In this paper, we consider the problem of regrouping a number of service sites into a smaller number of service sites called centers. Each service site is represented as a point in the plane and has an associated value of service demand. We aim to group the sites so that each group has the balanced service demand and the sum of distances from the sites in the group to their corresponding center is minimized. To solve this problem, we propose a hybrid genetic algorithm that is combined with Voronoi diagrams. We provide a variety of experimental results by changing the weights of the two factors: service demands and distances. Our hybrid algorithm finds good approximate solutions in a shorter computation time in comparison with optimal solution by integer programming.

Given a protein, it is often necessary to study its geometric and physicochemical properties for studying its structure and predicting funtions of a protein. In this case, a connolly surface of a protein plays important roles for these purpose. A protein consists of a set of amino acids and a set of atoms comprise an amino acide. Since an atom can be represented by a hard 3D sphere in van der Waals model, a protein is usually modeled as a set of 3D spheres. In this paper, we present the algorithm for computing a connolly surface using Euclidean Voronoi diagram atoms of a protein. The algorithm initially locates the exterior aotms of a protein where connolly surface patches exist and computes the patches by tracking their boundary curves. Since a Euclidean Voronoi diagram is uniquely defined independent of probe radius different from other geometric structures, the connolly surfaces defined by probes of different radii can be computed without re-computing the Euclidean Voronoi diagram.

Being in an internet era, the rapid transmission of 3D mesh models is getting more Important and efforts toward the compression of various aspects of mesh models have been provided Even though a mesh model usually consists of coor-dinates of vertices and

As the transmission of 3D shape models through Internet becomes more important, the compression issue of shape models gets more critical. The issues for normal vectors have not yet been explored as much as it deserves, even though the size of the data for normal vectors can be significantly larger than its counterparts of topology and geometry. Presented in this paper is an approach to compress the normal vectors of a shape model represented in a mesh using the concept of clustering. It turns out that the proposed approach has a significant compression ratio without a serious sacrifice of the visual quality of the model.

Presented in this paper is an algorithm to compute the Voronoi diagram of a circle set from the Voronoi diagram of a point set. The circles are located in Euclidean plane, the radii of the circles are non-negative and not necessarily equal, and the circles are allowed to intersect each other. The idea of the algorithm is to use the topology of the point set Voronoi diagram as a seed so that the correct topology of the circle set Voronoi diagram can be obtained through a number of edge flipping operations. Then, the geometries of the Voronoi edges of the circle set Voronoi diagram are computed. The main advantages of the proposed algorithm are in its robustness, speed, and the simplicity in its concept as well as implementation.