Unfolding via Progressive Mesh Approximation

TL;DR

This paper introduces a novel method combining progressive mesh approximation with a robust unfolding algorithm, allowing the approximation to adapt during unfolding to improve success rate and efficiency.

Contribution

It proposes a new approach that integrates mesh simplification with unfolding, enabling dynamic approximation adjustments to overcome unfoldability challenges.

Findings

Faster unfolding process compared to previous methods

Higher reliability in unfolding complex geometries

Adaptive approximation improves success rate

Abstract

When folding a 3D object from a 2D material like paper, typically only an approximation of the original surface geometry is needed. Such an approximation can effectively be created by a (progressive) mesh simplification approach, e.g. using an edge collapse technique. Moreover, when searching for an unfolding of the object, this approximation is assumed to be fixed. In this work, we take a different route and allow the approximation to change while searching for an unfolding. This way, we increase the chances to overcome possible ununfoldability issues. To join the two concepts of mesh approximation and unfolding, our work combines the edge collapsing mesh simplification technique with a Tabu Unfolder, a robust mesh unfolding approach. We empirically show that this strategy performs faster and that it is more reliable than prior state of the art methods.