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bgramatrix3d.pas
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bgramatrix3d.pas
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{ ***************************************************************************
* *
* This file is part of BGRABitmap library which is distributed under the *
* modified LGPL. *
* *
* See the file COPYING.modifiedLGPL.txt, included in this distribution, *
* for details about the copyright. *
* *
* This program is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
* *
************************* BGRABitmap library ******************************
- Drawing routines with transparency and antialiasing with Lazarus.
Offers also various transforms.
- These routines allow to manipulate 32bit images in BGRA format or RGBA
format (depending on the platform).
- This code is under modified LGPL (see COPYING.modifiedLGPL.txt).
This means that you can link this library inside your programs for any purpose.
Only the included part of the code must remain LGPL.
- If you make some improvements to this library, please notify here:
http://www.lazarus.freepascal.org/index.php/topic,12037.0.html
********************* Contact : Circular at operamail.com *******************
******************************* CONTRIBUTOR(S) ******************************
- Edivando S. Santos Brasil | [email protected]
(Compatibility with FPC ($Mode objfpc/delphi) and delphi VCL 11/2018)
***************************** END CONTRIBUTOR(S) *****************************}
Unit BGRAMatrix3D;
{$i bgrabitmap.inc}{$H+}
{$i bgrasse.inc}
{$ifdef CPUI386}
{$asmmode intel}
{$ENDIF}
{$ifdef cpux86_64}
{$asmmode intel}
{$ENDIF}
interface
uses
BGRATypes, BGRABitmapTypes, BGRASSE,
BGRATransform;
type
TMatrix3D = packed array[1..3,1..4] of single;
TMatrix4D = packed array[1..4,1..4] of single;
TProjection3D = packed record
Zoom, Center: TPointF;
end;
TComputeProjectionFunc = function(AViewCoord: TPoint3D_128): TPointF of object;
function MatrizMult(const A: TMatrix3D; const M: TPoint3D): TPoint3D; overload;
function MatrizMult({$IFDEF OBJ}constref{$ELSE}const{$ENDIF} A: TMatrix3D; var M: TPoint3D_128): TPoint3D_128; overload;
function MultiplyVect3DWithoutTranslation({$IFDEF OBJ}constref{$ELSE}const{$ENDIF} A: TMatrix3D; {$IFDEF OBJ}constref{$ELSE}const{$ENDIF} M: TPoint3D_128): TPoint3D_128;
function MatrizMult(A,B: TMatrix3D): TMatrix3D; overload;
function Matrix3D(m11,m12,m13,m14, m21,m22,m23,m24, m31,m32,m33,m34: single): TMatrix3D; overload;
function Matrix3D(vx,vy,vz,ofs: TPoint3D): TMatrix3D; overload;
function Matrix3D(vx,vy,vz,ofs: TPoint3D_128): TMatrix3D; overload;
function MatrixIdentity3D: TMatrix3D;
function MatrixInverse3D(A: TMatrix3D): TMatrix3D;
function MatrixTranslation3D(ofs: TPoint3D): TMatrix3D;
