2024/08/13 by Manas Bhargava, Camille Schreck, Bhargava, Manas +11 · 1 citation
Computer Science · #Computational Geometry and Mesh Generation #FOS: Computer and information sciences #Graphics (cs.GR)
paper · pdf · doi:10.48550/arxiv.2408.06944
openalex publication_date 2024/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.