We propose a new adaptive space deformation method for interactive shape modeling. A novel energy formulation based on elastically coupled volumetric cells yields intuitive detail preservation even under large deformations. By enforcing rigidity of the cells, we obtain an extremely robust numerical solver for the resulting nonlinear optimization problem. Scalability is achieved using an adaptive spatial discretization that is decoupled from the resolution of the embedded object. Our approach is versatile and easy to implement, supports thin-shell and solid deformations of 2D and 3D objects, and is applicable to arbitrary sample-based representations, such as meshes, triangle soups, or point clouds. © 2007 The Eurographics Association and Blackwell Publishing Ltd.