Generate Sweep of non-planar surface from rotation matrices and translation vectors

I need to be able to approximate the swept volume generated by sweeping a 2d-surface (possibly non-planar) in 3d-space. The sweep can be parametrized by a 3x3 rotation matrix R(t) depending on a parameter t (we can think of it as time) and a translation vector also depending on t.

In the documentation I have seen the class BRepOffsetAPI_MakeEvolved which can generate a 3d-solid by moving a (planar) shape along a wire. I could take one point of my shape and apply the rotation and translation to get a wire. However then as far as I understood the shape will always have the same orientation w.r.t. the wire. This is not what I want, since in my case the orientation is given by the rotation matrix R(t).

Is there any possibility to compute the swept volumes also for non-planar shapes and with the possibility to prescribe the orientation of the shape with a function of time?