#### 10.2.16 Mtransform3D

• Mtransform3D( <3Dpoints list>, <3dmatrix> )
• Description: that function returns the <3Dpoints list> transformed by the <3dmatrix>. This marix represents the analytic expression of an affine map of the space, this is a three vectors list: the vector3D1 is the translation vector, vector3D2 is the first column vector of the matrix of the linear part in the canonical base, vector3D3 is the second column vector of the matrix of the linear part, and vector3D4 is the third column vector of the matrix of the linear part. For example, the matrix of the identity is written like the following: [M(0,0,0), M(1,0,0), M(0,1,0), M(0,0,1)] or [Origin, vecI, vecJ, vecK] (this is the default matrix). (See also the commands GetMatrix3D, ComposeMatrix3D, and IdMatrix3D).

 \begin{texgraph}[name=Mtransform3D,export=pgf]    view(-5,5,-3,6), Marges(0,0,0,0), size(7.5),    viewDir(115,70),    P:=shift3d(Pyramide( [Origin,M(1,-1,0),M(3,1,0),                   M(3,3,0),M(1,4,0)],M(1,1,3)),2*vecJ),    miroir:=[M(-4,0,0),M(4,0,0),M(4,0,5),M(-4,0,5),jump],    P’:=reverse3d( Mtransform3D( P,                      matrix3d(sym3d(M,[Origin,vecJ])))),    FillStyle:=full, FillColor:=brown, Width:=8,    DrawFacet( P’, [color:=FillColor]),    DrawFacet( miroir,                   [FillOpacity:=0.5, color:=lightgray]             ),    DrawPoly(P,4)   \end{texgraph}

The Mtransform3D() command