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Kamera mit Anleitung (3)

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Andyh
Betreff des Beitrags: Kamera mit Anleitung (3)
Verfasst: Fr Okt 14, 2005 11:24
DGL Member
Registriert: Do Jun 09, 2005 13:48
Beiträge: 117
Wohnort: Sankt Augustin
Und hier die Funktionssammlung:
Code:
 
unit OpenGLUtil;
 
interface
 
uses DglOpenGL, Math, Windows, Graphics, SysUtils, Dialogs;
 
type
  TProjection=(Frustum, Orthographic, Perspective);
 
  TGLPlace=packed record
    X,Y,Z: glFloat;
  end;
 
  TScale=packed record
    X,Y,Z: glFloat;
  end;
 
  TGLPosition=packed record
    X,Y,Z,W: glFloat;
  end;
 
  TPosition = packed record
    X,Y,Z,W: GLdouble;
  end;
 
  TGLVector = packed record
    X,Y,Z: GLfloat;
  end;
  TGLVectorArray = array of TGLvector;
  TGLfloatArray = array of TGLfloat;
 
  TGKVector = packed record
    X,Y,Z: GLfloat;
  end;
 
  TAngle = packed record
    X,Y,Z: GLdouble;
  end;
 
  TGLColor=record
    red,green,blue,alpha: GLclampf;
  end;
 
  TRotation = packed record
    angle, x, y, z: GLfloat;
  end;
 
  TTextureInfo = packed record
    BitmapName: string;
    TextureNum: GLUint;
  end;
  TTextureList = array of TTextureInfo;
 
  TMatrix = array [0..3,0..3] of TGLFloat;
  TArrMatrix = array [0..15] of TGLFloat;
  TFrustum = array [0..5,0..3] of TGLFloat;
  TArrVector = array [0..3] of TGLFloat;
 
  function Multiply (Color: TGLcolor; mult: TGLdouble): TGLcolor;
  procedure MatrixMultiply(M1, M2:TArrMatrix; var M3: TArrMatrix);
  function MakeVector(X,Y,Z:TGLFloat):TArrVector;overload;
  function MakeVector(X,Y,Z,W:TGLFloat):TArrVector;overload;
  procedure Normalize(aVector:TArrVector;var RVec:TArrVector);overload;
  procedure Normalize(aVector:TGLVector;var RVec:TGLVector);overload;
  function GetIdentity:TMatrix;
  function GetArrIdentity:TArrMatrix;
  function MatrixTranspose(const M:TMatrix):TMatrix;register;
  function VectorRotateX(v:TArrVector;a:TGLFloat):TArrVector;overload;
  function VectorRotateY(v:TArrVector;a:TGLFloat):TArrVector;overload;
  function VectorRotateZ(v:TArrVector;a:TGLFloat):TArrVector;overload;
  function VectorRotateX(v:TGLVector;a:TGLFloat):TGLVector;overload;
  function VectorRotateY(v:TGLVector;a:TGLFloat):TGLVector;overload;
  function VectorRotateZ(v:TGLVector;a:TGLFloat):TGLVector;overload;
 
  function GL2GKVector (V: TGLVector): TGKVector;
  function GK2GLVector (V: TGKVector): TGLVector;
  function GL2WinColor (GLcol: TGLcolor): TColor;
  function Win2GLColor (WinCol: Tcolor): TGLcolor;
  function CalcNormale (V1, V2, V3: TGLVector): TGLVector;
  function CrossProduct(V1, V2: TGLVector): TGLVector;
  function DotProduct (V1, V2: TGLVector): GLdouble;
  function LoadTexture(Filename: String; var Texture: GLuint): Boolean;
  function Magnitude(V1 : TGLVector) : GLfloat;
  function MultiplyVektor (V1, V2: TGLVector): TGLVector;
  function ScalarProduct (V1, V2: TGLVector): GLdouble;
  function SubtractVector (Vec1, Vec2: TGLVector): TGLVector;overload;
  function SubtractVector (Vec: TGLVector; X, Y, Z: TGLdouble): TGLVector;overload;
  function AddVector (Vec1, Vec2: TGLVector): TGLVector;overload;
  function AddVector (Vec: TGLVector; X, Y, Z: TGLdouble): TGLVector;overload;
  procedure CopyVector (FromVektor: TGLVector; var ToVektor: TGLVector);
  procedure InitVector (var V1: TGLVector; x, y, z: TGLdouble);overload;
  procedure InitVector (var V1: TGKVector; x, y, z: TGLdouble);overload;
  procedure InitVector (var V1: TArrVector; x, y, z: TGLdouble);overload;
  procedure InitScale (var S1: TScale; x, y, z: TGLdouble);
  procedure LoadBitmap(Filename: String;
                       out Width: Cardinal;
                       out Height: Cardinal;
                       out pData: Pointer);
  procedure GetRotation (V1, V2: TGLVector;
                         var Rotation: TRotation;
                         var normale: TGLVector);
  function MakeTextureFromBitmap (Bitmap: string; var BitmapList: TTextureList): GLenum;
  procedure EnableTexture (Texture: GLenum; TextureTiled: boolean);
  procedure DisableTexture;
  function TextToGLVector (VTxt: string): TGLVector;
  function TextToGKVector (VTxt: string): TGKVector;
  function GKVectorToText (V1: TGKVector): string;
  function GLVectorToText (V1: TGLVector): string;
  function MyCone (Start, Ende: TGLVector;
                   RadiusStart, RadiusEnde: TGLfloat;
                   Slices: Integer): boolean;
  function InvertMatrix (src: TArrMatrix; var inverse: TArrMatrix): boolean;
 
const
  C_X = 0;
  C_Y = 1;
  C_Z = 2;
  C_W = 3;
  C_EPS:TGLFloat=0.01;
  C_DEGTORAD:TGLFloat=3.1412/180;
  C_RADTODEG:TGLFloat=180/3.1412;
  C_LAMBDA_INCREMENT:TGLFloat=0.01;
 
 
implementation
 
function MyPower (Base: extended; Exp: integer): extended;
// ist nicht ausprogrammiert, funktioniert nur für eine 
// einfache zweierpotenz
begin
  result := Base * Base;
end;
 
procedure CopyVector (FromVektor: TGLVector; var ToVektor: TGLVector);
begin
  ToVektor.X := FromVektor.X;
  ToVektor.Y := FromVektor.Y;
  ToVektor.Z := FromVektor.Z;
end;
 
function SubtractVector (Vec1, Vec2: TGLVector): TGLVector;
// subtrahiert Vec2 von vec1 und gibt das ergebnis in vec3 zurück
var
  Vec3: TGLVector;
begin
  Vec3 .X := Vec1.X - Vec2.X;
  Vec3 .Y := Vec1.Y - Vec2.Y;
  Vec3 .Z := Vec1.Z - Vec2.Z;
  result := Vec3;
end;
 
function SubtractVector (Vec: TGLVector; X, Y, Z: TGLdouble): TGLVector;
// subtrahiert X, Y, Z von vec.x, vec.y, vec.z  und gibt das
// ergebnis zurück
begin
  Vec .X := Vec.X - X;
  Vec .Y := Vec.Y - Y;
  Vec .Z := Vec.Z - Z;
  result := Vec;
end;
 
function AddVector (Vec1, Vec2: TGLVector): TGLVector;
// addiert Vec2 auf vec1 und gibt das ergebnis in vec3 zurück
var
  Vec3: TGLVector;
begin
  Vec3 .X := Vec1.X + Vec2.X;
  Vec3 .Y := Vec1.Y + Vec2.Y;
  Vec3 .Z := Vec1.Z + Vec2.Z;
  result := Vec3;
end;
 
function AddVector (Vec: TGLVector; X, Y, Z: TGLdouble): TGLVector;
// addiert X, Y, Z auf vec.x, vec.y, vec.z  und gibt das
// ergebnis zurück
begin
  Vec .X := Vec.X + X;
  Vec .Y := Vec.Y + Y;
  Vec .Z := Vec.Z + Z;
  result := Vec;
end;
 
function Magnitude(V1 : TGLVector) : GLfloat;
var
  Ergebnis: GLdouble;
begin
// gibt die länge des vektors zurück
  Ergebnis := MyPower(V1.X,2)+MyPower(V1.Y,2)+MyPower(V1.Z,2);
  try
    result := sqrt(Ergebnis);
  except
    result := 0;
  end;
end;
 
function DotProduct (V1, V2: TGLVector): GLdouble;
var
  len1, len2: GLdouble;
  Ergebnis: GLdouble;
begin
  len1 := Magnitude (V1);
  len2 := Magnitude (V2);
  Ergebnis := ScalarProduct (V1, V2);
  Ergebnis := arccos (Ergebnis / (len1 * len2));
  result := radtodeg (Ergebnis) * 2.0;
end;
 
function CrossProduct(V1, V2: TGLVector): TGLVector;
var
  CrossVec: TGLVector;
begin
  CrossVec.X := ((V1.Y*V2.Z) - (V1.Z*V2.Y));
  CrossVec.Y := ((V1.Z*V2.X) - (V1.X*V2.Z));
CrossVec.Z := ((V1.X*V2.Y) - (V1.Y*V2.X));
  result := CrossVec;
 end;
 
function CalcNormale (V1, V2, V3: TGLVector): TGLVector;
var
  Kreuz: TGLvector;
  V1V2, V1V3: TGLvector;
begin
  // gibt die normale von 3 vektoren zurück (die senkrechte auf die
  // durch die drei vektoren gebildete ebene)
  V1V2 := SubtractVector (V2, V1);
  V1V3 := SubtractVector (V3, V1);
 
  Kreuz := CrossProduct (V1V2, V1V3);
 
  Normalize (Kreuz, result);
end;
 
procedure InitVector (var V1: TGLVector; x, y, z: TGLdouble);
begin
  V1.x := x;
  V1.y := y;
  V1.z := z;
end;
 
procedure InitVector (var V1: TGKVector; x, y, z: TGLdouble);
begin
  V1.x := x;
  V1.y := y;
  V1.z := z;
end;
 
procedure InitVector (var V1: TArrVector; x, y, z: TGLdouble);
begin
  V1[C_X] := x;
  V1[C_Y] := y;
  V1[C_Z] := z;
end;
 
procedure InitScale (var S1: TScale; x, y, z: TGLdouble);
begin
  S1.x := x;
  S1.y := y;
  S1.z := z;
end;
 
function MultiplyVektor (V1, V2: TGLVector): TGLVector;
var
  multVec: TGLVector;
begin
// zwei vektoren miteinander multiplizieren
  multVec.X := V1.X * V2.X;
  multVec.Y := V1.Y * V2.Y;
  multVec.Z := V1.Z * V2.Z;
  result := multvec;
end;
 
function ScalarProduct (V1, V2: TGLVector): GLdouble;
begin
// die summe der potenzen der einzelnen achsen von zwei vektoren errechnen
  result := (V1.X*V2.X +
             V1.Y*V2.Y +
             V1.Z*V2.Z);
end;
 
function LoadTexture(Filename: String; var Texture: GLuint): Boolean;
var
  pData: Pointer;
  Width: Cardinal;
  Height: Cardinal;
begin
  pData :=nil;
  LoadBitmap(Filename, Width, Height, pData);
 
  if (Assigned(pData)) then
    Result := True
  else
  begin
    Result := False;
    MessageBox(0, PChar('Unable to load ' + filename), 'Loading Textures', MB_OK);
    Halt(1);
  end;
 
  glGenTextures(1, @Texture);
  glBindTexture(GL_TEXTURE_2D, Texture);
  glTexEnvi(GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_MODULATE);  {Texture blends with object background}
 
  glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR); { only first two can be used }
  glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR); { all of the above can be used }
 
  gluBuild2DMipmaps(GL_TEXTURE_2D, 3, Width, Height, GL_RGB, GL_UNSIGNED_BYTE, pData);
end;
 
procedure LoadBitmap(Filename: String;
                     out Width: Cardinal;
                     out Height: Cardinal;
                     out pData: Pointer);
var
  FileHeader: BITMAPFILEHEADER;
  InfoHeader: BITMAPINFOHEADER;
  Palette: array of RGBQUAD;
  BitmapFile: THandle;
  BitmapLength: Cardinal;
  PaletteLength: Cardinal;
  ReadBytes: Cardinal;
  Front: ^Byte;
  Back: ^Byte;
  Temp: Byte;
  I : Cardinal;
begin
  BitmapFile := CreateFile(PChar(Filename), GENERIC_READ, FILE_SHARE_READ, nil, OPEN_EXISTING, 0, 0);
  if (BitmapFile = INVALID_HANDLE_VALUE) then begin
    MessageBox(0, PChar('Error opening \"' + Filename), PChar('BMP Unit'), MB_OK);
    Exit;
  end;
 
  // Get header information
  ReadFile(BitmapFile, FileHeader, SizeOf(FileHeader), ReadBytes, nil);
  ReadFile(BitmapFile, InfoHeader, SizeOf(InfoHeader), ReadBytes, nil);
 
  // Get palette
  PaletteLength := InfoHeader.biClrUsed;
  SetLength(Palette, PaletteLength);
  ReadFile(BitmapFile, Palette, PaletteLength, ReadBytes, nil);
  if (ReadBytes <> PaletteLength) then begin
    MessageBox(0, PChar('Error reading palette'), PChar('BMP Unit'), MB_OK);
    Exit;
  end;
 
  Width := InfoHeader.biWidth;
  Height := InfoHeader.biHeight;
  BitmapLength := InfoHeader.biSizeImage;
  if BitmapLength = 0 then
    BitmapLength := Width * Height * InfoHeader.biBitCount Div 8;
 
  // Get the actual pixel data
  GetMem(pData, BitmapLength);
  ReadFile(BitmapFile, pData^, BitmapLength, ReadBytes, nil);
  if (ReadBytes <> BitmapLength) then begin
    MessageBox(0, PChar('Error reading bitmap data'), PChar('BMP Unit'), MB_OK);
    Exit;
  end;
  CloseHandle(BitmapFile);
 
  // Bitmaps are stored BGR and not RGB, so swap the R and B bytes.
  for I :=0 to Width * Height - 1 do
  begin
    Front := Pointer(Cardinal(pData) + I*3);
    Back := Pointer(Cardinal(pData) + I*3 + 2);
    Temp := Front^;
    Front^ := Back^;
    Back^ := Temp;
  end;
end;
 
function GK2GLVector (V: TGKVector): TGLVector;
// ändert Gauss-Krüger Koordinaten in OpenGL Koordinaten um
begin
  result.X := V.X;
  result.Y := V.Z;
  result.Z := V.Y;
end;
 
function GL2GKVector (V: TGLVector): TGKVector;
// ändert OpenGL Koordinaten in Gauss-Krüger Koordinaten um
begin
  result.X := V.X;
  result.Y := V.Z;
  result.Z := V.Y;
end;
 
function Win2GLColor (WinCol: TColor): TGLcolor;
begin
  result.Red := GetRValue (WinCol);
  result.Green := GetGValue (WinCol);
  result.Blue := GetBValue (WinCol);
  result.Alpha := 1.0;
end;
 
function GL2WinColor (GLcol: TGLcolor): TColor;
begin
  result := Rgb (StrToInt (FloatToStr (int (GLcol.Red))),
                 StrToInt (FloatToStr (int (GLcol.Green))),
                 StrToInt (FloatToStr (int (GLcol.Blue))));
end;
 
procedure GetRotation (V1, V2: TGLVector;
                       var Rotation: TRotation;
                       var normale: TGLVector);
var
  tmpCyl, tmpZiel, nullVec: TGLVector;
  ResultLen: TGLVector;
  VectorLength: GLfloat;
begin
  // temporäre vektoren initialisieren
  InitVector (nullVec, 0,0,0);
  InitVector (tmpCyl, 0,0,0);
 
  // länge des zu drehenden objekts ermitteln
  ResultLen := SubtractVector (V2, V1);
  VectorLength := Magnitude (ResultLen);
 
  // vektoren zur bildung der dreiecksfläche bilden.
  // die schenkel schneiden sich im nullpunkt
  // der Cylinder läuft immer entlang der Z-Achse
  tmpCyl.Z := VectorLength;
  tmpZiel := SubtractVector (V2, V1);
  tmpZiel.Z := tmpZiel.Z + VectorLength;
 
  // senkrechte zu den beiden vektoren bilden
  // (um diese achse soll nachher gedreht werden)
  // drehachse für späteren gebrauch speichern
  normale := CalcNormale (tmpCyl, tmpZiel, nullVec);
 
  // um \"Angle\" Grad soll nachher gedreht werden
  Rotation.Angle := DotProduct(tmpCyl, tmpZiel);
  Rotation.X     := normale.X;
  Rotation.Y     := normale.Y;
  Rotation.Z     := normale.Z;
end;
 
function MakeTextureFromBitmap (Bitmap: string; var BitmapList: TTextureList): GLenum;
// die funktion lädt die in Bitmap übergebene Grafik und gibt die Textturnummer
// zurück. ist das bitmap schon im array BitmapList enthalten, wird die bereits
// vergeben nummer zurückgegeben.
var
  i, Laenge: integer;
begin
  result := 0;
  if length (trim (Bitmap)) = 0 then
    exit;
  Bitmap := trim (uppercase (Bitmap));
  // suchen, ob die textur schon geladen wurde
  Laenge := length (BitmapList);
  if Laenge > 0 then
    for i := 0 to Laenge-1 do
    begin
      if (BitmapList[i].BitmapName = Bitmap) and
         (BitmapList[i].TextureNum > 0) then
        result := BitmapList[i].TextureNum;
    end;
 
  if (result = 0) then
  begin
    setlength (BitmapList, Laenge+1);
    BitmapList[Laenge].BitmapName := Bitmap;
    BitmapList[Laenge].TextureNum := 0;
    if LoadTexture (Bitmap, BitmapList[Laenge].TextureNum) then
      result := BitmapList[Laenge].TextureNum;
  end;
end;
 
procedure EnableTexture (Texture: GLenum; TextureTiled: boolean);
begin
  glEnable(GL_TEXTURE_2D);
  glBindTexture(GL_TEXTURE_2D, Texture);
  glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST);
  glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_NEAREST);
  if TextureTiled then
  begin
    glTexparameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_REPEAT);
    glTexparameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_REPEAT);
  end
  else
  begin
    glTexparameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP);
    glTexparameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP);
  end;
end;
 
procedure DisableTexture;
begin
  glDisable(GL_TEXTURE_2D);
end;
 
function TextToGLVector (VTxt: string): TGLVector;
const
  subdelim: char = '/';
var
  posi: integer;
  V1: TGLVector;
begin
  InitVector (V1,0,0,0);
  posi := pos (subdelim, VTxt);
  if posi > 0 then
  begin
    V1.X := StrToFloat (copy (VTxt, 1, posi-1));
    VTxt := copy (VTxt, posi+1, length (VTxt));
    posi := pos (subdelim, VTxt);
  end;
  if posi > 0 then
  begin
    V1.Y := StrToFloat (copy (VTxt, 1, posi-1));
    VTxt := copy (VTxt, posi+1, length (VTxt));
  end;
  if length (VTxt) > 0 then V1.Z := StrToFloat (VTxt);
 
  result := V1;
end;
 
function TextToGKVector (VTxt: string): TGKVector;
const
  subdelim: char = '/';
var
  posi: integer;
  V1: TGKVector;
begin
  InitVector (V1,0,0,0);
  posi := pos (subdelim, VTxt);
  if posi > 0 then
  begin
    V1.X := StrToFloat (copy (VTxt, 1, posi-1));
    VTxt := copy (VTxt, posi+1, length (VTxt));
    posi := pos (subdelim, VTxt);
  end;
  if posi > 0 then
  begin
    V1.Y := StrToFloat (copy (VTxt, 1, posi-1));
    VTxt := copy (VTxt, posi+1, length (VTxt));
  end;
  if length (VTxt) > 0 then V1.Z := StrToFloat (VTxt);
 