function MatrixScale3D(size: TPoint3D): TMatrix3D;
function MatrixRotateX(angle: single): TMatrix3D;
function MatrixRotateY(angle: single): TMatrix3D;
function MatrixRotateZ(angle: single): TMatrix3D;
function MatrizMult4D(const A, B: TMatrix4D): TMatrix4D;
function MatrixIdentity4D: TMatrix4D;
function AffineMatrixToMatrix4D(AValue: TAffineMatrix): TMatrix4D;
{$IFDEF BGRASSE_AVAILABLE}
procedure Matrix3D_SSE_Load(const A: TMatrix3D);
procedure MatrixMultiplyVect3D_SSE_Aligned(var M: TPoint3D_128; out N: TPoint3D_128);
procedure MatrixMultiplyVect3D_SSE3_Aligned(var M: TPoint3D_128; out N: TPoint3D_128);
procedure MatrixMultiplyVect3DWithoutTranslation_SSE_Aligned(var M: TPoint3D_128; out N: TPoint3D_128);
procedure MatrixMultiplyVect3DWithoutTranslation_SSE3_Aligned(var M: TPoint3D_128; out N: TPoint3D_128);
{$ENDIF}
implementation
procedure multiplyVect3(const A : TMatrix3D; const vx,vy,vz,vt: single; out outx,outy,outz: single);
begin
outx := vx * A[1,1] + vy * A[1,2] + vz * A[1,3] + vt * A[1,4];
outy := vx * A[2,1] + vy * A[2,2] + vz * A[2,3] + vt * A[2,4];
outz := vx * A[3,1] + vy * A[3,2] + vz * A[3,3] + vt * A[3,4];
end;
procedure multiplyVect4(const A : TMatrix4D; const vx,vy,vz,vt: single; out outx,outy,outz,outt: single);
begin
outx := vx * A[1,1] + vy * A[1,2] + vz * A[1,3] + vt * A[1,4];
outy := vx * A[2,1] + vy * A[2,2] + vz * A[2,3] + vt * A[2,4];
outz := vx * A[3,1] + vy * A[3,2] + vz * A[3,3] + vt * A[3,4];
outt := vx * A[4,1] + vy * A[4,2] + vz * A[4,3] + vt * A[4,4];
end;
function MatrizMult(const A: TMatrix3D; const M: TPoint3D): TPoint3D;
begin
result.x := M.x * A[1,1] + M.y * A[1,2] + M.z * A[1,3] + A[1,4];
result.y := M.x * A[2,1] + M.y * A[2,2] + M.z * A[2,3] + A[2,4];
result.z := M.x * A[3,1] + M.y * A[3,2] + M.z * A[3,3] + A[3,4];
end;
function MatrizMult4D(const A, B: TMatrix4D): TMatrix4D;
begin
multiplyVect4(A, B[1,1],B[2,1],B[3,1],B[4,1], result[1,1],result[2,1],result[3,1],result[4,1]);
multiplyVect4(A, B[1,2],B[2,2],B[3,2],B[4,2], result[1,2],result[2,2],result[3,2],result[4,2]);
multiplyVect4(A, B[1,3],B[2,3],B[3,3],B[4,3], result[1,3],result[2,3],result[3,3],result[4,3]);
multiplyVect4(A, B[1,4],B[2,4],B[3,4],B[4,4], result[1,4],result[2,4],result[3,4],result[4,4]);
end;
function MatrixIdentity4D: TMatrix4D;
begin
result[1,1] := 1; result[2,1] := 0; result[3,1] := 0; result[4,1] := 0;
result[1,2] := 0; result[2,2] := 1; result[3,2] := 0; result[4,2] := 0;
result[1,3] := 0; result[2,3] := 0; result[3,3] := 1; result[4,3] := 0;
result[1,4] := 0; result[2,4] := 0; result[3,4] := 0; result[4,4] := 1;
end;
function AffineMatrixToMatrix4D(AValue: TAffineMatrix): TMatrix4D;
begin
result[1,1] := AValue[1,1]; result[2,1] := AValue[1,2]; result[3,1] := 0; result[4,1] := AValue[1,3];
result[1,2] := AValue[2,1]; result[2,2] := AValue[2,2]; result[3,2] := 0; result[4,2] := AValue[2,3];
