = 533
+  ClientWidth = 779
+  DesignTimePPI = 107
+  OnActivate = FormActivate
+  LCLVersion = '2.0.12.0'
+  object Image1: TImage
+    Left = 8
+    Height = 472
+    Top = 48
+    Width = 757
+  end
+end
diff --git a/unit2.pas b/unit2.pas
new file mode 100644
index 0000000..a870b32
--- /dev/null
+++ b/unit2.pas
@@ -0,0 +1,38 @@
+unit Unit2;
+
+{$mode objfpc}{$H+}
+
+interface
+
+uses
+  Classes, SysUtils, Forms, Controls, Graphics, Dialogs, ExtCtrls;
+
+type
+
+  { TForm2 }
+
+  TForm2 = class(TForm)
+    Image1: TImage;
+    procedure FormActivate(Sender: TObject);
+  private
+
+  public
+
+  end;
+
+var
+  Form2: TForm2;
+
+implementation
+
+{$R *.lfm}
+
+{ TForm2 }
+
+procedure TForm2.FormActivate(Sender: TObject);
+begin
+  //
+end;
+
+end.
+
diff --git a/vecmath.pas b/vecmath.pas
new file mode 100644
index 0000000..5e374dd
--- /dev/null
+++ b/vecmath.pas
@@ -0,0 +1,538 @@
+unit vecMath;
+
+interface
+
+uses math, Types, SysUtils, ComCtrls;
+
+Type TDetMethode = (dmLaPlace,dmLaPlace0,dmGauss);
+     TMatrix = class
+               private
+                _zanz,_sanz: integer;
+                Komps: array of array of extended; // [zeile,spalte]
+                procedure wsanz(sanz: integer);
+                procedure wzanz(zanz: integer);
+                function ra(z,s: integer): extended;
+                procedure wa(z,s: integer; _a: extended);
+                function rPart(l,t,r,b: integer): TMatrix;
+               public
+                Progressbar: TProgressbar;
+                property xdim: integer read _sanz
+                                       write wsanz;
+                property ydim: integer read _zanz
+                                       write wzanz;
+                property a[z,s: integer]: extended read ra
+                                                   write wa;
+                property part[l,t,r,b: integer]: TMatrix read rPart;
+                constructor create;
+                destructor destroy; override;
+                function asPoint: TPoint; overload;
+                function asPoint(scale: extended): TPoint; overload;
+                procedure assign(M: TMatrix);
+                procedure assignId(dim: integer);
+                procedure assign0;
+                function duplicate: TMatrix;
+                procedure plus(M: TMatrix);
+                procedure minus(M: TMatrix);
+                procedure times(x: extended);
+                procedure times_(R: TMatrix);
+                procedure _times(L: TMatrix);
+                procedure cross(M: TMatrix);
+                function det: extended; overload;
+                function det(methode: TDetMethode): extended; overload;
+                function det_laPlace(spare_optimize: boolean): extended;
+                function det_gauss: extended;
+                procedure transp;
+                procedure orthogonalize; overload;
+                procedure orthogonalize(normalize: boolean); overload;
+                function len: extended; // only for vectors!