  result := V1;
end;
 
function GKVectorToText (V1: TGKVector): string;
const
  subdelim: char = '/';
var
  VTxt: string;
begin
  VTxt := FloatToStr (V1.X) + subdelim;
  VTxt := VTxt + FloatToStr (V1.Y) + subdelim;
  VTxt := VTxt + FloatToStr (V1.Z);
  result := VTxt;
end;
 
function GLVectorToText (V1: TGLVector): string;
const
  subdelim: char = '/';
var
  VTxt: string;
begin
  VTxt := FloatToStr (V1.X) + subdelim;
  VTxt := VTxt + FloatToStr (V1.Y) + subdelim;
  VTxt := VTxt + FloatToStr (V1.Z);
  result := VTxt;
end;
 
function MyCone (Start, Ende: TGLVector;
                 RadiusStart, RadiusEnde: TGLfloat;
                 Slices: Integer): boolean;
var
  Slice: Integer;
  Laenge, xdelta, zdelta: TGLfloat;
  V1, V2, V3, V4: TGLvector;
  A, B: Single;
  tmpVec: TGLvector;
begin
  result := true;
  // laenge des kegels berechnen
  // hierbei wird davon ausgegangen, dass der kegel senkrecht steht
  // Laenge := Ende.y - Start.y;
  tmpVec := SubtractVector (Start, Ende);
  Laenge := Magnitude (tmpVec);
  // radiusdifferenz berechnen
  xdelta := Start.x - Ende.x;
  zdelta := Start.z - Ende.z;
  xdelta := -xdelta;
  //zdelta := zdelta;
  glBegin (GL_TRIANGLE_STRIP);
  // der kegel wird entlang der z-achse gezeichnet
  V1.z := 0;
  V2.z := 0;
  V3.z := Laenge;
  V4.z := Laenge;
  for Slice := 1 to Slices do begin
    A := 2 * PI * Slice / Slices;
    B := 2 * PI * (Slice+1) / Slices;
    V1.x := sin(A)*RadiusStart;
    V1.y := cos(A)*RadiusStart;
    V2.x := sin(B)*RadiusStart;
    V2.y := cos(B)*RadiusStart;
    // umsetzung von y nach z-achse
    V3.x := (sin(B)*RadiusEnde)+xdelta;
    V3.y := (cos(B)*RadiusEnde)+zdelta;
    V4.x := (sin(A)*RadiusEnde)+xdelta;
    V4.y := (cos(A)*RadiusEnde)+zdelta;
    //Normale := CalcNormale (V1, V3, V2);
    //glNormal3fv(@Normale);
    if Slice = 1 then
    begin
      glTexCoord2f(1,0); glVertex3fv(@V1);
      glTexCoord2f(1,1); glVertex3fv(@V4);
      glTexCoord2f(1-Slice/Slices,0); glVertex3fv(@V2);
      glTexCoord2f(1-Slice/Slices,1); glVertex3fv(@V3);
    end
    else
    begin
      glTexCoord2f(1-Slice/Slices,0); glVertex3fv(@V2);
      glTexCoord2f(1-Slice/Slices,1); glVertex3fv(@V3);
    end;
    // aktuellen und nächsten punkt des kreises (oben und unten)
    // nehmen und ein rechteck zeichnen. alle rechtecke zusammen sollten
    // einen geschlossenen kegel ergeben.
    //glBegin(GL_QUADS);
    //  glNormal3fv(@Normale);
    //  glTexCoord2f(0,0); glVertex3fv(@V2);
    //  glTexCoord2f(1,0); glVertex3fv(@V1);
    //  glTexCoord2f(1,1); glVertex3fv(@V4);
    //  glTexCoord2f(0,1); glVertex3fv(@V3);
    //glEnd;
  end;
  glEnd;  // (GL_TRIANGLE_STRIP)
end;
 
