2026-09-18T19:10:26Zhttps://api.repository.cam.ac.uk/server/oai/requestoai:www.repository.cam.ac.uk:1810/3589812023-12-22T14:23:18Zcom_1810_213729com_1810_256065col_1810_219485
Applications of Geometric Algebra in Mathematical Engineering
https://doi.org/10.17863/CAM.102306
Hadfield, Hugo
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Lasenby, Joan
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.
University of Cambridge
2023-08-01
Thesis
Doctoral
Doctor of Philosophy (PhD)
eng
Hugo Hadfield acknowledges support from the EPSRC and ARM via ICASE award UKRI project number 1949701.
https://www.repository.cam.ac.uk/handle/1810/358981
https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/c84feef2-a72b-42e9-897f-3b6c94351bf1/download
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https://creativecommons.org/licenses/by/4.0/
clifford algebra
computer vision
Geometric algebra
geometry
graphics
quaternion
robotics