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.

翻译：当从纸张等二维材料折叠三维物体时，通常只需对原始曲面几何形状进行近似。这种近似可通过（渐进式）网格简化方法高效实现，例如采用边坍缩技术。此外，在寻找物体展开图时，该近似被视为固定不变的。本研究另辟蹊径，允许在展开过程中动态调整近似值，从而增加克服潜在不可展开性问题的可能性。为融合网格近似与展开两个概念，本研究将边坍缩网格简化技术与Tabu Unfolder（一种鲁棒的网格展开方法）相结合。实验表明，该方法相较于现有最优技术具有更快的运算速度和更高的可靠性。