Euclidean Voronoi diagram of spheres in 3D has not been explored as much as it deserves even though it has significant potential impacts on diverse applications in both science and engineering. In addition, studies on the data structure for its topology have not been reported yet. Presented in this paper is the topological representation for Euclidean Voronoi diagram of spheres which is represented as a cell structure as one of typical non-manifold models. The topological representation is a variation of radial edge data structure with a consideration on the topological characteristics of Euclidean Voronoi diagram of spheres distinguished from general non-manifold models and Euclidean Voronoi diagram of points. Various topological queries in the Voronoi diagram are also presented and analyzed.

Abstract
 1. 서론
 2. 구집합 보로노이 다이어그램
  2.1 정의
  2.2 모서리 추적 알고리듬
 3. 구집합 보로노이 다이어그램의 위상적 특징
 4. 구집합 보로노이 다이어그램의 위상 표현
 5. 공간 추론을 위한 위상요소간의 조회
 6. 결론
 참고문헌

• 조영송(한양대학교 Voronoi Diagram 연구단)
• 김동욱(한양대학교 Voronoi Diagram 연구단)
• 김덕수(한양대학교 산업공학과)