Hugo Hadfield

PhD Thesis

My PhD research focus was in designing novel computer vision and computer graphics algorithms using conformal geometric algebra (CGA) . I was supervised by Joan Lasenby .

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.

PDF
The PDF of my thesis can be found here.

HTML
The process of converting a full size latex document like a thesis to HTML is still pretty error prone but the results can be really good when it works. I've had a go converting my thesis to HTML with latex2html, check out the results here.

Open Source Software
To see what code I am working on now check out the pygae organisation on Github. To see what direction my research is going check out my ORCID profile.

Tutorials
The Clifford python package documentation

Slides.com Tutorials