10.5 3D transformation matrix

A 3D matrix is alist in the form [vector3D1, vector3D2, vector3D3, vector3D4]. That list represent the analytic expression of a space affine map. This is a three vectors list: vector3D1 that 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 that is the third column vector of the matrix of the linear part.

If f is a space affine map, then its linear part is Lf=f-f(Origin), the translation vector is f(Origin), and its matrix is: [f(Origin), Lf(vecI), Lf(vecJ), Lf(vecK)].

For example, the matrix of the identity is: [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 ComposeMatrix3D, GetMatrix3D, SetMatrix3D and IdMatrix3D.

  10.5.1 invmatrix3d
  10.5.2 matrix3d
  10.5.3 mulmatrix3d