Spline Surface Intersections Optimized for GPUs

  • Sverre Briseid
  • Tor Dokken
  • Trond Runar Hagen
  • Jens Olav Nygaard
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3994)


A commodity-type graphics card with its graphics processing unit (GPU) is used to detect, compute and visualize the intersection of two spline surfaces, or the self-intersection of a single spline surface. The parallelism of the GPU facilitates fast and efficient subdivision and bounding box testing of smaller spline patches and their corresponding normal subpatches. This subdivision and testing is iterated until a prescribed level of accuracy is reached, after which results are returned to the main computer. We observe speedups up to 17 times relative to a contemporary 64 bit CPU.


Intersection Curve Algebraic Degree Spline Surface Intersection Algorithm Degenerate Normal 
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  1. 1.
    Dokken, T.: Aspect of Intersection algorithms and Approximation. Thesis for the doctor philosophias degree, University of Oslo, Norway, 52–105 (1997)Google Scholar
  2. 2.
    Farin, G.: Curves and surfaces for CAGD: a practical guide. Morgan Kaufmann Publishers Inc., San Francisco (2002)Google Scholar
  3. 3.
    Hohmeyer, M.E.: Robust and Efficient Surface Intersection for Solid Modelling, Report No. UCB/CSD 92/681, Computer Science Division, University of California (1992)Google Scholar
  4. 4.
    Horn, D.: Stream Reduction Operations for GPGPU Applications. In: GPUGems 2: Programming Techniques for High-Performance Graphics and General-Purpose Computation, pp. 573–587. Addison-Wesley, Reading (2005)Google Scholar
  5. 5.
    Patrikalakis, N.M.: Shape Interrogation for Computer Aided Design and Manufacturing. Springer, Secaucus (2002)MATHGoogle Scholar
  6. 6.
    Sederberg, T.W., Zundel, A.K.: Pyramides that bound surface patches. In: CVGIP: Graphics Models and Image Processing, pp. 75–81 (1996)Google Scholar
  7. 7.
    Sinha, P., Klassen, E., Wang, K.K.: Exploiting topological and geometric properties for selective subdivision. In: ACM Symposium on Computational Geometry, pp. 39–45. ACM Press, New York (1985)Google Scholar
  8. 8.
    Skytt, V.: A recursive approach to surface-surface intersection. In: Dæhlen, M., Mørken, K., Schumaker, L.L. (eds.) Mathematical Methods for Curves and Surfaces: Tromsø 2004. Nashboro Press, Brentwood (2005) 3272̆014338Google Scholar
  9. 9.
    Skytt, V.: Challenges in surface-surface intersections. In: Dokken, T., Jüttler, B. (eds.) Computational Methods for Algebraic Spline Surfaces (COMPASS), pp. 11–26. Springer, Heidelberg (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sverre Briseid
    • 1
  • Tor Dokken
    • 1
    • 2
  • Trond Runar Hagen
    • 1
    • 2
  • Jens Olav Nygaard
    • 1
  1. 1.Dept. of Applied Math.SINTEFBlindernNorway
  2. 2.Centre of Mathematics for Applications (CMA)University of OsloNorway

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