Mesh Simplification For Unfolding

TL;DR

This paper introduces a novel geometric relaxation method for unfolding 3D shapes into the plane without overlaps by locally modifying the shape, enabling practical fabrication from paper.

Contribution

It proposes a new approach that modifies input shapes to achieve overlap-free unfoldings, overcoming limitations of previous methods that allow distortions or multiple patches.

Findings

Successfully unfolds complex shapes without overlaps

Quantitative and qualitative validation on large datasets

Fabrication of real paper shapes from unfolded models

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.