Skip to main content
SpringerLink
Log in

Voronoi Diagrams of Line Segments in 3D, with Application to Automatic Rigging

  • Conference paper
Advances in Visual Computing (ISVC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 8887))

Included in the following conference series:

Abstract

We present a novel solution to the open problem of computing a Voronoi diagram of line segments in 3D, with application to automatic rigging. As part of this solution, we present a generalized equation for all Voronoi diagrams of line segments in 3D via a game theoretic formulation, and follow it up with a presentation of an alternative method involving the specification of a system of linear equations. We show that our Voronoi diagram method can be used to create a Voronoi partitioning of an input model, and how such a segmentation process can be used for automatic rigging.

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

Access this chapter

Log in via an institution
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. Aurenhammer, F., Klein, R.: Votonoi Diagrams. In: Handb. Comput. Geom., pp. 201–290. Elsevier (2000)

    Google Scholar 

  2. Baran, I., Popovic, J.: Automatic Rigging and Animation of 3D Characters. ACM Transactions on Graphics 26 (2007)

    Google Scholar 

  3. Bharaj, G., Thormahlen, T., Seidel, H., Theobalt, C.: Automatically Rigging Multi-component Characters. Eurographics 31, 755–764 (2012)

    Google Scholar 

  4. Chen, X., Golovinskiy, A., Funkhouser, T.: A Benchmark for 3D Mesh Segmentation. ACM Trans. Graph. 28, 73:1–73:12 (2009)

    Google Scholar 

  5. Hemmer, M., Setter, O., Halperin, D.: Constructing the Exact Voronoi Diagram of Arbitrary Lines in Three-Dimensional Space with Fast Point-Location. In: de Berg, M., Meyer, U. (eds.) ESA 2010, Part I. LNCS, vol. 6346, pp. 398–409. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  6. Hoff, K., Culver, T., Keyser, J., Lin, M., Manocha, D.: Fast Computation of Generalized Voronoi Diagrams Using Graphics Hardware. In: SIGGRAPH, pp. 277–286 (1999)

    Google Scholar 

  7. Kalogerakis, E., Hertzmann, A., Singh, K.: Learning 3D Mesh Segmentation and Labeling. ACM Transactions on Graphics 29, 102:1–102:12 (2010)

    Google Scholar 

  8. Leyton-Brown, K., Shoham, Y.: Essentials of Game Theory: A Concise. Multidisciplinary Introduction 2, 1–88 (2008)

    Google Scholar 

  9. Littman, M., Stone, P.: A Polynomial-time Nash Equilibrium Algorithm for Repeated Games. Decis. Support Syst. 39, 55–66 (2005)

    Article  Google Scholar 

  10. Lu, L., Levy, B., Wang, W.: Centroidal Voronoi Tessellation of Line Segments and Graphs. Comp. Graph. Forum 31, 775–784 (2012)

    Article  Google Scholar 

  11. Miller, C., Arikan, O., Fussell, D.: Frankenrigs: Building Character Rigs from Multiple Sources. IEEE Transactions on Visualization and Computer Graphics 17, 1060–1070 (2011)

    Article  Google Scholar 

  12. Pantuwong, N., Sugimoto, M.: A fully automatic rigging algoritm for 3D character animation. In: SIGGRAPH Asia, p. 30:1 (2011)

    Google Scholar 

  13. Weisstein, E.W.: CRC Concise Encyclopedia of Mathematics. CRC Press LLC, Boca Raton (1999)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Holcomb Technologies, Irving, TX, 75062, USA

    Jeffrey W. Holcomb

  2. Department of Computer Engineering, University of Texas at Dallas, Richardson, TX, 75080, USA

    Jeffrey W. Holcomb & Jorge A. Cobb

Authors
  1. Jeffrey W. Holcomb
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jorge A. Cobb
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Nevada at Reno, USA

    George Bebis

  2. NASA Ames Research Center, Moffett Field, CA, USA

    Richard Boyle

  3. Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Bahram Parvin

  4. Desert Research Institute, Reno, NV, USA

    Darko Koracin

  5. The University of Texas at Dallas, 75080, Richardson, TX, USA

    Ryan McMahan

  6. NextGen Interactions, 27604, Raleigh, NC, USA

    Jason Jerald

  7. Indiana University, 46202, Indianapolis, IN, USA

    Hui Zhang

  8. Microsoft Research, 1 Microsoft Way, 98052, Redmond, WA, USA

    Steven M. Drucker

  9. University of Delaware, 19716-2712, Newark, DE, USA

    Chandra Kambhamettu

  10. Intel Corp., 95054, Santa Clara, CA, USA

    Maha El Choubassi

  11. Computer Graphics and Interactive Media Lab, Department of Computer Science, University of Houston, 77004, Houston, TX, USA

    Zhigang Deng

  12. NVIDIA, 34788, Leesburg, FL, USA

    Mark Carlson

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Holcomb, J.W., Cobb, J.A. (2014). Voronoi Diagrams of Line Segments in 3D, with Application to Automatic Rigging. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2014. Lecture Notes in Computer Science, vol 8887. Springer, Cham. https://doi.org/10.1007/978-3-319-14249-4_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-14249-4_8

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-14248-7

  • Online ISBN: 978-3-319-14249-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation