几何展开与折叠算法及应用综述

展开与折叠是计算机图形学中的重要研究问题，已经广泛应用于工业制造、建筑设计、医学治疗和航空航天等方面.通过回顾近年来图形学中展开与折叠方面的主要研究问题,总结整理它们的典型算法.首先介绍展开与折叠的基本概念，并从机器人设计、计算机动画、深度学习和其他4个领域介绍它们的应用情况.之后，按照展开程度分类，从完全展开和近似展开2方面总结展开问题的研究进展和典型算法思想；按照折叠形式不同，将折叠问题分为Origami折叠和Kirigami折叠2类，分别论述其研究进展并总结算法思路.之后，整理展开与折叠的评价指标，总结各类展开与折叠算法的特点，并分析比较它们的优势与不足.最后，总结并提出展开与折叠的4个发展趋势.

Survey on Geometric Unfolding,Folding Algorithms and Applications

Unfolding and folding problem is a popular research topic in computer graphics, and has a wide range of applications, such as industrial manufacturing, architectural design, medical treatment, and aviation technology. In this survey, we review the basic concepts of unfolding and folding problem, introduce the research and application in four fields: robot design, computer animation, deep learning and others. We discuss the research work of unfolding and folding problem in detail. First, according to the different degrees of unfolding, we summarize research progress and typical algorithm ideas from two aspects: full unfolding and approximate unfolding. Full unfolding is to unfold 3D objects into 2D space without overlapping and deformation. However, most objects cannot be directly unfolded, and only an approximately unfolded structure can be solved. Approximate unfolding is a non-overlapping and deformed process, which is unfolded into the plane domain by mapping. How to find the smallest deformation is the key to approximate unfolding. Second, according to the different folding forms, the folding problem is divided into two types: Origami and Kirigami. We divide Origami into rigid folding and curved folding according to the different forms of crease, such as straight crease and curved crease. Kirigami is a special folding method that combines cutting and folding technology, which drives folding by the elastic force or other external forces generated by cutting. Here, we mainly consider the technology or algorithm of using Kirigami technology to construct auxetic structures. In addition, in order to compare the advantages and disadvantages of the algorithm, we summarize the commonly used algorithm indicators of unfolding and folding algorithm. Then, we evaluate the typical algorithm in recent years, and analyze advantages and disadvantages. Finally, we summarize and propose the development trend of unfolding and folding, including algorithm accuracy and robustness, fold volumetric objects, self-driven process and intelligent application of Kirigami technology.