M.Sc. Thesis Defense: 5-6-7 Meshes - Nima Aghdaii
This thesis introduces a new type of meshes called 5-6-7 meshes. For many mesh processing tasks, low- or high-valence vertices are undesirable. At the same time, it is not always possible to achieve complete vertex valence regularity, i.e., to only have valence-6 vertices. A 5-6-7 mesh is a closed triangle mesh where each vertex has valence 5, 6, or 7. An intriguing question is whether it is always possible to convert an arbitrary mesh into a 5-6-7 mesh.
We answer this question in the positive by presenting a 5-6-7 remeshing algorithm which converts a closed triangle mesh with arbitrary genus into a 5-6-7 mesh, which closely approximates the geometry of the original mesh and has a comparable vertex count as the original mesh. We demonstrate the results of our remeshing algorithm on meshes with sharp features and different topology and complexity.