Abstract: It is a challenging problem to effectively edit mesh data in computer graphics. This paper develops a novel framework to achieve high performance and shape preservation. For the static triangular meshes, a deformation-aware simplification is first introduced to build a hierarchical representation, and then the deformation of the simplified mesh is passed to the original mesh to efficiently obtain an initial result. Lastly, a set of rigid transformations is iteratively computed to preserve the shape features and arrive at the final deformation result. Moreover, the above idea is extended to the time-varying mesh sequences to address spacetime deformation, deformation transfer and shape interpolation. The experiments show that our framework accommodates dense meshes and generates versatile results even under large deformations.