几何折叠综述

Survey on Geometric Folding

近年来三维模型的几何折叠在工业设计、医疗器械、机器人运动和生物模拟的领域得到广泛应用,其核心基础理论已经成为计算机图形学的热门问题.本文整理分析了近年来几何折叠方向的经典算法,首先介绍了几何折叠在生物医疗、工业设计和机器人设计等3个领域的应用情况;然后根据折叠对象不同,将几何折叠问题分为杆折叠、平面折叠和三维折叠3类,并进一步将平面折叠分为折痕设计、切割和自折叠路径规划,分别总结论述其研究进展和算法思想.之后给出几何折叠算法的评价指标和典型折叠算法的对比分析;最后结合机器学习和自驱动材料等交叉学科,预测几何折叠今后的发展方向.

In recent years,the geometric folding of three-dimensional model has been widely used in fields of industrial design,medical devices,robot motion and biological simulation,and its core basic theory has become a hot issue in computer graphics.This paper collates and analyzes the classical algorithms of geometric folding in recent years.Firstly,the applications of geometric folding in biomedical,industrial design and robot design are introduced.Then,according to the different folding objects,the geometric folding problem is divided into three categories:bar folding,plane folding and three-dimensional folding.Plane folding is further divided into crease design,cutting and self-folding path planning,and their research progress and algorithm ideas are summarized and discussed respectively.After that,the evaluation index of geometric folding algorithm is given,and the comparative analysis of typical folding algorithms is given.Finally,combined with machine learning and self-driving materials and other cross-disciplines,the future development direction of geometric folding is predicted.