result[1,3] := 0; result[2,3] := 0; result[3,3] := 1; result[4,3] := 0;
result[1,4] := 0; result[2,4] := 0; result[3,4] := 0; result[4,4] := 1;
end;
{$IFDEF BGRASSE_AVAILABLE}
var SingleConst1 : single = 1;
procedure Matrix3D_SSE_Load(const A: TMatrix3D);
begin
{$IFDEF cpux86_64}
asm
mov rax, A
movups xmm5, [rax]
movups xmm6, [rax+16]
movups xmm7, [rax+32]
end;
{$ELSE}
asm
mov eax, A
movups xmm5, [eax]
movups xmm6, [eax+16]
movups xmm7, [eax+32]
end;
{$ENDIF}
end;
procedure MatrixMultiplyVect3D_SSE_Aligned(var M: TPoint3D_128; out N: TPoint3D_128);
var oldMt: single;
begin
oldMt := M.t;
M.t := SingleConst1;
{$IFDEF cpux86_64}
asm
mov rax, M
movaps xmm0, [rax]
mov rax, N
movaps xmm2,xmm0
mulps xmm2,xmm5
//mix1
movaps xmm3, xmm2
shufps xmm3, xmm3, $4e
addps xmm2, xmm3
//mix2
movaps xmm3, xmm2
shufps xmm3, xmm3, $11
addps xmm2, xmm3
movss [rax], xmm2
movaps xmm2,xmm0
mulps xmm2,xmm6
//mix1
movaps xmm3, xmm2
shufps xmm3, xmm3, $4e
addps xmm2, xmm3
//mix2
movaps xmm3, xmm2
shufps xmm3, xmm3, $11
addps xmm2, xmm3
movss [rax+4], xmm2
mulps xmm0,xmm7
//mix1
movaps xmm3, xmm0
shufps xmm3, xmm3, $4e
addps xmm0, xmm3
//mix2
movaps xmm3, xmm0
shufps xmm3, xmm3, $11
addps xmm0, xmm3
movss [rax+8], xmm0
end;
{$ELSE}
asm
mov eax, M
movaps xmm0, [eax]
mov eax, N
movaps xmm2,xmm0
mulps xmm2,xmm5
//mix1
movaps xmm3, xmm2
shufps xmm3, xmm3, $4e
addps xmm2, xmm3
//mix2
movaps xmm3, xmm2
shufps xmm3, xmm3, $11
addps xmm2, xmm3
movss [eax], xmm2
movaps xmm2,xmm0
mulps xmm2,xmm6
//mix1
movaps xmm3, xmm2
shufps xmm3, xmm3, $4e
addps xmm2, xmm3
//mix2
movaps xmm3, xmm2
shufps xmm3, xmm3, $11
addps xmm2, xmm3
movss [eax+4], xmm2
mulps xmm0,xmm7
//mix1
movaps xmm3, xmm0
shufps xmm3, xmm3, $4e
addps xmm0, xmm3
//mix2
movaps xmm3, xmm0
shufps xmm3, xmm3, $11
addps xmm0, xmm3
movss [eax+8], xmm0
end;
{$ENDIF}
M.t := oldMt;
N.t := 0;
end;
procedure MatrixMultiplyVect3D_SSE3_Aligned(var M: TPoint3D_128; out N: TPoint3D_128);
var oldMt: single;
begin
oldMt := M.t;
M.t := SingleConst1;
{$IFDEF cpux86_64}
asm
mov rax, M
movaps xmm0, [rax]
mov rax, N
movaps xmm2,xmm0
mulps xmm2,xmm5
haddps xmm2,xmm2
haddps xmm2,xmm2
movss [rax], xmm2
movaps xmm2,xmm0
mulps xmm2,xmm6
haddps xmm2,xmm2
haddps xmm2,xmm2
movss [rax+4], xmm2
mulps xmm0,xmm7
haddps xmm0,xmm0
haddps xmm0,xmm0
movss [rax+8], xmm0
end;
{$ELSE}
asm
mov eax, M
movaps xmm0, [eax]
mov eax, N
movaps xmm2,xmm0
mulps xmm2,xmm5
haddps xmm2,xmm2
haddps xmm2,xmm2
movss [eax], xmm2
movaps xmm2,xmm0
mulps xmm2,xmm6
haddps xmm2,xmm2
haddps xmm2,xmm2
movss [eax+4], xmm2
mulps xmm0,xmm7
haddps xmm0,xmm0
haddps xmm0,xmm0
movss [eax+8], xmm0
end;
{$ENDIF}
M.t := oldMt;
end;
procedure MatrixMultiplyVect3DWithoutTranslation_SSE_Aligned(
var M: TPoint3D_128; out N: TPoint3D_128);
begin
{$IFDEF cpux86_64}
asm
mov rax, M
