An Extension of Combinatorial Design of Petaloid Smocking via Regular Polygon Pasting

Abstract

This paper proposes an extension of combinatorial design of petaloid smocking via regular polygon pasting. We have proposed a method for petaloid smocking pattern generation and combinatorial design. Although it can construct the crease pattern of petaloid smocking by preserving the labels on folding lines, combinatorial design was rather limited due to the constraints induced from regular polygons. In this paper we extend the designable objects to general polygon twists based on regular polygon pasting, and show their geometric characteristics. Also, we propose a method for constructing the crease pattern of combinatorial petaloid smocking based on polygon twists. The proposed method is implemented using GeoGebra, and it is validated via clothes making with a newly designed combinatorial petaloid smocking.