Friday, July 31, 2009

Almost isometric mesh parameterization

A short post after a long inactivity just before going to Siggraph.

Many users of MeshLab complained the lack of texturing tools. As you probably know perfect, nice, clean, robust, automatic texture parametrization is a kind of 'holy grail' in CG. There are many many solutions around and a huge literature on that, but no silver bullet.
We (mostly Nico and Marco) added our 5 cents to the literature with yet another approach [1] that is able to produce parametrizations that exhibit a very low distortion and are composed by a small number of large regular patches. The parametrization domain is a collection of equilateral triangular 2D regions enriched with explicit adjacency relationships (we call it abstract because no explicit 3D embedding is necessary). It is tailored in order to minimize the distortion, resulting in excellent parametrization qualities, even when meshes with complex shapes and topology are mapped into domains composed of a small number of large contiguous regions.

An interesting consequence of having a texturing domain that is composed by 'abstract' equilateral triangles is that you can exploit this parametrization to build high quality remeshing that are better that the current state of the art. Look at the top figures to get an idea of the quality of the produced meshes. As usual all the gory details of the technique in the below paper preprint and a working open source implementation in the next versions of MeshLab.

[1] Nico Pietroni, Marco Tarini, Paolo Cignoni, Almost isometric mesh parameterization through abstract domains, IEEE Transaction on Visualization and Computer Graphics, Volume In press - 2009