VoroCrust Illustrated: Theory and Challenges (Multimedia Exposition)

Authors Ahmed Abdelkader, Chandrajit L. Bajaj, Mohamed S. Ebeida, Ahmed H. Mahmoud, Scott A. Mitchell, John D. Owens, Ahmad A. Rushdi



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Ahmed Abdelkader
Chandrajit L. Bajaj
Mohamed S. Ebeida
Ahmed H. Mahmoud
Scott A. Mitchell
John D. Owens
Ahmad A. Rushdi

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Ahmed Abdelkader, Chandrajit L. Bajaj, Mohamed S. Ebeida, Ahmed H. Mahmoud, Scott A. Mitchell, John D. Owens, and Ahmad A. Rushdi. VoroCrust Illustrated: Theory and Challenges (Multimedia Exposition). In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 77:1-77:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.SoCG.2018.77

Abstract

Over the past decade, polyhedral meshing has been gaining popularity as a better alternative to tetrahedral meshing in certain applications. Within the class of polyhedral elements, Voronoi cells are particularly attractive thanks to their special geometric structure. What has been missing so far is a Voronoi mesher that is sufficiently robust to run automatically on complex models. In this video, we illustrate the main ideas behind the VoroCrust algorithm, highlighting both the theoretical guarantees and the practical challenges imposed by realistic inputs.
Keywords
  • sampling
  • surface reconstruction
  • polyhedral meshing
  • Voronoi

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References

  1. A. Abdelkader, C. Bajaj, M. Ebeida, A. Mahmoud, S. Mitchell, J. Owens, and A. Rushdi. VoroCrust illustrated: theory and challenges (video content). URL: http://computational-geometry.org/SoCG-videos/socg18video/videos/VoroCrust/.
  2. A. Abdelkader, C. Bajaj, M. Ebeida, A. Mahmoud, S. Mitchell, J. Owens, and A. Rushdi. Sampling conditions for conforming Voronoi meshing by the VoroCrust algorithm. In 34th International Symposium on Computational Geometry (SoCG 2018), pages 1:1-1:16, 2018. URL: http://dx.doi.org/10.4230/LIPIcs.SoCG.2018.1.
  3. A. Abdelkader, C. Bajaj, M. Ebeida, A. Mahmoud, S. Mitchell, J. Owens, and A. Rushdi. VoroCrust: Voronoi meshing without clipping. Manuscript, In preparation. Google Scholar
  4. A. Abdelkader, C. Bajaj, M. Ebeida, and S. Mitchell. A Seed Placement Strategy for Conforming Voronoi Meshing. In Canadian Conference on Computational Geometry, 2017. Google Scholar
  5. J. Ahrens, B. Geveci, and C. Law. Paraview: An end-user tool for large-data visualization. In C. Hansen and C. Johnson, editors, Visualization Handbook, pages 717-731. Butterworth-Heinemann, 2005. Google Scholar
  6. N. Amenta and R.-K. Kolluri. The medial axis of a union of balls. Computational Geometry, 20(1):25-37, 2001. Selected papers from the 12th Annual Canadian Conference. Google Scholar
  7. N. Bellomo, F. Brezzi, and G. Manzini. Recent techniques for PDE discretizations on polyhedral meshes. Mathematical Models and Methods in Applied Sciences, 24(08):1453-1455, 2014. Google Scholar
  8. T. Brochu, C. Batty, and R. Bridson. Matching fluid simulation elements to surface geometry and topology. ACM Trans. Graph., 29(4):47:1-47:9, 2010. Google Scholar
  9. F. Chazal and D. Cohen-Steiner. A condition for isotopic approximation. Graphical Models, 67(5):390-404, 2005. Solid Modeling and Applications. Google Scholar
  10. F. Chazal and A. Lieutier. Smooth manifold reconstruction from noisy and non-uniform approximation with guarantees. Computational Geometry, 40(2):156-170, 2008. Google Scholar
  11. S.-W. Cheng, T. Dey, and J. Shewchuk. Delaunay Mesh Generation. CRC Press, 2012. Google Scholar
  12. Microsoft Corporation. Bing Speech API. URL: https://azure.microsoft.com/en-us/services/cognitive-services/speech/.
  13. M. Ebeida and S. Mitchell. Uniform random Voronoi meshes. In International Meshing Roundtable (IMR), pages 258-275, 2011. Google Scholar
  14. R. Eymard, T. Gallouët, and R. Herbin. Finite volume methods. In Techniques of Scientific Computing (Part 3), volume 7 of Handbook of Numerical Analysis, pages 713-1018. Elsevier, 2000. Google Scholar
  15. R.-V. Garimella, J. Kim, and M. Berndt. Polyhedral mesh generation and optimization for non-manifold domains. In International Meshing Roundtable (IMR), pages 313-330. Springer International Publishing, 2014. Google Scholar
  16. OpenShot Studios, LLC. OpenShot Video Editor. URL: http://www.openshot.org/.
  17. M. Peric and S. Ferguson. The advantage of polyhedral meshes. Dynamics - Issue 24, page 4–5, Spring 2005. The customer magazine of the CD-adapco Group, currently maintained by Siemens at http://siemens.com/mdx. The issue is available at http://mdx2.plm.automation.siemens.com/magazine/dynamics-24 (accessed March 29, 2018).
  18. C. Reas and B. Fry. Processing: A Programming Handbook for Visual Designers and Artists. The MIT Press, 2014. Google Scholar
  19. M. Sents and C. Gable. Coupling LaGrit Unstructured Mesh Generation and Model Setup with TOUGH2 Flow and Transport. Comput. Geosci., 108(C):42-49, 2017. Google Scholar
  20. M. Yip, J. Mohle, and J. Bolander. Automated modeling of three‐dimensional structural components using irregular lattices. Computer-Aided Civil and Infrastructure Engineering, 20(6):393-407, 2005. Google Scholar
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