Triangle meshes are widely used to represent 3D surfaces in geometry processing, with applications across physical simulation, visual computing, and geometric learning. Intrinsic triangulations depart from the usual formulation for a triangle mesh: rather than storing a position associated with each vertex, we instead store a length associated with each edge. This viewpoint, rich in theory from discrete differential geometry, enables powerful new algorithms by operating in a more general space of triangulations.

This thesis will explore the theory and practice of intrinsic triangulations in geometry processing. Presented advancements will include a new signpost data structure for efficiently encoding intrinsic triangulations, an algorithm for computing geodesic paths via intrinsic edge flips, and a generalized covering space which extends intrinsic triangulations to nonmanifold meshes and even point clouds. In practice, we will show how intrinsic triangulations offer a much-needed solution for robust geometry processing, enabling existing algorithms to operate directly on low-quality data encountered in practice.

Thesis Committee:
Keenan Crane (Chair)
Ioannis Gkioulekas
Anupam Gupta
Maks Ovsjanikov (École Polytechnique)

Zoom Participation. See announcement.