Hyperbolic centroidal Voronoi tessellation

The centroidal Voronoi tessellation (CVT) has found versatile applications in geometric modeling, computer graphics, and visualization. In this paper, we extend the concept of the CVT from Euclidean space to hyperbolic space. A novel hyperbolic CVT energy is defined, and the relationship between minimizing this energy and the hyperbolic CVT is proved. We also show by our experimental results that the hyperbolic CVT has the similar property as its Euclidean counterpart where the sites are uniformly distributed according to given density values. Two algorithms

• Type: Conference
• Year: 2010
• Where: SMA
• Authors: Guodong Rong, Miao Jin, Xiaohu Guo
• Keywords: Algorithms, Computer Graphics, Hyperbolic Cvt, SMA 2010, Solid Modeling