+                function zlen(z: integer): extended;
+                function slen(s: integer): extended;
+                function toStr: string;
+                function fromString(str: string): boolean;
+               end;
+
+implementation
+
+function istZahl(str: string): boolean;
+var hK: boolean;
+begin
+ result:=false;
+ if length(str)=0 then exit;
+ hK:=false;
+ if str[1]='-' then delete(str,1,1);
+ if length(str)=0 then exit;
+ if not (str[1] in ['0'..'9']) then exit;
+ while (length(str)>0) and ((str[1] in ['0'..'9']) or
+                            ((str[1] = ',') and not hK)) do
+  begin
+   hK:=hK or (str[1]=',');
+   delete(str,1,1);
+  end;
+ result:=length(str)=0;
+end;
+
+procedure TMatrix.wsanz(sanz: integer);
+var i: integer;
+begin
+ if sanz>=0 then _sanz:=sanz;
+ setlength(Komps,_zanz);
+ for i:=0 to _zanz-1 do
+  setlength(Komps[i],_sanz);
+end;
+
+procedure TMatrix.wzanz(zanz: integer);
+var i: integer;
+begin
+ if zanz>=0 then _zanz:=zanz;
+ setlength(Komps,_zanz);
+ for i:=0 to _zanz-1 do
+  setlength(Komps[i],_sanz);
+end;
+
+function TMatrix.ra(z,s: integer): extended;
+begin
+ if (z>=0) and (z<_zanz) and
+    (s>=0) and (s<_sanz) then result:=Komps[z,s]
+                         else result:=0;
+end;
+
+procedure TMatrix.wa(z,s: integer; _a: extended);
+begin
+ if (z>=0) and (z<_zanz) and
+    (s>=0) and (s<_sanz) then Komps[z,s]:=_a;
+end;
+
+function TMatrix.rPart(l,t,r,b: integer): TMatrix;
+var z,s: integer;
+begin
+ l:=max(l,0);
+ t:=max(t,0);
+ r:=max(l,r);
+ b:=max(t,b);
+ r:=min(r,xdim-1);
+ b:=min(b,ydim-1);
+ result:=TMatrix.create;
+ result.ydim:=b-t+1;
+ result.xdim:=r-l+1;
+ for z:=t to b do
+  for s:=l to r do
+   result.a[z-t,s-l]:=a[z,s];
+end;
+
+constructor TMatrix.create;
+begin
+ inherited create;
+ _zanz:=3;
+ xdim:=1;
+ Progressbar:=nil;
+end;
+
+destructor TMatrix.destroy;
+begin
+ inherited destroy;
+end;
+
+function TMatrix.asPoint: TPoint;
+begin
+ result:=asPoint(1);
+end;
+
+function TMatrix.asPoint(scale: extended): TPoint;
+begin
+ if xdim>ydim then result:=Point(round(a[0,0]*scale),
+                                 round(a[0,1]*scale))
+              else result:=Point(round(a[0,0]*scale),
+                                 round(a[1,0]*scale));
+end;
+
+procedure TMatrix.assign(M: TMatrix);
+var z,s: Integer;
+begin
+ ydim:=M.ydim;
+ xdim:=M.xdim;
+ for z:=0 to ydim-1 do
+  for s:=0 to xdim-1 do
+   a[z,s]:=M.a[z,s];
+end;
+
+function TMatrix.duplicate: TMatrix;
+begin
+ Result:=TMatrix.create;
+ Result.assign(self);
+end;
+
+procedure TMatrix.plus(M: TMatrix);
+var z,s: Integer;
+begin
+ if (M.xdim = xdim) and
+    (M.ydim = ydim) then
+  for z:=0 to ydim-1 do
+   for s:=0 to xdim-1 do
+    a[z,s]:=a[z,s]+M.a[z,s];
+end;
+
+procedure TMatrix.minus(M: TMatrix);
+var z,s: Integer;
+begin
+ if (M.xdim = xdim) and
+    (M.ydim = ydim) then
+  for z:=0 to ydim-1 do