movaps xmm0, [rax]
mov rax, N
movaps xmm2,xmm0
mulps xmm2,xmm5
//mix1
movaps xmm3, xmm2
shufps xmm3, xmm3, $4e
addps xmm2, xmm3
//mix2
movaps xmm3, xmm2
shufps xmm3, xmm3, $11
addps xmm2, xmm3
movss [rax], xmm2
movaps xmm2,xmm0
mulps xmm2,xmm6
//mix1
movaps xmm3, xmm2
shufps xmm3, xmm3, $4e
addps xmm2, xmm3
//mix2
movaps xmm3, xmm2
shufps xmm3, xmm3, $11
addps xmm2, xmm3
movss [rax+4], xmm2
mulps xmm0,xmm7
//mix1
movaps xmm3, xmm0
shufps xmm3, xmm3, $4e
addps xmm0, xmm3
//mix2
movaps xmm3, xmm0
shufps xmm3, xmm3, $11
addps xmm0, xmm3
movss [rax+8], xmm0
end;
{$ELSE}
asm
mov eax, M
movaps xmm0, [eax]
mov eax, N
movaps xmm2,xmm0
mulps xmm2,xmm5
//mix1
movaps xmm3, xmm2
shufps xmm3, xmm3, $4e
addps xmm2, xmm3
//mix2
movaps xmm3, xmm2
shufps xmm3, xmm3, $11
addps xmm2, xmm3
movss [eax], xmm2
movaps xmm2,xmm0
mulps xmm2,xmm6
//mix1
movaps xmm3, xmm2
shufps xmm3, xmm3, $4e
addps xmm2, xmm3
//mix2
movaps xmm3, xmm2
shufps xmm3, xmm3, $11
addps xmm2, xmm3
movss [eax+4], xmm2
mulps xmm0,xmm7
//mix1
movaps xmm3, xmm0
shufps xmm3, xmm3, $4e
addps xmm0, xmm3
//mix2
movaps xmm3, xmm0
shufps xmm3, xmm3, $11
addps xmm0, xmm3
movss [eax+8], xmm0
end;
{$ENDIF}
end;
procedure MatrixMultiplyVect3DWithoutTranslation_SSE3_Aligned(
var M: TPoint3D_128; out N: TPoint3D_128);
begin
{$IFDEF cpux86_64}
asm
mov rax, M
movaps xmm0, [rax]
mov rax, N
movaps xmm2,xmm0
mulps xmm2,xmm5
haddps xmm2,xmm2
haddps xmm2,xmm2
movss [rax], xmm2
movaps xmm2,xmm0
mulps xmm2,xmm6
haddps xmm2,xmm2
haddps xmm2,xmm2
movss [rax+4], xmm2
mulps xmm0,xmm7
haddps xmm0,xmm0
haddps xmm0,xmm0
movss [rax+8], xmm0
end;
{$ELSE}
asm
mov eax, M
movaps xmm0, [eax]
mov eax, N
movaps xmm2,xmm0
mulps xmm2,xmm5
haddps xmm2,xmm2
haddps xmm2,xmm2
movss [eax], xmm2
movaps xmm2,xmm0
mulps xmm2,xmm6
haddps xmm2,xmm2
haddps xmm2,xmm2
movss [eax+4], xmm2
mulps xmm0,xmm7
haddps xmm0,xmm0
haddps xmm0,xmm0
movss [eax+8], xmm0
end;
{$ENDIF}
end;
{$ENDIF}
function MatrizMult({$IFDEF OBJ}constref{$ELSE}const{$ENDIF} A: TMatrix3D; var M: TPoint3D_128): TPoint3D_128;
{$IFDEF BGRASSE_AVAILABLE}var oldMt: single; resultAddr: pointer;{$ENDIF}
begin
{$IFDEF BGRASSE_AVAILABLE}
if UseSSE then
begin
oldMt := M.t;
M.t := SingleConst1;
resultAddr := @result;
{$IFDEF cpux86_64}
if UseSSE3 then
asm
mov rax, A
movups xmm5, [rax]
movups xmm6, [rax+16]
movups xmm7, [rax+32]
mov rax, M
movups xmm0, [rax]
mov rax, resultAddr
movaps xmm4,xmm0
mulps xmm4,xmm5
haddps xmm4,xmm4
haddps xmm4,xmm4
movss [rax], xmm4
movaps xmm4,xmm0
mulps xmm4,xmm6
haddps xmm4,xmm4
haddps xmm4,xmm4
movss [rax+4], xmm4
mulps xmm0,xmm7
haddps xmm0,xmm0
haddps xmm0,xmm0
movss [rax+8], xmm0
end else
asm
mov rax, A
movups xmm5, [rax]
movups xmm6, [rax+16]
movups xmm7, [rax+32]
mov rax, M
movups xmm0, [rax]
mov rax, resultAddr
movaps xmm4,xmm0
mulps xmm4,xmm5
//mix1
movaps xmm3, xmm4
