A Dissimilarity Measure for Comparing Origami Crease Patterns

A measure of dissimilarity (distance) is proposed for comparing origami crease patterns represented as geometric graphs. The distance measure is determined by minimum-weight matchings calculated between the edges as well as the vertices of the graphs being compared. The distances between pairs of edges and pairs of vertices of the graph are weighted linear combinations of six parameters that constitute geometric features of the edges and vertices. The results of a preliminary study performed with a collection of 45 crease patterns obtained from Mitani’s ORIPA web page, revealed which of these features appear to be more salient for obtaining a clustering of the crease patterns that appears to agree with human intuition.