Conformal Geometric Algebra as a Symbolic Interface for LLM-Driven 3D Scene Editing

Abstract

What symbolic format should an LLM emit to perform reliable 3D scene editing from natural language, and does algebraic structure contribute beyond compact syntax? We study this question using Conformal Geometric Algebra (CGA) as a compact symbolic interface, contrasted with a verbose Euclidean 4x4 matrix baseline and a non-CGA Compact SE3 control, in a natural-language 3D scene editing pipeline coupling controlled prompting with deterministic geometric execution. Our primary finding concerns compositional fidelity under sequential instruction chains: Simple CGA preserves exact ordered operation chains more reliably than Compact SE3 (97.5% vs 90.0%) at lower completion-token cost. In the powered hard semantic suite, compact representations all exceed the Euclidean 4x4 baseline. These findings have direct implications for real-time natural-language editing in immersive and interactive 3D environments.

Publication
CGI 2026 ENGAGE Workshop (to appear)