【作者】 李水乡； 赵健； 陆鹏； 孟令怡； 李腾； 金炜炜；

【Author】 Li Shui-Xiang Zhao Jian Lu Peng Meng Ling-Yi Li Teng Jin Wei-WeiDepartment of Mechanics and Aerospace Engineering,College of Engineering,Peking University,Beijing 100871,China

【机构】 北京大学工学院力学与空天技术系；

【摘要】 追求最密填充是人类的理想,也是实际问题的需要。最密填充对应于空间的最高利用率,几个世纪以来一直是填充研究中最重要的问题之一。本文评述了球体、正四面体、平头截体、椭球体、球柱体和柏拉图实体等基本三维实体在最密规则填充和随机填充领域的研究进展,并给出了基本三维实体在规则和随机填充两种情形下的最高填充率排序。结果表明,在两种情形下球体的填充率均最低,与Ulam猜想一致;在两种情形下立方体的填充率均为最高,且正四面体的随机填充率与立方体接近;而其他基本三维实体在两种情形下填充率的排序并不相同。最后,本文提出了当前填充研究领域的几个重要问题。更多还原

【Abstract】 Pursuing the densest packing has never lost its attraction to human beings,and is also the demand of practice.Densest packing corresponds to the ultimate use of space.For centuries,it has always been one of the most importantproblems for packing researches.Advances of the densest ordered and random packings of basic 3D objects,includingsphere,regular tetrahedron,frustum,ellipsoid,spherocylinder and Platonic solids,are reviewed.The maximum packingdensities under ordered packing and random close packing condition for the objects are compared and ranked.The resultsshow that sphere gives the minimum of packing density in both conditions among the objects,which consists with theUlam’s conjecture.Cube gives the maximum of packing density in both conditions,while the highest random packingdensity of regular tetrahedron is comparable to cube.However,the ranks of other objects in the two conditions are different.Finally,the paper presents three important problems in the field of packing investigation.更多还原