Browse > Article

A Study on Intersection Computation in Interval Arithmetic  

Ko, Kwang-Hee (광주과학기술원 기전공학과)
Publication Information
Korean Journal of Computational Design and Engineering / v.15, no.3, 2010 , pp. 178-188 More about this Journal
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
validated ODE solver; interval arithmetic; approximation; tracing method; tangential intersection; transversal intersection; surface-to-surface intersection;
Citations & Related Records
연도 인용수 순위
  • Reference
1 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.   DOI   ScienceOn
2 Kotrox Inc. URL: http://www.kotrox.co.kr
3 3DVIA Virtools. URL: http://www.3ds.com/products/3dvia/3dvia-virtools
4 DMX (Distributed multihead x) project. URL: http://dmx.sourceforge.net
5 OpenSG project. URL: http://opensg.vrsource.org
6 OpenSceneGraph project. URL: http://www.open-scenegraph.org
7 OGRE3D (Object-oriented Graphics Rendering Engine) project. URL: http://www.ogre3d.org
8 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.
9 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.
10 OGRE on a Cluster project. URL: http://www.ogre3d.org/wiki/index.php/Ogre_on_a_Cluster
11 Raffin, B. and Soares, L., "PC Clusters for Virtual Reality", Proc Proc. IEEE Conf. Virtual Reality (VR '06), pp. 215-222, 2006.
12 Matrox Inc. URL: http://www.matrox.com
13 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.   DOI   ScienceOn
14 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.
15 Lorenz, M. and Brunnett, G., "Optimized Visualization for Tiled Displays", Proc. Parallel Graphics and Visualization 2006, Eurographics Association, pp. 127-130, 2006.
16 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.   DOI   ScienceOn
17 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.
18 Presagis VEGA Prime. URL: http://www.presagis.com/products/visualization/vegaprime
19 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.