Abstract: Acquisition of dynamic geometry is easier today. This makes compact and editable representations of source animated meshes more and more fascinating. Though several cage-based methods have been developed for reverse engineering of animated 3D models, none of them is truly error controllable. We address the problem by introducing a framework which alternatively repeats a dense cage reconstruction and a sparse cage reconstruction until the meshes recovered from the reconstructed cage sequence can approximate the source 3D models within a user specified error. We employ a usual cage-based reverse engineering method to fit a cage sequence to the source meshes with dense coordinates at the first phase and then reconstruct a new cage sequence with Poisson based reduction weights at the second phase. Different from existing methods, we allow updating the geometry (moving the control points) and topology (inserting new control points) of the reference cage according to the approximating accuracy. With the reconstructed cages as well as a set of sparse coordinates (or reduction weights), we can efficiently recover the animated sequence.