Recent Trends in Surface Parameterization Design

Marco Tarini, University of Insubria, Varese, Italy
Friday, November 4, 2011, 12:00pm
CAB, G 59


We all know how a good deal of research in CG went into 'finding good parameterizations of digital surfaces'. This is because automating that task is a precondition in countless important CG applications (all texture mapping based ones and remeshing, to name just two categories). But even the very meaning of the above sentence in quotes undergoes evolution, as our understanding of the nature of this intricate but crucial challenge improves. This talk describes two such evolutions, which we believe to be emerging trends, jointly with a couple of recent specific techniques stemming from these considerations.

Specifically: 1) For 'good parameterizations' it was originally meant, mostly, preservation of angles and areas. Then, in turn, also: seamlessness (few discontinuities, masked by well-behaved transition functions), global smoothness (continuity of gradient directions), adherence to a given target cross field, and, eventually, \emph{locally} good placement of cone singularities. The next step, in this catenation of desiderata, seem to be \emph{globally} good placement of cone singularities, by which we mean to also target their reciprocal alignment. The talk will expose what is motivating us toward this (n+1)-th objective, as well as a pioneering approach to purse that (striving not to lose contact with the other n).

2) For 'digital surfaces' it is usually meant, almost exclusively: triangulated meshes which are two-manifold and free from topological noise or artifacts (often even waterproof). However, the more we are advancing in this field, and the bolder we get in applying it to complex real-world models (think of what comes out of present-day range scanning techniques), the more it becomes evident that this ideal case is often just not realistic. The standard pipeline of work, which dictates that the digital surface must first undergo several stages of heavy duty preprocessing until is made totally clean and coherent, might be becoming of limited applicability too. Let's see, instead, what can be done to extend the concept of parametrization-design by making this step drastically less strict in what it takes as input.