shufps xmm3, xmm3, $4e
addps xmm4, xmm3
//mix2
movaps xmm3, xmm4
shufps xmm3, xmm3, $11
addps xmm4, xmm3
movss [rax], xmm4
movaps xmm4,xmm0
mulps xmm4,xmm6
//mix1
movaps xmm3, xmm4
shufps xmm3, xmm3, $4e
addps xmm4, xmm3
//mix2
movaps xmm3, xmm4
shufps xmm3, xmm3, $11
addps xmm4, xmm3
movss [rax+4], xmm4
mulps xmm0,xmm7
//mix1
movaps xmm3, xmm0
shufps xmm3, xmm3, $4e
addps xmm0, xmm3
//mix2
movaps xmm3, xmm0
shufps xmm3, xmm3, $11
addps xmm0, xmm3
movss [rax+8], xmm0
end;
{$ELSE}
if UseSSE3 then
asm
mov eax, A
movups xmm5, [eax]
movups xmm6, [eax+16]
movups xmm7, [eax+32]
mov eax, M
movups xmm0, [eax]
mov eax, resultAddr
movaps xmm4,xmm0
mulps xmm4,xmm5
haddps xmm4,xmm4
haddps xmm4,xmm4
movss [eax], xmm4
movaps xmm4,xmm0
mulps xmm4,xmm6
haddps xmm4,xmm4
haddps xmm4,xmm4
movss [eax+4], xmm4
mulps xmm0,xmm7
haddps xmm0,xmm0
haddps xmm0,xmm0
movss [eax+8], xmm0
end else
asm
mov eax, A
movups xmm5, [eax]
movups xmm6, [eax+16]
movups xmm7, [eax+32]
mov eax, M
movups xmm0, [eax]
mov eax, resultAddr
movaps xmm4,xmm0
mulps xmm4,xmm5
//mix1
movaps xmm3, xmm4
shufps xmm3, xmm3, $4e
addps xmm4, xmm3
//mix2
movaps xmm3, xmm4
shufps xmm3, xmm3, $11
addps xmm4, xmm3
movss [eax], xmm4
movaps xmm4,xmm0
mulps xmm4,xmm6
//mix1
movaps xmm3, xmm4
shufps xmm3, xmm3, $4e
addps xmm4, xmm3
//mix2
movaps xmm3, xmm4
shufps xmm3, xmm3, $11
addps xmm4, xmm3
movss [eax+4], xmm4
mulps xmm0,xmm7
//mix1
movaps xmm3, xmm0
shufps xmm3, xmm3, $4e
addps xmm0, xmm3
//mix2
movaps xmm3, xmm0
shufps xmm3, xmm3, $11
addps xmm0, xmm3
movss [eax+8], xmm0
end;
{$ENDIF}
M.t := oldMt;
result.t := 0;
end else
{$ENDIF}
begin
result.x := M.x * A[1,1] + M.y * A[1,2] + M.z * A[1,3] + A[1,4];
result.y := M.x * A[2,1] + M.y * A[2,2] + M.z * A[2,3] + A[2,4];
result.z := M.x * A[3,1] + M.y * A[3,2] + M.z * A[3,3] + A[3,4];
result.t := 0;
end;
end;
function MultiplyVect3DWithoutTranslation({$IFDEF OBJ}constref{$ELSE}const{$ENDIF} A: TMatrix3D; {$IFDEF OBJ}constref{$ELSE}const{$ENDIF} M: TPoint3D_128): TPoint3D_128;
begin
{$IFDEF BGRASSE_AVAILABLE}
if UseSSE then
begin
if UseSSE3 then
asm
mov eax, A
movups xmm5, [eax]
movups xmm6, [eax+16]
movups xmm7, [eax+32]
mov eax, M
movups xmm0, [eax]
mov eax, result
movaps xmm4,xmm0
mulps xmm4,xmm5
haddps xmm4,xmm4
haddps xmm4,xmm4
movss [eax], xmm4
movaps xmm4,xmm0
mulps xmm4,xmm6
haddps xmm4,xmm4
haddps xmm4,xmm4
movss [eax+4], xmm4
mulps xmm0,xmm7
haddps xmm0,xmm0
haddps xmm0,xmm0
movss [eax+8], xmm0
end else
asm
mov eax, A
movups xmm5, [eax]
movups xmm6, [eax+16]
movups xmm7, [eax+32]
mov eax, M
movups xmm0, [eax]
mov eax, result
movaps xmm4,xmm0
mulps xmm4,xmm5
//mix1
movaps xmm3, xmm4
shufps xmm3, xmm3, $4e
addps xmm4, xmm3
//mix2
movaps xmm3, xmm4
shufps xmm3, xmm3, $11
addps xmm4, xmm3
movss [eax], xmm4
movaps xmm4,xmm0
mulps xmm4,xmm6
//mix1
movaps xmm3, xmm4
