On 3D Shape Synthesis

We present a novel approach to 3D shape synthesis of closed surfaces. A curved or polyhedral 3D object of genus zero is represented by a curvature distribution on a spherical mesh that has nearly uniform distribution with known connectivity among mesh nodes. This curvature distribution, i.e., the result of forward mapping from shape space to curvature space, is used as the intrinsic shape representation because it is invariant to rigid transformation and scale factor. Furthermore, with regularity constraints on the mesh, the inverse mapping from curvature space to shape space always exists and can be recovered using an iterative method. Therefore, the task of synthesizing a new shape from two known objects becomes one of interpolating the two known curvature distributions, and then mapping the interpolated curvature distribution back to a 3D morph. Using the distance between two curvature distributions, we can quantitatively control the shape synthesis process to yeild smooth curvature migration. Experiments show that our method produces smooth and realistic shape morphs.