“Whoa! It’s like Spotify but for academic articles.”

Instant Access to Thousands of Journals for just $40/month

Try 2 weeks free now

3D hyperbolic Voronoi diagrams

Voronoi diagrams have useful applications in various fields and are one of the most fundamental concepts in computational geometry. Although Voronoi diagrams in the plane have been studied extensively, using different notions of sites and metrics, little is known for other geometric spaces. In this paper, we are interested in the Voronoi diagram of a set of sites in the 3D hyperbolic upper half-space. We first present some introductory results in 3D hyperbolic upper half-space and then give an incremental algorithm to construct Voronoi diagram. Finally, we consider five models of 3D hyperbolic manifolds that are equivalent under isometries. By these isometries we can transform the Voronoi diagram of each model to others. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computer-Aided Design Elsevier
Loading next page...

You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy unlimited access and
personalized recommendations from
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $40/month

Try 2 weeks free now

Explore the DeepDyve Library

How DeepDyve Works

Spend time researching, not time worrying you’re buying articles that might not be useful.

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from Springer, Elsevier, Nature, IEEE, Wiley-Blackwell and more.

All the latest content is available, no embargo periods.

See the journals in your area

Simple and Affordable Pricing

14-day free trial. Cancel anytime, with a 30-day money-back guarantee.

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Best Deal — 25% off

Annual Plan

  • All the features of the Professional Plan, but for 25% off!
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

billed annually