Edge Tracing Algorithm for Computation of Euclidean Voronoi Diagram for Protein and its Applications

3차원에서 단백질의 보로노이 다이아그램 계산을 위한 모서리추적 알고리즘 및 응용

Although there are many applications of Euclidean Voronoi diagram for spheres in a 3D space in various disciplines from sciences and engineering, it has not been studied as much as it deserves. In this paper, we present an edge-tracing algorithm to compute the Euclidean Voronoi diagram of 3-dimensional spheres in O(mn) in the worst-case, where m is the number of edges of Voronoi diagram and n is the number of spheres. After building blocks for the algorithm, we show an example of Voronoi diagram for atoms using actual protein data and discuss its applications for protein analysis.