B43: Diffusion-based parametrization of surfaces on 3D-meshes

Schmidt,M., Guthe,M., Blanz,V.

This work presents a new approach towards parametrization on three-dimensional wireframe models. The method is derived from a specific phenomenon of cellular development in nature. It recreates the effect of diffusion of messengers through tissue, which leads to the formation of extremities and other anatomical structures depending on the position on the tissue surface. This process of diffusion on the surface is analyzed and simplified for usage as a parametrization of mesh surfaces. The presented approach uses the similarity of wireframe meshes and graphs in order to carry out the mechanism of diffusion. For this it implements a specialized algorithm based on Dijkstra's algorithm for finding the shortest paths.
The results of this mechanism are saved and organized in a binary tree structure, which allows for simple and efficient con-struction of correspondence between two distinct meshes. The paper concludes with an outlook on possibilities of further development and enhancements of the approach.