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Piecewise Linear Approximation for Scientific Data

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Geometric Modeling: Theory and Practice

Part of the book series: Focus on Computer Graphics ((FOCUS COMPUTER))

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Abstract

The visualization of scientific data allows for a faster and better insight in measurements and numerical computations. In order to generate reliable image results, the rendering has to be based on an error control. Since many visualization techniques use linear approximation schemes, we give estimates of the approximation error in arbitrary dimensions. Our results can be considered as generalizations and improvements of already existing estimates for curves and surfaces.

Supported by the Deutsche Forschungsgemeinschaft, SFB 382

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References

  1. K. Brodlie. A classification scheme for scientific data. In R.A. Earnshaw and D. Watson, editors, Animation and Scientific Visualisation, Tools and Applications, pages 125–140. Academic Press, London, 1993.

    Google Scholar 

  2. C. de Boor. A Practical Guide to Splines. Springer, 1978.

    Google Scholar 

  3. L. De Floriani, E. Puppo, and P. Magillo. A formal approach to multiresolution modeling. In Proceedings Blaubeuren II), 1996.

    Google Scholar 

  4. Matthias Eck, Tony DeRose, Tom Duchamp, Hugues Hoppe, Michael Lounsbery, and Werner Stuetzle. Multiresolution analysis of arbitrary meshes. In Robert Cook, editor, SIGGRAPH 95 Conference Proceedings, Annual Conference Series, pages 173–182. ACM SIGGRAPH, Addison Wesley, August 1995. held in Los Angeles, California, 06–11 August 1995.

    Google Scholar 

  5. D. Filip, R. Magedson, and R. Markot. Surface algorithms using bounds on derivatives. Computer Aided Geometric Design, 3(4):295–311, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  6. Mark Hall and Joe Warren. Adaptive polygonalization of implicitly defined surfaces. IEEE Computer Graphics and Applications, 10(6):33–42, November 1990.

    Article  Google Scholar 

  7. R. Klein. Polygonalization of algebraic surfaces. In P.J. Laurent, A. Le Méhauté, and L. L Schumaker, editors, Curves and Surfaces II. AKPeters, Boston, 1993.

    Google Scholar 

  8. R. Klein. Linear approximation of trimmed surfaces. In R.R. Martin, editor, The Mathematics Of Surfaces VI, pages 209–212, 1994.

    Google Scholar 

  9. Marc Levoy. Display of surfaces from volume data. IEEE Computer Graphics and Applications, 8(3):29–37, May 1988.

    Article  Google Scholar 

  10. Marc Levoy. Efficient ray tracing of volume data. ACM Transactions on Graphics, 9(3):245–261, July 1990.

    Article  MATH  Google Scholar 

  11. William E. Lorensen and Harvey E. Cline. Marching cubes: A high resolution 3D surface construction algorithm. In Maureen C. Stone, editor, Computer Graphics (SIGGRAPH ’87 Proceedings), volume 21, pages 163–169, July 1987.

    Google Scholar 

  12. R. Rau. An object-oriented framework for the visualization of scientific data. Submitted for publication, 1996.

    Google Scholar 

  13. William J. Schroeder, Jonathan A. Zarge, and William E. Lorensen. Decimation of triangle meshes. In Edwin E. Catmull, editor, Computer Graphics (SIGGRAPH ’92 Proceedings), volume 26, pages 65–70, July 1992.

    Google Scholar 

  14. X. Sheng and B. E. Hirsch. Triangulation of trimmed surfaces in parametric space. Computer Aided Design, 24(8):437–444, August 1992.

    Article  MATH  Google Scholar 

  15. Peter Shirley and Allan Tuchman. A polygonal approximation to direct scalar volume rendering. In Computer Graphics (San Diego Workshop on Volume Visualization), volume 24, pages 63–70, November 1990.

    Google Scholar 

  16. Brian Von Herzen and Alan H. Barr. Accurate triangulations of deformed, intersecting surfaces. In Maureen C. Stone, editor, Computer Graphics (SIGGRAPH ’87 Proceedings), volume 21, pages 103–110, July 1987.

    Google Scholar 

  17. Lee Westover. Footprint evaluation for volume rendering. In Forest Baskett, editor, Computer Graphics (SIGGRAPH ’90 Proceedings), volume 24, pages 367–376, August 1990.

    Google Scholar 

  18. G. M. Ziegler. Lectures on Polytopes. Springer, 1995.

    Google Scholar 

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© 1997 Springer-Verlag Berlin Heidelberg

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Strasser, W., Klein, R., Rau, R. (1997). Piecewise Linear Approximation for Scientific Data. In: Strasser, W., Klein, R., Rau, R. (eds) Geometric Modeling: Theory and Practice. Focus on Computer Graphics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60607-6_22

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  • DOI: https://doi.org/10.1007/978-3-642-60607-6_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61883-6

  • Online ISBN: 978-3-642-60607-6

  • eBook Packages: Springer Book Archive

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