In this paper, we propose a complete 3D mesh morphing technique dedicated to closed, genus-0 3D models. The two 3D objects are first mapped onto a common spherical domain. For this purpose, we employ a parameterization method, based on a modified version of the Gaussian curvature, that returns a locally flattened version of the original model with a quasi convex structure, which can be simply projected onto the unit sphere. By overlapping the two embeddings and warping them in a suitable manner with the aid of RBF functions, we establish a correspondence between the models. We also introduce a new method to create a metamesh model that share the topology of both input objects and which can easily be transformed from the source model into the target. The experimental results obtained show that the obtained transitions are smooth, consistent with respect to both geometry and topology, and visually pleasant.