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Bibliographic Details
Main Author: Yoshino, Takashi
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2605.01184
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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