Spherical Geometrical Bases of Spherical Origami
This work turns spherical origami from a niche idea into something you can actually reason about mathematically. It extends the usual Euclidean origami definitions to the unit sphere and derives explicit spherical equations for all seven Huzita–Justin axioms, which is the core rule set many folding systems rely on.
The other useful piece for developers is the 3D folding model: instead of geodesics, the paper uses equidistant curves as fold curves, which broadens the kinds of folds you can represent on spherical sheets. The framework is not just theoretical; it was used to generate computer graphics of spherical origami birds, suggesting it could be relevant anywhere you need believable folding, curved-surface deformation, or geometry-driven procedural art.
“all seven Huzita--Justin axioms are shown to admit explicit equations in spherical geometry”
- what
- The paper formalizes spherical origami with a rigorous geometrical framework for both on-sphere and 3D folding cases.
- who
- Author: Takashi Yoshino; source: arXiv cs.GR / cs.CG.
- when
- Submitted 2 May 2026, revised 17 May 2026 (v2).
- impact
- Could inform procedural folding, curved-surface deformation, and geometry tools for graphics-heavy game content.
Useful geometry framework with direct graphics applications.
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