Speaker: Nathan King
Abstract
Objects can be represented in various forms, including meshes, point clouds, parameterizations, and neural implicits. Traditionally, many algorithms are limited to a single specific representation. We focus on geometry processing with any representation supporting closest-point queries, making these methods universally applicable. Furthermore, objects can be manifold or nonmanifold, open or closed, orientable or not, and of any codimension or even mixed codimension.
Our work solves PDEs common in geometry processing using the closest point method (CPM). We develop fundamental extensions of CPM to enable its use for the first time with many applications in geometry processing. The major impediment was the inability to impose interior boundary conditions (IBCs) with CPM. We develop a general framework for IBC enforcement that also only requires closest point queries. We then deviate from the common grid-based CPM and further develop a discretization-free CPM by extending a Monte Carlo method to surface PDEs. This enables CPM to enjoy common benefits of Monte Carlo methods, e.g., localized solutions, which are useful for view-dependent applications. Finally, interesting open problems in closest point geometry processing are discussed.
Bio
Nathan King is a Research Scientist at Shapr3D, where he focuses on geometric modelling and physics simulation. His recent PhD at the University of Waterloo developed computational methods involving closest point representations, with a particular interest in geometry processing and physics-based animation applications.