Spherical Geometrical Bases of Spherical Origami
For origami researchers and geometers, this provides a foundational theory for spherical origami, though it is an incremental extension of Euclidean origami to a new geometry.
This paper establishes a rigorous geometrical framework for spherical origami, extending Euclidean origami definitions to the sphere and introducing equidistant curves for 3D folding, validated by constructing spherical origami birds.
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.