کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
441231 691413 2011 22 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Centroidal Voronoi tessellation in universal covering space of manifold surfaces
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر گرافیک کامپیوتری و طراحی به کمک کامپیوتر
پیش نمایش صفحه اول مقاله
Centroidal Voronoi tessellation in universal covering space of manifold surfaces
چکیده انگلیسی

The centroidal Voronoi tessellation (CVT) has found versatile applications in geometric modeling, computer graphics, and visualization, etc. In this paper, we first extend the concept of CVT from Euclidean space to spherical space and hyperbolic space, and then combine all of them into a unified framework – the CVT in universal covering space. The novel spherical and hyperbolic CVT energy functions are defined, and the relationship between minimizing the energy and the CVT is proved. We also show by our experimental results that both spherical and hyperbolic CVTs have the similar property as their Euclidean counterpart where the sites are uniformly distributed with respect to given density values. As an example of the application, we utilize the CVT in universal covering space to compute uniform partitions and high-quality remeshing results for genus-0, genus-1, and high-genus (genus > 1) surfaces.


► We extended the concept of CVT to spherical space and hyperbolic space.
► We demonstrated the uniformity of the sites in the CVT in each space.
► We formally defined the CVT energy in each space.
► We proved minimizing the CVT energy leads to CVT configuration in each space.
► We defined the CVT in universal covering space and use it on surface remeshing.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer Aided Geometric Design - Volume 28, Issue 8, November 2011, Pages 475–496
نویسندگان
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