Title: Next-Generation Geometry Processing: From Numerical to Symbolic Computation

Abstract:
Geometry Processing has now reached its maturity. Methods that are both efficient and robust have been developed, for difficult problems such as discrete fairing, mesh parameterization and surface reconstruction... However, most problems are far away from being closed. One of the difficulty is the more and more elaborate mathematical formalism used by the community, leading to complicated numerical optimization methods. Transforming the theory into efficient software requires a deep understanding of the underlying mathematics, and non-trivial manipulations of the equations. Traditionally, algebraic transforms of these equations can be automatically computed by CAS (Computer Algebra Software) then copy-pasted in the numerical optimization code. Our vision is that next generation geometry processing will need a new class of optimization methods, where symbolic and numerical interact in a tighter and more dynamic way. We demonstrate this point of view applied to non-linear geometry processing and to information theory (sampling).