Kirigami, the traditional Japanese art of paper cutting and folding generalizes origami and has initiated new research in material science as well as graphics. In this paper we use its capabilities to perform geometric modeling with corrugated surface representations possessing an isometric unfolding into a planar domain after appropriate cuts are made. We initialize our box-based kirigami structures from orthogonal networks of curves, compute a first approximation of their unfolding via mappings between meshes, and complete the process by global optimization. Besides the modeling capabilities we also study the interesting geometry of special kirigami structures from the theoretical side. This experimental paper strives to relate unfoldable checkerboard arrangements of boxes to principal meshes, to the transformation theory of discrete differential geometry, and to a version of the Gauss theorema egregium.

中文翻译：

---

自由四边形剪纸

剪纸是日本传统的剪纸和折叠艺术，它概括了折纸，并在材料科学和图形学方面开展了新的研究。在本文中，我们使用它的功能来执行几何建模，其中波纹表面表示在进行适当的切割后具有等距展开到平面域中。我们从曲线的正交网络初始化我们基于盒子的剪纸结构，通过网格之间的映射计算它们展开的第一近似值，并通过全局优化完成该过程。除了建模能力外，我们还从理论方面研究了特殊剪纸结构的有趣几何形状。这篇实验论文力求将盒子的可展开棋盘排列与主网格联系起来，