Computer Science Thesis Proposal

  • Remote Access - Zoom
  • Virtual Presentation - ET
  • NICHOLAS SHARP
  • Ph.D. Student
  • Computer Science Department
  • Carnegie Mellon University
Thesis Proposals

Intrinsic Triangulations in Geometry Processing

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.

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