{-----------------------------------------------------------------------------}
{----------------------------- für TRUVCamera --------------------------------}
{-----------------------------------------------------------------------------}
 
procedure MatrixMultiply(M1, M2: TArrMatrix; var M3: TArrMatrix);
// multiplies two 4x4 matrices
begin   
  glPushMatrix();
  glLoadMatrixf(@M1);
  glMultMatrixf(@M2);
  glGetFloatv(GL_MODELVIEW_MATRIX,@M3);
  glPopMatrix();
end;
 
function MakeVector(X,Y,Z:TGLFloat):TArrVector;
begin
  result[0]:=x;
  result[1]:=y;
  result[2]:=z;
end;
 
function MakeVector(X,Y,Z,W:TGLFloat):TArrVector;
begin
  result[0]:=x;
  result[1]:=y;
  result[2]:=z;
  result[3]:=w;
end;
 
procedure Normalize(aVector:TArrVector;var RVec:TArrVector);
var
   d:double;
begin
  InitVector (RVec,1,1,1);
  d:=Sqrt(Sqr(aVector[C_X])+Sqr(aVector[C_Y])+Sqr(aVector[C_Z]));
  if d=0 then
  begin
    //raise exception.Create('Zero length vector(Normalize 1)');
    exit;
  end;
  RVec[C_X]:=aVector[C_X]/d;
  RVec[C_Y]:=aVector[C_Y]/d;
  RVec[C_Z]:=aVector[C_Z]/d;
end;
 
procedure Normalize(aVector:TGLVector; var RVec:TGLVector);
var
   d:double;
begin
  InitVector (RVec,1,1,1);
  d:=Sqrt(Sqr(aVector.X)+Sqr(aVector.Y)+Sqr(aVector.Z));
  if d=0 then
  begin
    //raise exception.Create('Zero length vector(Normalize 2)');
    exit;
  end;
  RVec.X:=aVector.X/d;
  RVec.Y:=aVector.Y/d;
  RVec.Z:=aVector.Z/d;
end;
 
function GetIdentity:TMatrix;
begin
  result[0,0]:=1.0;result[0,1]:=0.0;result[0,2]:=0.0;result[0,3]:=0.0;
  result[1,0]:=0.0;result[1,1]:=1.0;result[1,2]:=0.0;result[1,3]:=0.0;
  result[2,0]:=0.0;result[2,1]:=0.0;result[2,2]:=1.0;result[2,3]:=0.0;
  result[3,0]:=0.0;result[3,1]:=0.0;result[3,2]:=0.0;result[3,3]:=1.0;
end;
 
function GetArrIdentity:TArrMatrix;
begin
  result[0]:=1.0;result[1]:=0.0;result[2]:=0.0;result[3]:=0.0;
  result[4]:=0.0;result[5]:=1.0;result[6]:=0.0;result[7]:=0.0;
  result[8]:=0.0;result[9]:=0.0;result[10]:=1.0;result[11]:=0.0;
  result[12]:=0.0;result[13]:=0.0;result[14]:=0.0;result[15]:=1.0;
end;
 
function MatrixTranspose(const M:TMatrix):TMatrix;register;
var
   i,j:integer;
begin
     for i:=0 to 3 do
         for j:=0 to 3 do
             result[i,j]:=M[j,i];
end;
 
function VectorRotateX(v:TArrVector;a:TGLFloat):TArrVector;
var
   temp: TArrVector;
   sine,cosine:TGLFloat;
begin
     a:=a*C_DEGTORAD;
     sine:=Sin(a);
     cosine:=Cos(a);
 
     temp[C_X] := v[C_x];
     temp[C_Y] := (v[C_Y] * cosine) + (v[C_Z] * -sine);
     temp[C_Z] := (v[C_Y] * sine) + (v[C_Z] * cosine);
     result := temp;
end;
 
function VectorRotateY(v: TArrVector;a:TGLFloat):TArrVector;
var
   temp: TArrVector;
   sine,cosine:TGLFloat;
begin
     a:=a*C_DEGTORAD;
     sine:=Sin(a);
     cosine:=Cos(a);
 
     temp[C_x] := (v[C_x] * cosine) + (v[C_z] * sine);
     temp[C_y] := v[C_y];
     temp[C_z] := (v[C_x] * -sine) + (v[C_z] * cosine);
     result := temp;
end;
 
