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Minkowski和是计算几何和机器人学研究重要内容之一,在几何推理、路径规划和计算机辅助制造等领域有着重要的作用.经过近三十年的发展,研究人员已经给出了一些精确有效的Minkowski和计算方法.本文介绍Minkowski和的基本概念、性质和主要计算方法,说明了Minkowski和计算的要点和关键环节,对主要计算方法从可行性、精度、效率和适用性四个方面进行了对比分析,综述了Minkowski和计算的研究进展情况,最后讨论了目前存在的主要问题并指出下一步深入研究的思路和方向,为Minkowski和计算的理论研究和实践应用提供了有价值的参考.
Minkowski is one of the most important parts in computational geometry and robotics research and has played an important role in such fields as geometric reasoning, path planning and computer aided manufacturing. After nearly three decades of development, researchers have provided some accurate and effective Minkowski And calculation method.This paper introduces the basic concepts, properties and main calculation methods of Minkowski sum, explains the key points and key points of Minkowski and calculation, compares and analyzes the main calculation methods from the four aspects of feasibility, accuracy, efficiency and applicability , Summarizes the research progress of Minkowski and computing, and finally discusses the main existing problems and points out the ideas and directions for further research. It provides a valuable reference for the theoretical research and practical application of Minkowski and computing.