题  目： Centroidal Voronoi Tessellation on Parameterized Surfaces

报告人： Xiaohu Guo, Assistant Professor

        Computer Science at University of Texas at Dallas

时  间：12/20/2011 16:30--18:00

地  点： 管研楼1611

摘  要：The centroidal Voronoi tessellation (CVT) has found versatile applications in geometric modeling, computer graphics, and visualization. In this talk, I will introduce our latest work on computing CVT on the parameterization domain of manifold surfaces. In particular, we compute the CVT directly on the universal covering space (UCS) of the surface. For closed genus-1 surfaces, their UCS can be embedded in 2D planar domain; The UCS of closed genus-0 surfaces can be embedded in 2D spherical space; For closed high-genus (genus>1) surfaces, their UCS can be embedded in 2D hyperbolic plane. We compute CVT on the 2D Euclidean, spherical, and hyperbolic spaces, and map the CVT results from the UCS onto the surface. In this way the sites can move freely along or cross any cutting boundaries in the parameterization domain. The talk will focus on the case of hyperbolic CVT, its centroid and CVT-energy definition, as well as its convergence property. I will also show how to use the CVT in UCS to generate uniform partitions and high quality remeshing results for genus-0, genus-1, and high-genus (genus>1) surfaces.

主办单位：中国科学技术大学数学科学学院

        国家数学与交叉科学中心合肥分中心

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