CreaseSchnitte

CreaseSchnitte is a conceptual framework within the mathematics of origami that links crease-pattern analysis with the study of cross-sections of folded surfaces. The name combines "crease" (the line along which material is folded) with "Schnitte" (the German word for cross-section), emphasizing how a two-dimensional crease network determines a family of spatial slices in the folded object. The term appears in discussions of origami geometry as a way to reason about the three-dimensional consequences of planar fold patterns.

In CreaseSchnitte, researchers examine how cross-sections, produced by intersecting planes with a folded model, reflect the underlying crease network and folding sequence. The approach emphasizes local compatibility at vertices (for example, angle constraints akin to Kawasaki's and Maekawa's theorems) and global considerations of rigidity and realizability. By comparing cross-sections across different fold orders, one can infer properties of the resulting 3D form from planar data alone.

Applications are found in the design of deployable structures, architectural origami, and packaging, where predicting three-dimensional shape from a crease map is valuable. The framework also serves as a teaching tool to illustrate connections between planar graphs and spatial geometry. CreaseSchnitte is related to, but distinct from, crease-pattern theory and rigid origami, offering a cross-sectional perspective on foldability and shape generation.