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：本文建立了球面折纸的严格几何框架，该框架基于球面几何使用球面纸张进行折纸。研究涵盖两种情形：限制在单位球面（$\mathbb{S}^2$）上的折纸，以及球面纸张在空间中的三维折叠。对于$\mathbb{S}^2$上的折纸，将欧几里得折纸的定义系统地扩展至球面情境，并证明所有七条Huzita–Justin公理在球面几何中均具有显式方程。对于三维折叠，引入等距曲线作为折叠曲线，取代测地线从而支持更丰富的折叠类型。通过成功构建球面折纸鸟的计算机图形验证了该框架，同时展示了所提出方法的理论完备性与实际应用价值。