Skip to main content

BULL! - The Molecular Geometry Engine Based on Voronoi Diagram, Quasi-Triangulation, and Beta-Complex

  • Conference paper
Mathematical Software – ICMS 2014 (ICMS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8592))

Included in the following conference series:

Abstract

Libraries are available for the power diagram and the ordinary Voronoi diagram of points upon which application programs can be easily built. However, its counterpart for the Voronoi diagram of spheres does not exist despite of enormous applications, particularly those in molecular worlds. In this paper, we present the BULL! library which abbreviates “Beta Universe Library Liberandam!” for computing the Voronoi diagram of spheres, transforming it to the quasi-triangulation, and extracting the beta-complex. Being an engine library implemented in the standard C++, application programmers can simply call API-functions of BULL! to build application programs correctly, efficiently, and easily. The BULL! engine is designed so that the application programs developed by embedding API-functions are completely independent of the future modifications of the engine.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Voronoi Diagram Research Center, http://voronoi.hanyang.ac.kr/

  2. Aurenhammer, F.: Power diagrams: Properties, algorithms and applications. SIAM Journal on Computing 16, 78–96 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  3. Aurenhammer, F.: Voronoi diagrams – a survey of a fundamental geometric data structure. ACM Computing Surveys 23(3), 345–405 (1991)

    Article  Google Scholar 

  4. Cho, Y., Kim, D., Kim, D.S.: Topology representation for the Voronoi diagram of 3D spheres. International Journal of CAD/CAM 5(1), 59–68 (2005), http://www.ijcc.org

    Google Scholar 

  5. Edelsbrunner, H., Mücke, E.P.: Three-dimensional alpha shapes. ACM Transactions on Graphics 13(1), 43–72 (1994)

    Article  MATH  Google Scholar 

  6. Kim, D.S., Cho, Y., Kim, D.: Euclidean Voronoi diagram of 3D balls and its computation via tracing edges. Computer-Aided Design 37(13), 1412–1424 (2005)

    Article  MATH  Google Scholar 

  7. Kim, D.S., Cho, Y., Sugihara, K.: Quasi-worlds and quasi-operators on quasi-triangulations. Computer-Aided Design 42(10), 874–888 (2010)

    Article  MATH  Google Scholar 

  8. Kim, D.S., Cho, Y., Sugihara, K., Ryu, J., Kim, D.: Three-dimensional beta-shapes and beta-complexes via quasi-triangulation. Computer-Aided Design 42(10), 911–929 (2010)

    Article  Google Scholar 

  9. Kim, D.S., Kim, D., Cho, Y., Sugihara, K.: Quasi-triangulation and interworld data structure in three dimensions. Computer-Aided Design 38(7), 808–819 (2006)

    Article  Google Scholar 

  10. Kim, D.S., Kim, J.K., Cho, Y., Kim, C.M.: Querying simplexes in quasi-triangulation. Computer-Aided Design 44(2), 85–98 (2012)

    Article  Google Scholar 

  11. Kim, D., Kim, D.S.: Region-expansion for the Voronoi diagram of 3D spheres. Computer-Aided Design 38(5), 417–430 (2006)

    Article  MATH  Google Scholar 

  12. Kim, J.K., Cho, Y., Kim, D., Kim, D.S.: Voronoi diagrams, quasi-triangulations, and beta-complexes for disks in ℝ2: The theory and implementation in BetaConcept. Journal of Computational Design and Engineering 1(2), 78–86 (2014)

    MathSciNet  Google Scholar 

  13. Okabe, A., Boots, B., Sugihara, K., Chiu, S.N.: Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, 2nd edn. John Wiley & Sons, Chichester (1999)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kim, DS. et al. (2014). BULL! - The Molecular Geometry Engine Based on Voronoi Diagram, Quasi-Triangulation, and Beta-Complex. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_33

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-44199-2_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44198-5

  • Online ISBN: 978-3-662-44199-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics