Spherical Geometrical Bases of Spherical Origami
This study addresses the absence of a rigorous geometric framework for spherical origami, particularly concerning folding rules on the unit sphere and their realization in three-dimensional space. The work proposes the first complete axiomatic system for spherical origami by extending the classical Huzita–Justin axioms from Euclidean to spherical geometry, providing explicit equations for all seven axioms. Innovatively, it replaces geodesics with isometric curves as three-dimensional creases, thereby expanding the repertoire of realizable folded forms. By integrating spherical and differential geometry with computational origami theory and computer graphics, the authors successfully generate a spherical origami bird model, demonstrating both the theoretical completeness and practical feasibility of the proposed framework.