Date of Award

2015

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

McDonald, Patrick

Keywords

Geodesic Distance Computation, Geometry, Heat Method

Area of Concentration

Mathematics

Abstract

The computation of the geodesic distance to a point or subset of a given domain is a basic and expedient problem, with applications ranging from computer graphics to robot motion to medical imaging. We explore the recently developed heat method of geodesic distance computation, a versatile technique that can be adapted to many types of discrete objects generalizing smooth geometric objects (triangle meshes, more general polygonal meshes, point cloud data). We cover the motivating theory in the smooth setting; we also introduce aspects of discrete differential geometry. The heat method is then tested for efficacy on a selection of triangle meshes. These include common meshes used for benchmarking as well as meshes taken from digital design files intended for 3D printing and other applications. We simultaneously investigate the choice of time step for the implicit Euler integration used in the heat method.

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