Applications of Geometric Algebra in Mathematical Engineering


Type
Thesis
Change log
Authors
Abstract

Geometric Algebra (GA) has found success in various areas of the physical sciences and engineering over the last decade but remains relatively underutilised in industry and several key topics in the field remain unexplored. This thesis focuses on the practical applications of Geometric Algebra in various interconnected areas of mathematical engineering. In Part I we explore the properties of the objects resulting from the addition of blades in Conformal Geometric Algebra (CGA) and how we might use these objects in computer graphics and robotics algorithms. In Part II we explore how Screw Theory embeds into CGA, how to use this embedding for simulation of the dynamics of rigid bodies, and how practitioners can leverage the geometric primitives built into CGA to represent and solve constraints in multi-body robotic systems.

Description
Date
2023-08-01
Advisors
Lasenby, Joan
Keywords
clifford algebra, computer vision, Geometric algebra, geometry, graphics, quaternion, robotics
Qualification
Doctor of Philosophy (PhD)
Awarding Institution
University of Cambridge
Sponsorship
EPSRC (1949701)
Engineering and Physical Sciences Research Council (1949701)
EPSRC (1949701)
Hugo Hadfield acknowledges support from the EPSRC and ARM via ICASE award UKRI project number 1949701.