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Practical Boolean Operations on Point-Sampled Models

  • Xujia Qin
  • Weihong Wang
  • Qu Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3980)

Abstract

Boolean operation is an important way in geometry modeling. This paper proposes a novel Boolean operations algorithm for point-sampled models based on implicit function transforming. In the algorithm, the point models are converted to implicit surfaces at first, and then Boolean operations for implicit surface are used to the point models. The simple forms of Boolean operations for implicit surfaces are presented. The method of RBF variational interpolation based on scattered points is used to convert the point models into implicit surfaces. Using this algorithm, complex point model can be constructed from several point models. This Boolean operations algorithm for point models is also suitable for Boolean operations for mesh models. It can implement the editing process of Cut-and-Paste for mesh models.

Keywords

Boolean Operation Point Model Mesh Model Move Little Square Implicit Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Mantyla, M.: An introduction to solid modeling. Computer Science Press, Rockville (1988)Google Scholar
  2. 2.
    Rusinkiewicz, S., Levoy, M.: Qsplat: A multi-resolution point rendering system of large meshes. In: Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, New Orleans, Louisiana, pp. 343–352 (2000)Google Scholar
  3. 3.
    Pauly, M., Gross, M., Zurich, E.: Spectral processing of pointsampled geometry. In: Computer Graphics Proceedings,Annual Conference Series, ACM SIGGRAPH, Los Angeles,California, pp. 379–390 (2001)Google Scholar
  4. 4.
    Zwicker, M., Pauly, M., Knoll, O., et al.: Pointshop 3D: An interactive system for point-based surface editing. In: Computer Graphics Proceedings, Annual Conference Series,ACM SIGGRAPH, San Antonio, Texas, pp. 322–329 (2002)Google Scholar
  5. 5.
    Alexa, M., Behr, J., et al.: Computing and rendering point set surfaces. IEEE Transactions on Visaulization and Computer Graphics 9(1), 3–15 (2003)CrossRefGoogle Scholar
  6. 6.
    Pauly, M., Keiser, R., Kobbelt, P.L., et al.: Shape modeling with point-sampled geometry. In: Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, San Diego, California, pp. 641–650 (2003)Google Scholar
  7. 7.
    Ohtake, Y., Belyaev, A., Alexa, M., et al.: Multi-level partition of unity implicits. In: Computer Graphics Proceedings,Annual Conference Series, ACM SIG GRAPH, San Diego,California, pp. 463–470 (2003)Google Scholar
  8. 8.
    Adams, B., Dutre, P.: Interactive Boolean operations on surfelbounded solids. In: Computer Graphics Proceedings,Annual Conference Series, ACM SIGGRAPH, San Diego,California, pp. 26–31 (2003)Google Scholar
  9. 9.
    Hoffmann, M.C.: Geometric and Solid Modeling: An Introduction. Morgan Kaufmann Publishers Inc., San Francisco (1989)Google Scholar
  10. 10.
    Kristjansson, D., Biermann, H., Zorin, D.: Approximate Boolean operations on free-form solids. In: Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, Los Angeles, California, pp. 185–194 (2001)Google Scholar
  11. 11.
    Museth, K., Breen, D., Whitaker, R., et al.: Level set surface editing operators. ACM Transactions on Graphics 21(3), 330–338 (2002)CrossRefGoogle Scholar
  12. 12.
    Hoffmann, M.C., Hopcroft, E.J.: Robust set operations on polyhydral solids. IEEE Computer Graphics and Applications 9(6), 50–59 (1989)CrossRefGoogle Scholar
  13. 13.
    Wyvill, B., Gallin, E., Guy, A.: Extending the CSG tree: warping,blending and Boolean operations in an implicit surface modeling system. Computer Graphics Forum 18(2), 149–158 (1999)CrossRefGoogle Scholar
  14. 14.
    Pasko, A., Adzhiev, V., Sourin, A., Savchenko, V.: Function Representation in Geometric Modeling: Concepts, Implementation and Applications. The Visual Computer 11(8), 429–446 (1995)CrossRefGoogle Scholar
  15. 15.
    Morse, B.S., Yoo, T.S., Rheingans, P., et al.: Interpolating Implicit Surfaces From Scattered Surface Data Using Compactly Supported Radial Basis Functions. In: Proceedings of Shape Modeling Conference, Genova, Italy, May 2001, pp. 89–98 (2001)Google Scholar
  16. 16.
    Loop, C.: Smooth subdivision surfaces based on triangles. Department of Mathematics. University of Utah, USA (1987)Google Scholar
  17. 17.
    Biermann, H., Martin, I., Bernardini, F., Zorin, D.: Cut-and-Paste editing of multiresolution surfaces. ACM Transactions on Graphics 21(3), 330–338 (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Xujia Qin
    • 1
    • 2
  • Weihong Wang
    • 1
    • 3
  • Qu Li
    • 1
  1. 1.College of Software EngineeringZhejiang University of TechnologyHangZhou
  2. 2.State Key Lab of CAD&CGZhejiang UniversityHanzhou
  3. 3.State key Lab. of Software Development EnvironmentBeijing University of Aeronautics and AstronauticsBeijing

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