PhD Research
Doctoral research in geometric algebra.
My doctoral research explores how Geometric Algebra can provide unified tools for problems in computer graphics and computer vision. The thesis is structured around three main research directions.
Geometric Algebra and Bézier Curves
This research investigates how Projective Geometric Algebra (PGA) can provide new algebraic tools for the construction and analysis of Bézier curves.
The related paper, Projective Geometric Algebra powers up Bézier Curves, was accepted and presented at WSCG 2026 in May 2026. It is listed on the Publications page and will be linked there once it becomes available online.
Projective invariants and transformations in PGA
This research develops projective invariants and projective transformations directly within Projective Geometric Algebra (PGA). It first establishes generalized cross-ratios for geometric objects in n-dimensional plane-based PGA, then uses these invariants as a foundation for defining transformations and homographies.
The cross-ratio results are available as a preprint, while the work on projective transformations and homographies is ongoing. Both outputs are listed on the Publications page.
Conic Conformal Geometric Algebra
This research studies Conic Conformal Geometric Algebra (CCGA) and its use for representing, constructing, and manipulating conic sections within a unified algebraic framework.
The work was presented at ENGAGE 2026 in July 2026 and received the Best Presentation Award (certificate).
The associated paper is a work in progress and is listed on the Publications page.
The software developed alongside this work is presented separately on the MultiVector page.