The beta-complex is a construct derived from the Voronoi diagram of spherical balls of arbitrary radii and has proven a powerful capability for proximity reasoning among spherical balls in three-dimensional space. Important applications related to molecular shapes in structural/computational molecular biology have been correctly, efficiently, and conveniently solved in the unified framework of the beta-complex and the Voronoi diagram. The beta-complex is a generalization of the ordinary alpha-complex. However, there are similarities and dissimilarities between the two complexes and it is necessary to correctly understand these similarities and dissimilarities to choose the right complex to solve application problems at hand. This paper presents the similarities and dissimilarities between these constructs and illustrates the consequence of the dissimilarity in application problems from both theoretical and practical points of view using examples of atomic arrangements.

中文翻译：

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Beta复杂与Alpha复杂：相似和不相似。

beta-complex是从任意半径的球形球的Voronoi图得出的构造，并已证明在三维空间中的球形球之间具有接近推理的强大功能。在β-复合物和Voronoi图的统一框架中，已正确，有效且方便地解决了与结构/计算分子生物学中的分子形状有关的重要应用。beta复杂体是普通alpha复杂体的概括。但是，这两个复合体之间存在相似点和不同点，因此有必要正确理解这些相似点和不同点，以选择合适的复合物来解决当前的应用程序问题。