Discovering Folding Lines for Surface Compression

Abstract

The miniaturization of shell structures presents a versatile and complex challenge, bridging geometry with diverse practical applications. In this paper, we introduce a novel approach for computing origami crease patterns to compress arbitrary 3D shell objects. First, we employ the adapted Material Point Method (MPM) to simulate the compression of a target surface and obtain an initial folded configuration. Since MPM produces overly smooth curved surfaces, their crease patterns are unsuitable for practical origami fabrication. We then propose a novel Folding Line Extraction (FLE) method that optimizes these smoothed surfaces to extract folding lines that achieve the target compression with minimal deformation and stretching outside the crease lines. This method produces smooth curved folding lines. Fabrication and experimental validation of the extracted patterns demonstrate their effectiveness and applicability in real-world scenarios.