Mesh Simplification For Unfolding

Manas Bhargava, Camille Schreck, Marco Freire, Pierre-Alexandre Hugron, Sylvain Lefebvre, Silvia Sellán, Bernd Bickel

Abstract: We present a computational approach for unfolding 3D shapes isometrically into the plane as a single patch without overlapping triangles. This is a hard, sometimes impossible, problem, which existing methods are forced to soften by allowing for map distortions or multiple patches. Instead, we propose a geometric relaxation of the problem: we modify the input shape until it admits an overlap-free unfolding. We achieve this by locally displacing vertices and collapsing edges, guided by the unfolding process. We validate our algorithm quantitatively and qualitatively on a large dataset of complex shapes and show its proficiency by fabricating real shapes from paper.