Mathematics in Computer Science
The first phase of TreeMaker, a well-known method for origami design, decomposes a planar polygon (the “paper”) into regions. If some region is not convex, TreeMaker indicates it with an error message and stops. Otherwise, a second phases is invoked which computes a crease pattern called a “universal molecule”. In this paper we introduce and study geodesic universal molecules, which also work with non-convex polygons and thus extend the applicability of the TreeMaker method. We characterize the family of disk-like surfaces, crease patterns and folded states produced by our generalized algorithm. They include non-convex polygons drawn on the surface of an intrinsically flat piecewise-linear surface which have self-overlap when laid open flat, as well as surfaces with negative curvature at a boundary vertex.
Algorithmic origami, Metric tree, Non-convex polygon, Planar subdivision
© Springer International Publishing 2016
Bowers, John C. and Streinu, Ileana, "Geodesic Universal Molecules" (2016). Computer Science: Faculty Publications, Smith College, Northampton, MA.