SumofSquares Geometry Processing
Abstract
Geometry processing presents a variety of difficult numerical problems, each seeming to require its own tailored solution. This breadth is largely due to the expansive list of geometric primitives, e.g., splines, triangles, and hexahedra, joined with an everexpanding variety of objectives one might want to achieve with them. With the recent increase in attention toward higherorder surfaces, we can expect a variety of challenges porting existing solutions that work on triangle meshes to work on these more complex geometry types. In this paper, we present a framework for solving many core geometry processing problems on higherorder surfaces. We achieve this goal through sumofsquares optimization, which transforms nonlinear polynomial optimization problems into sequences of convex problems whose complexity is captured by a single degree parameter. This allows us to solve a suite of problems on higherorder surfaces, such as continuous collision detection and closest point queries on curved patches, with only minor changes between formulations and geometries.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.08451
 Bibcode:
 2021arXiv211008451M
 Keywords:

 Computer Science  Computational Geometry;
 Computer Science  Graphics;
 I.3.5
 EPrint:
 doi:10.1145/3478513.3480551