摘要:作为曲面变形领域的重要课题，展开与折叠已经成为近年来的研究热点.为了满足三维物体在美学、力学等方面的约束，通常需要为其设计展开与折叠结构.利用计算机相关技术模拟物体的展开与折叠，可设计出满足约束条件的几何结构.目前，展开与折叠广泛应用于工业设计、生物医疗、智能机器人、家具设计等领域.主要介绍近年来计算机展开与折叠物体的研究现状：首先对展开与折叠算法进行分类，并简述每类方法的基本思想；然后对各类方法进行归纳分析，总结各类方法的优势与局限性；最后给出相应的评价准则，用于进一步对比.曲面的折叠与展开方法逐步发展创新，趋于成熟，但由于实际应用需求复杂，变形结果并不完美.对目前的折叠与展开方法进行综述，能够为未来的工作提供研究方向.



Abstract:As an important topic in the field of surface deformation, flattening and folding has become a research hotspot in recent years. In order to satisfy the constraints of aesthetics and mechanics, it is necessary to design flattening and folding structure. Using computer technology to simulate the flattening and folding of objects, geometric structures that meet the constraints can be designed. At present, flattening and folding are widely used in industrial design, biomedicine, intelligent robot, furniture design, and other fields. This paper mainly introduces the research status of computer flattening and folding objects in recent years. Firstly, the algorithms of flattening and folding are classified, and the basic ideas of each method are briefly described. Then, the various methods are analyzed, and their advantages and limitations are summarized. Finally, the corresponding evaluation criteria are given for further comparison. The flattening and folding method of curved surface has been developed and innovated step by step, and tends to be mature. However, due to the complex practical application requirements, the deformation results may not be perfect. A review of the current flattening and folding methods can provide research direction for future work.



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