Skip to main content

Piecewise approximate implicitization: experiments using industrial data

  • Conference paper
Book cover Algebraic Geometry and Geometric Modeling

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chuang, J., Hoffmann, C.: On local implicit approximation and its applications. ACM Trans. Graphics 8, 4:298-324, (1989)

    Article  MATH  Google Scholar 

  2. Corless, R., Giesbrecht, M., Kotsireas, I., Watt., S.: Numerical implicitization of parametric hypersurfaces with linear algebra. In: AISC’2000 Proceedings, Springer, LNAI 1930.

    Google Scholar 

  3. Cox, D., Little, J., O’Shea, D.: Ideals, Varieties and Algorithms, Springer, New York 1997.

    Google Scholar 

  4. Cox, D., Little, J., O’Shea, D,: Using algebraic geometry, Springer Verlag, New York 1998.

    MATH  Google Scholar 

  5. Cox, D., Goldman, R., Zhang, M.: On the validity of implicitization by moving quadrics for rational surfaces with no base points, J. Symbolic Computation, 11,(1999)

    Google Scholar 

  6. Dokken, T.: Approximate Implicitization, in: Lyche, T., Schumaker, L. (eds.), Mathematical methods in CAGD, Nashboro Press, 2001, 1-25.

    Google Scholar 

  7. Dokken, T., Thomassen, J.: Overview of Approximate Implicitization, in: Topics in Algebraic Geometry and Geometric Modeling, AMS Cont. Math. 334 (2003), 169-184.

    MathSciNet  Google Scholar 

  8. Dokken, T., Thomassen, J.: Weak approximate implicitization, preprint, 2005.

    Google Scholar 

  9. Elkadi, M., Mourrain B.: Residue and Implicitization Problem for Rational Surfaces, Applicable Algebra in Engineering, Communication and Computing, (2004),361-379.

    Google Scholar 

  10. Farin, G.: Curves and Surfaces for Computer Aided Geometric Design, Academic Press, 2002.

    Google Scholar 

  11. PoVRAY Benchmarks, http://new.haveland.com/povbench/graph.php

  12. Hoffmann, C.: Implicit Curves and Surfaces in CAGD, Comp. Graphics and Applics. 13:79-88, (1993)

    Article  Google Scholar 

  13. Jüttler, B., Felis, A.: Least-squares fitting of algebraic spline surfaces, Advances in Computational Mathematics 17:135-152, (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. Jüttler, B., Wurm, E.: Approximate implicitization via curve fitting, in L. Kobbelt, P. Schröder, H. Hoppe (eds.), Symposium on Geometry Processing, Eurographics / ACM Siggraph, New York 2003, 240-247.

    Google Scholar 

  15. Lee, K.W.: Principles of CAD/CAM/CAE Systems, Prentice Hall, 1999.

    Google Scholar 

  16. Thomassen, J., Self-intersection problems and approximate implicitization, in: Dokken, T., Jüttler, B. (eds.), Computational Methods for Algebraic Spline Surfaces, Springer, Berlin 2005, 155-170.

    Chapter  Google Scholar 

  17. Sederberg, T., Chen F.: Implicitization using moving curves and surfaces. Siggraph 1995, 29:301-308, (1995)

    Google Scholar 

  18. Šır, Z.: Fitting of Piecewise Polynomial Implicit Surfaces, Proc. of the 24rd Conference on Geometry and Computer Graphics, University of Ostrava 2004, 202-206.

    Google Scholar 

  19. Gonzalez-Vega, L.: Implicitization of parametric curves and surfaces by using multidimensional Newton formulae. J. Symb. Comput. 23(2-3), 137-151 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  20. Wurm, E., Thomassen, J., Jüttler, B., Dokken, T.: Comparative Benchmark-ing of Methods for Approximate Implicitization, in: Neamtu, M., and Lucian, M. (eds.), Geometric Modeling and Computing: Seattle 2003, Nashboro Press, Brentwood 2004, 537-548.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Shalaby, M.F., Thomassen, J.B., Wurm, E.M., Dokken, T., Jüttler, B. (2006). Piecewise approximate implicitization: experiments using industrial data. In: Elkadi, M., Mourrain, B., Piene, R. (eds) Algebraic Geometry and Geometric Modeling. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-33275-6_3

Download citation

Publish with us

Policies and ethics