Please note: This master’s thesis presentation will take place online.
HongFei Huang, Master’s candidate
David R. Cheriton School of Computer Science
Supervisor: Professor Stephen Mann
Conformal Geometric Algebra (CGA) embeds 3D Euclidean geometry in a 5D vector space, unifying geometric primitives and transformations within a single algebraic framework. While existing desktop tools like GAViewer provide interactive CGA exploration on flat screens, immersive virtual reality allows users to directly inspect and manipulate these spatial structures. We present VR GAViewer, a standalone Meta Quest 3 application that brings interactive CGA computation and visualisation into immersive, hand-tracked virtual reality as an educational tool for beginners.
(1) We design a dual-mode interaction pipeline combining an ANTLR-based expression console with hand-based direct manipulation, featuring a dwell-based closed-fist point-spawning gesture and an interactive pinch-driven wedge builder for composing outer products in real time.
(2) We implement a grade-aware type classifier and geometric visual mapping that automatically connects 5D conformal multivectors to dedicated 3D representations (points, lines, circles, planes, spheres, and Euclidean bivectors/trivectors), gracefully handling degenerate boundaries.
(3) We develop a dynamic live-dependency system alongside a reusable versor subsystem. Rotors, translators, and screw motions can be constructed via gesture or algebraic expressions, displayed as geometric helices/arcs, and applied to targets through animated sandwich-product previews.
We demonstrate the system through eight on-device workflows and benchmark its performance on Meta Quest 3. Representative console submissions achieve 95th-percentile latencies below 6.8 ms, and the rendering pipeline sustains the 72 Hz display target frame rate under typical scene workloads, confirming the feasibility of interactive geometric algebra in standalone VR.
To attend this master's thesis presentation you can join virtually through Teams.