Abstract: Scalar fields guided deformation is one of the hot research issues in computer graphics.However, the problem of time efficiency of SFD is yet not to be solved. In this paper, a GPU-based shape deformation algorithm is proposed,integrating the advantage of both the representations of ADFs (adaptively sampled distance fields) and the physically-based modeling techniques.The octree-based ADFs are constructed and represented on the GPU. Then the deformation of the ADFs is governed by the principle of physical dynamics and achieved by manipulating the scalar fields directly. The algorithm constructs the ADFs and represents the octree structure on the GPU, which processes all the octree nodes at the same depth in parallel and provides fast access to the ADFs nodes with the look up tables. A dynamic adaptive resampling strategy for ADFs is employed during the deformation. Meanwhile, the physical properties are integrated into irregular fields for deformation and the stiffness of the non-uniform springs in the system is adaptive to spatial resolution of ADFs to avoid non-homogeneity in physics caused by the irregular structure. The results show that the time and space efficiency of our physically-based deformation algorithm based on the representation of ADFs are relatively high, which is over one order of magnitude faster than CPU algorithm. It also implies the algorithm has potential applications in physically-based interactive sculpting.