shufps xmm3, xmm3, $4e
addps xmm4, xmm3
//mix2
movaps xmm3, xmm4
shufps xmm3, xmm3, $11
addps xmm4, xmm3
movss [eax+4], xmm4
mulps xmm0,xmm7
//mix1
movaps xmm3, xmm0
shufps xmm3, xmm3, $4e
addps xmm0, xmm3
//mix2
movaps xmm3, xmm0
shufps xmm3, xmm3, $11
addps xmm0, xmm3
movss [eax+8], xmm0
end;
end else
{$ENDIF}
begin
result.x := M.x * A[1,1] + M.y * A[1,2] + M.z * A[1,3];
result.y := M.x * A[2,1] + M.y * A[2,2] + M.z * A[2,3];
result.z := M.x * A[3,1] + M.y * A[3,2] + M.z * A[3,3];
result.t := 0;
end;
end;
function MatrizMult(A,B: TMatrix3D): TMatrix3D;
begin
multiplyVect3(A, B[1,1],B[2,1],B[3,1],0, result[1,1],result[2,1],result[3,1]);
multiplyVect3(A, B[1,2],B[2,2],B[3,2],0, result[1,2],result[2,2],result[3,2]);
multiplyVect3(A, B[1,3],B[2,3],B[3,3],0, result[1,3],result[2,3],result[3,3]);
multiplyVect3(A, B[1,4],B[2,4],B[3,4],1, result[1,4],result[2,4],result[3,4]);
end;
function MatrixIdentity3D: TMatrix3D;
begin
result := Matrix3D( 1,0,0,0,
0,1,0,0,
0,0,1,0);
end;
function Matrix3D(m11, m12, m13, m14, m21, m22, m23, m24, m31, m32, m33,
m34: single): TMatrix3D;
begin
result[1,1] := m11;
result[1,2] := m12;
result[1,3] := m13;
result[1,4] := m14;
result[2,1] := m21;
result[2,2] := m22;
result[2,3] := m23;
result[2,4] := m24;
result[3,1] := m31;
result[3,2] := m32;
result[3,3] := m33;
result[3,4] := m34;
end;
function MatrixInverse3D(A: TMatrix3D): TMatrix3D;
var ofs: TPoint3D;
begin
ofs := Point3D(A[1,4],A[2,4],A[3,4]);
result[1,1] := A[1,1];
result[1,2] := A[2,1];
result[1,3] := A[3,1];
result[1,4] := 0;
result[2,1] := A[1,2];
result[2,2] := A[2,2];
result[2,3] := A[3,2];
result[2,4] := 0;
result[3,1] := A[1,3];
result[3,2] := A[2,3];
result[3,3] := A[3,3];
result[3,4] := 0;
result := MatrizMult(result,MatrixTranslation3D(-ofs));
end;
function Matrix3D(vx, vy, vz, ofs: TPoint3D): TMatrix3D;
begin
result := Matrix3D(vx.x, vy.x, vz.x, ofs.x,
vx.y, vy.y, vz.y, ofs.y,
vx.z, vy.z, vz.z, ofs.z);
end;
function Matrix3D(vx, vy, vz, ofs: TPoint3D_128): TMatrix3D;
begin
result := Matrix3D(vx.x, vy.x, vz.x, ofs.x,
vx.y, vy.y, vz.y, ofs.y,
vx.z, vy.z, vz.z, ofs.z);
end;
function MatrixTranslation3D(ofs: TPoint3D): TMatrix3D;
begin
result := Matrix3D(1,0,0,ofs.x,
0,1,0,ofs.Y,
0,0,1,ofs.z);
end;
function MatrixScale3D(size: TPoint3D): TMatrix3D;
begin
result := Matrix3D(size.x,0,0,0,
0,size.y,0,0,
0,0,size.z,0);
end;
function MatrixRotateX(angle: single): TMatrix3D;
begin
result := Matrix3D( 1, 0, 0, 0,
0, cos(angle), sin(angle), 0,
0, -sin(angle), cos(angle), 0);
end;
function MatrixRotateY(angle: single): TMatrix3D;
begin
result := Matrix3D( cos(angle), 0, -sin(angle), 0,
0, 1, 0, 0,
sin(angle), 0, cos(angle), 0);
end;
function MatrixRotateZ(angle: single): TMatrix3D;
begin
result := Matrix3D( cos(angle), sin(angle), 0, 0,
-sin(angle), cos(angle), 0, 0,
0, 0, 1, 0);
end;
end.