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In recent years, there have been extensive studies on biological systems such as proteins in various aspects. Being one of the important aspect, geometry is not the exception at all since the morphology mostly determines the functions of molecular systems. Hence, a strong driving force has been focused on the geometric aspect of such biological systems. Due to this consideration, the representation of proximity information among atoms(spheres) in the system has been one of the core research topics and the Voronoi diagram of atoms has been studied quite extensively in recent years[12,13]. By introducing the concept of α-shapes, Edelsbrunner and Mücke provided a basis for the applications of Voronoi diagram for a point set in reconstructing the shape from which the point set is produced[3]. They also provided very efficient codes to compute α-shapes using properties of Delaunay triangulation. Since α-shapes are fundamentally based on the rigorous theory of a Voronoi diagram of a point set and efficient and robust codes are available, α-shapes have been used in various applications. The main applications of α-shapes lie in the field of reasoning the surface shape which the point set defines. Based on this property, many researchers have tried to use it for reasoning the spatial structure of biological systems [4-7].

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