Applications of Geometric Algebra in Mathematical Engineering

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.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2023

Author dc:creator

• Hadfield, Hugo

Advisor dc:contributor.advisor

• Lasenby, Joan

• clifford algebra
• computer vision
• Geometric algebra
• geometry
• graphics
• quaternion
• robotics

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/739b6fd1-be77-436a-ae05-c02c1a87edc3/download
• https://creativecommons.org/licenses/by/4.0/

Language dc:language

eng

Author Identifier

0000-0003-4318-050X

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/358981