Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.01184 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914574053146624 |
|---|---|
| author | Yoshino, Takashi |
| author_facet | Yoshino, Takashi |
| contents | This paper establishes a rigorous geometrical framework for spherical origami, origami using spherical sheets based on spherical geometry. Two settings are treated: origami restricted to the unit sphere ($\mathbb{S}^2$), and three-dimensional folding of spherical sheets in space. For origami on $\mathbb{S}^2$, the definitions of Euclidean origami are systematically extended to the spherical setting, and all seven Huzita--Justin axioms are shown to admit explicit equations in spherical geometry. For three-dimensional folding, equidistant curves are introduced as fold curves, replacing geodesics and enabling a richer family of folds. The framework is validated by successfully constructing computer graphics of spherical origami birds, demonstrating both the theoretical completeness and practical utility of the proposed approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01184 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spherical Geometrical Bases of Spherical Origami Yoshino, Takashi Computational Geometry Graphics This paper establishes a rigorous geometrical framework for spherical origami, origami using spherical sheets based on spherical geometry. Two settings are treated: origami restricted to the unit sphere ($\mathbb{S}^2$), and three-dimensional folding of spherical sheets in space. For origami on $\mathbb{S}^2$, the definitions of Euclidean origami are systematically extended to the spherical setting, and all seven Huzita--Justin axioms are shown to admit explicit equations in spherical geometry. For three-dimensional folding, equidistant curves are introduced as fold curves, replacing geodesics and enabling a richer family of folds. The framework is validated by successfully constructing computer graphics of spherical origami birds, demonstrating both the theoretical completeness and practical utility of the proposed approach. |
| title | Spherical Geometrical Bases of Spherical Origami |
| topic | Computational Geometry Graphics |
| url | https://arxiv.org/abs/2605.01184 |