+   for s:=0 to xdim-1 do
+    a[z,s]:=a[z,s]-M.a[z,s];
+end;
+
+procedure TMatrix.times(x: extended);
+var z,s: Integer;
+begin
+ for z:=0 to ydim-1 do
+  for s:=0 to xdim-1 do
+   a[z,s]:=x*a[z,s];
+end;
+
+function TMatrix.det: extended;
+begin
+  result:=det_laPlace(true);
+end;
+
+function TMatrix.det(methode: TDetMethode): extended;
+begin
+  case methode of
+    dmLaPlace:  result:=det_laPlace(false);
+    dmLaPlace0: result:=det_laPlace(true);
+    dmGauss:    result:=det_gauss;
+    else result:=-1;
+  end{of case};
+end;
+
+function TMatrix.det_laPlace(spare_optimize: boolean): extended;
+var p:      array of Integer;
+    i,j,k,
+    tiefe:  Integer;
+    tmp:    extended;
+    UT:     boolean;
+begin
+ result:=0;
+ if xdim<>ydim then exit;
+ setlength(p,xdim);
+ for i:=0 to xdim-1 do
+  p[i]:=i;
+ if assigned(Progressbar) then begin
+   Progressbar.Position:=0;
+   Progressbar.Min:=0;
+   Progressbar.Max:=1;
+   tiefe:=-1;
+   repeat
+     inc(tiefe);
+     i:=0;
+     for j:=0 to xdim-1 do
+       if a[tiefe,j]<>0 then inc(i);
+     Progressbar.Max:=
+       Progressbar.Max*i;
+   until (Progressbar.Max>=100) or (tiefe>=xdim-1);
+   Progressbar.Step:=1;
+   Progressbar.Visible:=true;
+ end
+ else tiefe:=-2;
+ repeat
+  tmp:=1;
+  for i:=0 to xdim-1 do
+   begin
+    for j:=i+1 to xdim-1 do
+     if p[i]>p[j] then tmp:=-tmp;
+    tmp:=tmp*a[i,p[i]];
+   end;
+  result:=result+tmp;
+  if spare_optimize then begin
+    i:=0;
+    while (i<xdim-1) and (a[i,p[i]]<>0) do
+      inc(i);
+    for j:=i+1 to xdim-1 do
+      p[j]:=-1;
+  end
+  else
+    i:=xdim-1;
+  UT:=true;
+  while UT and (i>=0) do
+   begin
+    repeat
+     inc(p[i]);
+     UT:=spare_optimize and (p[i]<xdim) and (a[i,p[i]]=0);
+     for j:=0 to i-1 do
+      UT:=UT or (p[i]=p[j]);
+    until not UT;
+    if p[i]>=xdim then
+     begin
+      for j:=i to xdim-1 do
+       p[i]:=-1;
+      dec(i);
+      UT:=true;
+     end;
+   end;
+  if i<=tiefe then
+    Progressbar.StepIt;
+  if i>=0 then
+   for j:=i+1 to xdim-1 do
+    repeat
+     inc(p[j]);
+     UT:=false;
+     for k:=0 to j-1 do
+      UT:=UT or (p[j]=p[k]);
+    until not UT;
+ until UT and (i<0);
+ if assigned(Progressbar) then
+   Progressbar.Visible:=false;
+end;
+
+function TMatrix.det_gauss: extended;
+var M:       TMatrix;
+    I,J,K:   Longint;
+    tmp,fak: extended;
+    vz:      Longint;
+begin
+  result:=0;
+  if xdim<>ydim then exit;
+  M:=TMatrix.create;
+  M.assign(self);
+  vz:=1;
+  for I:=xdim-1 downto 0 do begin
+    J:=I;
+    while (J>=0) and (M.a[I,J]=0) do
+      dec(J);
+    if J<0 then begin
+      result:=0;
+      M.free;
+      exit;
+    end;
+    if J<>I then
+      for K:=0 to xdim-1 do begin
+        tmp:=M.a[K,I];
+        M.a[K,I]:=M.a[K,J];
+        M.a[K,J]:=tmp;
+        vz:=-vz;
+      end;
+    for J:=I-1 downto 0 do begin
+      fak:=M.a[J,I]/M.a[I,I];
