M.Sc Thesis

M.Sc StudentMogilnitsky Maxim
SubjectEfficient, Low Distortion, Conformal Parameterization
of Large Meshes
DepartmentDepartment of Computer Science
Supervisors PROF. Moshe Israeli (Deceased)
MRS Alla Sheffer


Parameterization of discrete surfaces is a fundamental and widely used operation in graphics, required, for instance, for texture mapping and remeshing. As 3D surfaces become more and more detailed, there is an increased need for fast techniques, capable of finding low-distortion conformal parameterizations of very large meshes. Based on Riemann theorem any smooth surface can be mapped conformally to a planar domain. This is not strictly true for a mesh, since a mesh is not smooth. However, a mesh can still be mapped to a planar domain with little conformal distortion. Existing parameterization methods either require a predefined convex boundary, such as harmonic or mean value techniques, or are slow and consume a lot of computational resources, thus making them impractical for large meshes. In this work we combine some of the best features of the existing schemes such as free boundaries and low distortion. The combined technique is accelerated by our coarse-to-fine multi-resolution technique. The presented method is fast and able to parameterize meshes with millions of faces in reasonable time. The mesh is first simplified by a simplifier adapted for this purpose. Then, the obtained coarse mesh is parameterized using the angle-based flattening algorithm. Finally, we restore the mesh resolution while continuously updating the parameterization of the current resolution. In our experiments the approach demonstrates good results for linear as well as non-linear parameterization update techniques. For medium size meshes we present a comparison to compatible parameterization techniques, showing that the drastic speed improvement we achieve does not decrease the parameterization quality.