Again create your own region. Its “center of mass” follows the nonlinear flow, while the region follows the linearized flow (about the trajectory of the center of mass). Polygonal shape is preserved (linearity!), but generally neither lengths, areas, nor angles are preserved. Options allow to use only geometrically important parts -- e.g. the flow of the skew symmetric part, or the trace of the linearization (integral versions of curl and divergence!)