Abstract
This paper proposes a smocking pattern generation method based on petaloid folding and combinatorial design of smocking patterns. Smocking is a handcraft technique of sewing and making pleats over cloth, however, it is not easy to generate the pattern for the desired shape on the surface of cloth. For the type of smocking which corresponds to petaloid folding in Origami, we propose to sew down the intersection of folded pieces of cloth so that the formed shape can be kept on the flexible cloth. We propose a smocking pattern generation method based on the geometric transformation of polygons in a crease pattern, and show the geometric characteristics in the transformation. Especially, we show the angle for petaloid folding of any triangles and the corresponding pattern. Furthermore, we propose an approach for combinatorial design of patterns based on pleats sharing, and show a class of combinatorial design by exploiting petaloid folding of a triangle. The proposed method is implemented using GeoGebra, and it is validated through a newly designed combinatorial pattern and smocked textile based on the generated pattern.