+      for K:=0 to xdim-1 do
+        M.a[J,K]:=M.a[J,K] - fak * M.a[I,K];
+    end;
+  end;
+  result:=vz;
+  for I:=0 to xdim-1 do
+    result:=result*M.a[I,I];
+  M.free;
+end;
+
+procedure TMatrix.transp;
+var xd,yd,z,s: integer;
+    tmp:       extended;
+begin
+ xd:=ydim;
+ yd:=xdim;
+ xdim:=max(xd,yd);
+ ydim:=max(xd,yd);
+ for z:=0 to ydim-1 do
+  for s:=z+1 to xdim-1 do
+   begin
+    tmp:=a[z,s];
+    a[z,s]:=a[s,z];
+    a[s,z]:=tmp;
+   end;
+ xdim:=xd;
+ ydim:=yd;
+end;
+
+function TMatrix.toStr: string;
+var z,s: integer;
+begin
+ result:='';
+ for z:=0 to ydim-1 do
+  begin
+   result:=result+#$0D#$0A;
+   for s:=0 to xdim-1 do
+    result:=result+floattostr(a[z,s])+' ';
+   delete(result,length(result),1);
+  end;
+ delete(result,1,2);
+end;
+
+function TMatrix.fromString(str: string): boolean;
+var str2:  string;
+    z,s,i: integer;
+begin
+ result:=false;
+ if length(str)=0 then exit;
+ i:=length(str);
+ if str[length(str)]<>#13 then str:=str+#13;
+ while pos(#$0A,str)>0 do
+  delete(str,pos(#$0A,str),1);
+ while (i>0) do
+  begin
+   if str[i]=#13 then str:=copy(str,1,i-1)+' '+copy(str,i,length(str)+1-i);
+   dec(i);
+  end;
+ str2:=str;
+ for z:=0 to ydim-1 do
+  begin
+   for s:=0 to xdim-1 do
+    begin
+     while (length(str)>0) and (str[1]=' ') do
+      delete(str,1,1);
+     if pos(' ',str)=0 then exit;
+     if not istZahl(copy(str,1,pos(' ',str)-1)) then exit;
+     delete(str,1,pos(' ',str));
+     while (length(str)>0) and (str[1]=' ') do
+      delete(str,1,1);
+    end;
+   if (length(str)=0) or not (str[1]=#$0D) then exit;
+   delete(str,1,1);
+  end;
+ result:=true;
+ for z:=0 to ydim-1 do
+  begin
+   for s:=0 to xdim-1 do
+    begin
+     while (length(str2)>0) and (str2[1]=' ') do
+      delete(str2,1,1);
+     if pos(' ',str2)=0 then exit;
+     a[z,s]:=strtofloat(copy(str2,1,pos(' ',str2)-1));
+     delete(str2,1,pos(' ',str2));
+     while (length(str2)>0) and (str2[1]=' ') do
+      delete(str2,1,1);
+    end;
+   if (length(str2)=0) or not (str2[1]=#$0D) then exit;
+   delete(str2,1,1);
+  end;
+end;
+
+procedure TMatrix.times_(R: TMatrix);
+var L:     TMatrix;
+    z,s,i: integer;
+begin
+ if R.ydim<>xdim then exit;
+ L:=duplicate;
+ xdim:=R.xdim;
+ for z:=0 to ydim-1 do
+  for s:=0 to xdim-1 do
+   begin
+    a[z,s]:=0;
+    for i:=0 to R.ydim-1 do
+     a[z,s]:=a[z,s] + L.a[z,i]*R.a[i,s];
+   end;
+end;
+
+procedure TMatrix._times(L: TMatrix);
+var R:     TMatrix;
+    z,s,i: integer;
+begin
+ if ydim<>L.xdim then exit;
+ R:=duplicate;
+ ydim:=L.ydim;
+ for z:=0 to ydim-1 do
+  for s:=0 to xdim-1 do
+   begin
+    a[z,s]:=0;
+    for i:=0 to R.ydim-1 do
+     a[z,s]:=a[z,s] + L.a[z,i]*R.a[i,s];
+   end;
+end;
+
+procedure TMatrix.cross(M: TMatrix);
+var x,y,z: extended;
+begin
+ if (xdim<>1) or (M.xdim<>1) or (ydim<>3) or (M.ydim<>3) then exit; // ziemlich speziell ...
