Simple Simulation of Curved Folds Based on Ruling-aware Triangulation

Abstract

Folding a thin sheet material such as paper along curves creates a developable surface composed of ruled surface patches. When using such surfaces in design, designers often repeat a process of folding along curves drawn on a sheet and checking the folded shape. Although several methods for constructing such shapes on a computer have been proposed, it is still difficult to check the folded shapes instantly from the crease patterns.In this paper, we propose a simple method that approximately realizes a simulation of curved folds with a triangular mesh from its crease pattern. The proposed method first approximates curves in a crease pattern with polylines and then generates a triangular mesh. In order to construct the discretized developable surface, the edges in the mesh are rearranged so that they align with the estimated rulings. The proposed method is characterized by its simplicity and is implemented on an existing origami simulator that runs in a web browser.