Korean Journal of Computational Design and Engineering (한국CDE학회논문집)

Society for Computational Design and Engineering (한국CDE학회)
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A Study on Intersection Computation in Interval Arithmetic

인터벌 연산 기반의 곡면간 교차선 계산에 관한 연구

  • 고광희 (광주과학기술원 기전공학과)
  • Received : 2009.10.05
  • Accepted : 2010.03.22
  • Published : 2010.06.01
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Abstract

This paper addresses the problem of determining if two surfaces intersect tangentially or transversally in a mathematically consistent manner and approximating an intersection curve. When floating point arithmetic is used in the computation, due to the limited precision, it often happens that the decision for tangential and transversal intersection is not clear cut. To handle this problem, in this paper, interval arithmetic is proposed to use, which provides a mathematically consistent way for such decision. After the decision, the intersection is traced using the validated ODE solver, which runs in interval arithmetic. Then an iterative method is used for computing the accurate intersection point at a given arc-length of the intersection curve. The computed intersection points are then approximated by using a B-spline curve, which is provided as one instance of intersection curve for further geometric processing. Examples are provided to demonstrate the proposed method.

Keywords

References

  1. Ball, R. and North, C., "Effects of Tiled High- Resolution Display on Basic Visualization and Navigation Tasks", Proc. Computer-Human Interaction (CHI '05), pp. 1196-1199, 2005.
  2. Grant Wallace, Otto J. Anshus, Peng Bi, Han Chen, Yuqun Chen, Douglas Clark, Perry Cook, Adam Finkelstein, Thomas Funkhouser, Anoop Gupta, Matthew Hibbs, Kai Li, Zhiyan Liu, Rudrajit Samanta, Rahul Sukthankar, and Olga Troyanskaya, "Tools and Applications for Large-Scale Display Walls", IEEE Computer Graphics and Applications, Vol. 25 No. 4, pp. 24-33, 2005. https://doi.org/10.1109/MCG.2005.89
  3. Ni, T., Schmidt, G. S., Staadt, O. G., Ball, R. and May, R., "A Survey of Large High-Resolution Display Technologies, Techniques, and Applications", Proc. IEEE Conf. Virtual Reality (VR '06), pp. 223-224, 2006.
  4. Hereld, M., Judson, I. R. and Stevens, R. L., "Introduction to Building Projection-based Tiled Display Systems", IEEE Computer Graphics and Applications, Vol. 20, No. 4, pp. 22-28, 2000. https://doi.org/10.1109/38.851746
  5. Han Chen, Douglas W. Clark, Zhiyan Liu, Grant Wallace, Kai Li and Yuqun Chen, "Software Environments For Cluster-Based Display Systems", Proc. 1st International Symposium on Cluster Computing and the Grid, pp. 202, 2001.
  6. Raffin, B. and Soares, L., "PC Clusters for Virtual Reality", Proc Proc. IEEE Conf. Virtual Reality (VR '06), pp. 215-222, 2006.
  7. Lorenz, M. and Brunnett, G., "Optimized Visualization for Tiled Displays", Proc. Parallel Graphics and Visualization 2006, Eurographics Association, pp. 127-130, 2006.
  8. Chen, H., Chen, Y., Finkelstein, A. et al., "Data Distribution Strategies for High Resolution Displays", Computers and Graphics, Vol. 25, No. 5, pp. 811-818, 2001. https://doi.org/10.1016/S0097-8493(01)00123-6
  9. Presagis VEGA Prime. URL: http://www.presagis.com/products/visualization/vegaprime
  10. 3DVIA Virtools. URL: http://www.3ds.com/products/3dvia/3dvia-virtools
  11. OpenSG project. URL: http://opensg.vrsource.org
  12. OpenSceneGraph project. URL: http://www.open-scenegraph.org
  13. OGRE3D (Object-oriented Graphics Rendering Engine) project. URL: http://www.ogre3d.org
  14. DMX (Distributed multihead x) project. URL: http://dmx.sourceforge.net
  15. Greg Humphreys, Matthew Eldridge, Ian Buck, Gordan Stoll, Matthew Everett and Pat Anrahan, "WireGL: A Scalable Graphics System for Clusters", Proc. SIGGRAPH, pp. 129-140, 2001.
  16. Humphreys, G., Houston, M., Ng, R., Frank, F., Ahern, S., Kirchner, P. and Klosowski, J., "Chromium: A Streamprocessing Framework for Interactive Rendering on Clusters", Proc. SIGGRAPH, pp. 693-702, 2002.
  17. OGRE on a Cluster project. URL: http://www.ogre3d.org/wiki/index.php/Ogre_on_a_Cluster
  18. Matrox Inc. URL: http://www.matrox.com
  19. Kotrox Inc. URL: http://www.kotrox.co.kr