+ x:=a[1,0]*M.a[2,0]-a[2,0]*M.a[1,0];
+ y:=a[2,0]*M.a[0,0]-a[0,0]*M.a[2,0];
+ z:=a[0,0]*M.a[1,0]-a[1,0]*M.a[0,0];
+ a[0,0]:=x;
+ a[1,0]:=y;
+ a[2,0]:=z;
+end;
+
+procedure TMatrix.orthogonalize;
+begin
+ orthogonalize(false);
+end;
+
+procedure TMatrix.orthogonalize(normalize: boolean);
+var zT,z,s:      integer;
+    diff,me,opp: TMatrix;
+    l:           extended;
+begin
+ if det=0 then exit;
+
+ diff:=TMatrix.create;
+ diff.xdim:=xdim;
+ diff.ydim:=1;
+ for zT:=0 to ydim-1 do
+  begin
+   diff.assign0;
+   for z:=0 to zT-1 do
+    begin
+     me:=part[0,zT,xdim-1,zT];
+     l:=me.len;
+     me.transp;
+     opp:=part[0,z,xdim-1,z];
+     me._times(opp);
+     l:=me.a[0,0]/l;
+     me.destroy;
+     opp.times(l);
+     diff.plus(opp);
+     opp.destroy;
+    end;
+   for s:=0 to xdim-1 do
+    a[zT,s]:=a[zT,s]-diff.a[0,s];
+   if normalize then
+    begin
+     me:=part[0,zT,xdim-1,zT];
+     l:=me.len;
+     me.destroy;
+     for s:=0 to xdim-1 do
+      a[zT,s]:=a[zT,s]/l;
+    end;
+  end;
+end;
+
+procedure TMatrix.assignId(dim: integer);
+var z,s: integer;
+begin
+ if dim<1 then exit;
+ xdim:=dim;
+ ydim:=dim;
+ for z:=0 to dim-1 do
+  for s:=0 to dim-1 do
+   a[z,s]:=byte(z=s);
+end;
+
+procedure TMatrix.assign0;
+var z,s: integer;
+begin
+ for z:=0 to ydim-1 do
+  for s:=0 to xdim-1 do
+   a[z,s]:=0;
+end;
+
+function TMatrix.len: extended;
+begin
+ if xdim=1 then result:=slen(0)
+           else result:=zlen(0);
+end;
+
+function TMatrix.zlen(z: integer): extended;
+var s: integer;
+begin
+ result:=0;
+ for s:=0 to xdim-1 do
+  result:=result + sqr(a[z,s]);
+ result:=sqrt(result);
+end;
+
+function TMatrix.slen(s: integer): extended;
+var z: integer;
+begin
+ result:=0;
+ for z:=0 to ydim-1 do
+  result:=result + sqr(a[z,s]);
+ result:=sqrt(result);
+end;
+
+end.
diff --git a/weihnachtsstern.ico b/weihnachtsstern.ico
new file mode 100644
index 0000000..0341321
--- /dev/null
+++ b/weihnachtsstern.ico
diff --git a/weihnachtsstern.lpi b/weihnachtsstern.lpi
new file mode 100644
index 0000000..4f33e80
--- /dev/null
+++ b/weihnachtsstern.lpi
@@ -0,0 +1,91 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<CONFIG>
+  <ProjectOptions>
+    <Version Value="11"/>
+    <General>
+      <SessionStorage Value="InProjectDir"/>
+      <MainUnit Value="0"/>
+      <Title Value="weihnachtsstern"/>
+      <Scaled Value="True"/>
+      <ResourceType Value="res"/>
+      <UseXPManifest Value="True"/>
+      <XPManifest>
+        <DpiAware Value="True"/>
+      </XPManifest>
+      <Icon Value="0"/>
+    </General>
+    <BuildModes Count="1">
+      <Item1 Name="Default" Default="True"/>
+    </BuildModes>
+    <PublishOptions>
+      <Version Value="2"/>
+      <UseFileFilters Value="True"/>
+    </PublishOptions>
+    <RunParams>
+      <FormatVersion Value="2"/>
+      <Modes Count="0"/>
+    </RunParams>
+    <RequiredPackages Count="1">
+      <Item1>
+        <PackageName Value="LCL"/>
+      </Item1>
+    </RequiredPackages>
+    <Units Count="4">
+      <Unit0>
+        <Filename Value="weihnachtsstern.lpr"/>
+        <IsPartOfProject Value="True"/>
+      </Unit0>
+      <Unit1>
+        <Filename Value="unit1.pas"/>
+        <IsPartOfProject Value="True"/>
+        <ComponentName Value="Form1"/>
+        <HasResources Value="True"/>
+        <ResourceBaseClass Value="Form"/>
+        <UnitName Value="Unit1"/>
+      </Unit1>
+      <Unit2>
+        <Filename Value="vecmath.pas"/>
+        <IsPartOfProject Value="True"/>
+        <UnitName Value="vecMath"/>
+      </Unit2>
+      <Unit3>
+        <Filename Value="unit2.pas"/>
+        <IsPartOfProject Value="True"/>
+        <ComponentName Value="Form2"/>
+        <HasResources Value="True"/>
+        <ResourceBaseClass Value="Form"/>
+        <UnitName Value="Unit2"/>
+      </Unit3>
+    </Units>
+  </ProjectOptions>
+  <CompilerOptions>
+    <Version Value="11"/>
+    <Target>
+      <Filename Value="weihnachtsstern"/>
+    </Target>
+    <SearchPaths>
+      <IncludeFiles Value="$(ProjOutDir)"/>
+      <UnitOutputDirectory Value="lib/$(TargetCPU)-$(TargetOS)"/>
+    </SearchPaths>
+    <Linking>
+      <Options>
+        <Win32>
+          <GraphicApplication Value="True"/>
+        </Win32>
+      </Options>
+    </Linking>
+  </CompilerOptions>
+  <Debugging>
+    <Exceptions Count="3">
+      <Item1>
+        <Name Value="EAbort"/>
+      </Item1>
+      <Item2>
+        <Name Value="ECodetoolError"/>
+      </Item2>
+      <Item3>
+        <Name Value="EFOpenError"/>
+      </Item3>
+    </Exceptions>
+  </Debugging>
+</CONFIG>
diff --git a/weihnachtsstern.lpr b/weihnachtsstern.lpr
new file mode 100644
index 0000000..f96dbfe
--- /dev/null
+++ b/weihnachtsstern.lpr
@@ -0,0 +1,23 @@
+program weihnachtsstern;
+
+{$mode objfpc}{$H+}
+
+uses
+  {$IFDEF UNIX}{$IFDEF UseCThreads}
+  cthreads,
+  {$ENDIF}{$ENDIF}
+  Interfaces, // this includes the LCL widgetset
+  Forms, Unit1, vecMath, Unit2
+  { you can add units after this };
+
+{$R *.res}
+
+begin
+  RequireDerivedFormResource:=True;
+  Application.Scaled:=True;
+  Application.Initialize;
+  Application.CreateForm(TForm1, Form1);
+  Application.CreateForm(TForm2, Form2);
+  Application.Run;
+end.
+
diff --git a/weihnachtsstern.lps b/weihnachtsstern.lps
new file mode 100644
index 0000000..c9772ec
--- /dev/null
+++ b/weihnachtsstern.lps
@@ -0,0 +1,176 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<CONFIG>
+  <ProjectSession>
+    <Version Value="11"/>
+    <BuildModes Active="Default"/>
+    <Units Count="4">
+      <Unit0>
+        <Filename Value="weihnachtsstern.lpr"/>
+        <IsPartOfProject Value="True"/>
+        <EditorIndex Value="-1"/>
+        <WindowIndex Value="-1"/>
+        <TopLine Value="-1"/>
+        <CursorPos X="-1" Y="-1"/>
+        <UsageCount Value="21"/>
+      </Unit0>
+      <Unit1>
+        <Filename Value="unit1.pas"/>
+        <IsPartOfProject Value="True"/>
+        <ComponentName Value="Form1"/>
+        <HasResources Value="True"/>
+        <ResourceBaseClass Value="Form"/>
+        <UnitName Value="Unit1"/>
+        <TopLine Value="666"/>
+        <CursorPos X="47" Y="882"/>
+        <UsageCount Value="21"/>
+        <Loaded Value="True"/>
+        <LoadedDesigner Value="True"/>
+      </Unit1>
+      <Unit2>
+        <Filename Value="vecmath.pas"/>
+        <IsPartOfProject Value="True"/>
+        <UnitName Value="vecMath"/>
+        <EditorIndex Value="2"/>
+        <TopLine Value="23"/>
+        <CursorPos X="30" Y="36"/>
+        <UsageCount Value="21"/>
+        <Loaded Value="True"/>
+      </Unit2>
+      <Unit3>
+        <Filename Value="unit2.pas"/>
+        <IsPartOfProject Value="True"/>
+        <ComponentName Value="Form2"/>
+        <HasResources Value="True"/>
+        <ResourceBaseClass Value="Form"/>
+        <UnitName Value="Unit2"/>
+        <IsVisibleTab Value="True"/>
+        <EditorIndex Value="1"/>
+        <TopLine Value="6"/>
+        <CursorPos X="4" Y="34"/>
+        <UsageCount Value="21"/>
+        <Loaded Value="True"/>
+        <LoadedDesigner Value="True"/>
+      </Unit3>
+    </Units>
+    <JumpHistory Count="29" HistoryIndex="28">
+      <Position1>
+        <Filename Value="unit1.pas"/>
+        <Caret Line="807" Column="10" TopLine="782"/>
+      </Position1>
+      <Position2>
+        <Filename Value="unit1.pas"/>
