Mesh Processing Using On-the-Fly Connectivity Reconstruction Given by Regular Triangulations

Several applications in visual and geometric computing require the ability to modify graphical models in such way that geometric queries or high quality renderings can be generated with great accuracy. Polygonal meshes are the popular choice of representation, and several mesh processing operations such as morphing, level-of-detail or deformation, among others, introduce challenges on how this task can be performed. A common problem that arises in such applications is that the result of a mesh processing operation can either require a costly mesh re-computation, thus impairing real-time usage, or it requires constant updates and additional storage to keep several information required to perform this task. In particular, the topological information is often harder to maintain updated, since it is often destroyed or modified during such operations. In this work we propose a new framework to reconstruct connectivity information in such way that the quality of the mesh can be recovered. The connectivity retrieval is accomplished by assigning weights to the vertices of the triangulation, converting it in a regular triangulation. Once weights have been computed, the connectivity can be rebuild by algorithms devoted to construct regular triangulation. The effectiveness of our new paradigm is illustrated through two mesh processing applications: mesh morphing and level-of-detail rendering.