Hierarchical least squares conformal map

A texture atlas is an efficient way to represent information (like colors, normals, displacement maps) on triangulated surfaces. The LSCM method (Least Square Conformal Maps) automatically generates a texture atlas from a meshed model. For large charts (over 100k facets), the convergence of the numerical solver may be slow. It is well known that the conformality criterion, minimized by LSCM, also corresponds to a harmonically condition, meaning that barycentric coordinates are locally preserved through the parametization. This has two different consequences: cascadic multigrid methods (coarse to fine) are well adapted to this criterion, and dramatically speed up the convergence of the numerical solver; the obtained parametization naturally minimizes texture swimming when used to texture-map a progressive mesh. In this paper, we introduce HLSCM (Hierarchical LSCM), a cascadic multigrid version of LSCM. As an example of possible applications, the paper shows how normal maps and simplified models can be automatically generated from large scanned meshes, the visual appearance of the model can be preserved even when 90% of the vertices are removed from the initial model.