+        <Caret Line="819" Column="8" TopLine="788"/>
+      </Position2>
+      <Position3>
+        <Filename Value="unit1.pas"/>
+        <Caret Line="909" Column="2" TopLine="907"/>
+      </Position3>
+      <Position4>
+        <Filename Value="unit2.pas"/>
+      </Position4>
+      <Position5>
+        <Filename Value="unit2.pas"/>
+        <Caret Line="35" Column="3" TopLine="7"/>
+      </Position5>
+      <Position6>
+        <Filename Value="unit1.pas"/>
+        <Caret Line="90" Column="25" TopLine="73"/>
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+      <Position7>
+        <Filename Value="unit1.pas"/>
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+      <Position8>
+        <Filename Value="unit1.pas"/>
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+        <Filename Value="unit1.pas"/>
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+        <Filename Value="unit1.pas"/>
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+      <Position11>
+        <Filename Value="unit1.pas"/>
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+      </Position11>
+      <Position12>
+        <Filename Value="unit1.pas"/>
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+      <Position13>
+        <Filename Value="unit1.pas"/>
+        <Caret Line="178" Column="17" TopLine="154"/>
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+      <Position14>
+        <Filename Value="unit1.pas"/>
+        <Caret Line="180" Column="29" TopLine="154"/>
+      </Position14>
+      <Position15>
+        <Filename Value="unit1.pas"/>
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+      <Position16>
+        <Filename Value="unit1.pas"/>
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+      <Position17>
+        <Filename Value="unit1.pas"/>
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+      <Position18>
+        <Filename Value="unit1.pas"/>
+        <Caret Line="188" Column="12" TopLine="180"/>
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+      <Position19>
+        <Filename Value="unit1.pas"/>
+        <Caret Line="189" Column="12" TopLine="180"/>
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+        <Filename Value="unit1.pas"/>
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+      <Position22>
+        <Filename Value="unit1.pas"/>
+        <Caret Line="640" Column="9" TopLine="622"/>
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+      <Position23>
+        <Filename Value="unit1.pas"/>
+      </Position23>
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+        <Filename Value="unit1.pas"/>
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+      </Position24>
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+        <Filename Value="unit1.pas"/>
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+        <Caret Line="810" Column="10" TopLine="785"/>
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+      <Position27>
+        <Filename Value="unit1.pas"/>
+        <Caret Line="833" Column="31" TopLine="808"/>
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+        <Filename Value="unit1.pas"/>
+        <Caret Line="56" Column="9" TopLine="41"/>
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+      <Position29>
+        <Filename Value="unit1.pas"/>
+        <Caret Line="833" Column="32" TopLine="807"/>
+      </Position29>
+    </JumpHistory>
+    <RunParams>
+      <FormatVersion Value="2"/>
+      <Modes Count="0" ActiveMode=""/>
+    </RunParams>
+  </ProjectSession>
+</CONFIG>
diff --git a/weihnachtsstern.res b/weihnachtsstern.res
new file mode 100644
index 0000000..1adb040
--- /dev/null
+++ b/weihnachtsstern.res