In this paper, we introduce a parallel numerical scheme, the lattice Boltzmann method, to shape modeling applications. The motivation of using this originally-designed fluid dynamics solver in surface modeling is its simplicity, locality, parallelism from the cellular-automata-originated updating rules, which can directly be mapped onto modern graphics hardware. A surface is implicitly represented by the signed distance field. The distances are then used in a modified LBM scheme as its computing primitive, instead of the densities in traditional LBM. The scheme can simulate curvature motions to smooth the surface with a diffusion process. Furthermore, an initial value level set method can be implemented for surface morphing. The distance difference between a morphing surface and a target surface defines the speed function of the evolving level sets, and is used as the driving force in the LBM. Our GPUaccelerated LBM algorithm has achieved outstanding performance for the denoising ...