function VectorRotateZ(v: TArrVector; a: TGLFloat):TArrVector;
var
  temp: TArrVector;
   sine,cosine:TGLFloat;
begin
     a:=a*C_DEGTORAD;
     sine:=Sin(a);
     cosine:=Cos(a);
     temp[C_x] := (v[C_x] * cosine) + (v[C_y] * -sine);
     temp[C_y] := (v[C_x] * sin(a)) + (v[C_y] * cosine);
     temp[C_z] := v[C_z];
     result := temp;
end;
 
function VectorRotateX(v:TGLVector;a:TGLFloat):TGLVector;
var
   temp: TGLVector;
   sine,cosine:TGLFloat;
begin
     a:=a*C_DEGTORAD;
     sine:=Sin(a);
     cosine:=Cos(a);
 
     temp.X := v.x;
     temp.Y := (v.Y * cosine) + (v.Z * -sine);
     temp.Z := (v.Y * sine) + (v.Z * cosine);
     result := temp;
end;
 
function VectorRotateY(v: TGLVector;a:TGLFloat):TGLVector;
var
   temp: TGLVector;
   sine,cosine:TGLFloat;
begin
     a:=a*C_DEGTORAD;
     sine:=Sin(a);
     cosine:=Cos(a);
 
     temp.x := (v.x * cosine) + (v.z * sine);
     temp.y := v.y;
     temp.z := (v.X * -sine) + (v.z * cosine);
     result := temp;
end;
 
function VectorRotateZ(v: TGLVector; a: TGLFloat):TGLVector;
var
  temp: TGLVector;
   sine,cosine:TGLFloat;
begin
     a:=a*C_DEGTORAD;
     sine:=Sin(a);
     cosine:=Cos(a);
     temp.x := (v.x * cosine) + (v.y * -sine);
     temp.y := (v.x * sin(a)) + (v.y * cosine);
     temp.z := v.z;
     result := temp;
end;
 
{-----------------------------------------------------------------------------}
{-------------------------------- allgemein ----------------------------------}
{-----------------------------------------------------------------------------}
 
function InvertMatrix (src: TArrMatrix; var inverse: TArrMatrix): boolean;
var
  t: TGLdouble;
  i, j, k, swap: integer;
  tmp: TMatrix;
begin
  result := false;
  inverse := GetArrIdentity;
 
  for i := 0 to 3 do
  begin
    for j := 0 to 3 do
    begin
      tmp[i][j] := src[i*4+j];
    end;
  end;
 
  for i := 0 to 3 do
  begin
    // look for largest element in column.
    swap := i;
    for j := i+1 to 3 do
    begin
      if abs(tmp[j][i]) > abs(tmp[i][i]) then
      begin
        swap := j;
      end;
    end;
 
    if not (swap = i) then
    begin
      // swap rows.
      for k := 0 to 3 do
      begin
        t := tmp[i][k];
        tmp[i][k] := tmp[swap][k];
        tmp[swap][k] := t;
 
        t := inverse[i*4+k];
        inverse[i*4+k] := inverse[swap*4+k];
        inverse[swap*4+k] := t;
      end;
    end;
 
    if tmp[i][i] = 0 then
    begin
    { no non-zero pivot.  the matrix is singular, which
      shouldn't happen.  This means the user gave us a bad
      matrix. }
      exit;
    end;
 
    t := tmp[i][i];
    for k := 0 to 3 do
    begin
      tmp[i][k] := tmp[i][k]/t;
      inverse[i*4+k] := inverse[i*4+k]/t;
    end;
 
    for j := 0 to 3 do
    begin
      if not (j = i) then
      begin
        t := tmp[j][i];
        for k := 0 to 3 do
        begin
          tmp[j][k] := tmp[j][k]-tmp[i][k]*t;
          inverse[j*4+k] := inverse[j*4+k]-inverse[i*4+k]*t;
        end;
      end;
    end;
  end;
  result := true;
end;
 
function Multiply (Color: TGLcolor; mult: TGLdouble): TGLcolor;
begin
  Color.red := Color.red * mult;
  Color.green := Color.green * mult;
  Color.blue := Color.blue * mult;
end;
 
end.
 
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