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.

翻译：本文为球面折纸（基于球面几何的球形纸张折纸）建立了严格的几何学框架。研究涵盖两种场景：限于单位球面$\mathbb{S}^2$上的折纸，以及球形纸张在三维空间中的折叠。对于$\mathbb{S}^2$上的折纸，本文系统地将欧几里得折纸的定义推广至球面情形，并证明所有七条Huzita-Justin公理均可表示为球面几何中的显式方程。针对三维折叠，引入等距曲线作为折叠曲线，以替代测地线并实现更丰富的折叠类型。通过成功构建球面折纸鸟的计算机图形验证了该框架的有效性，既展示了理论完备性，也证明了所提方法的实际效用。