Skip to main content

Globally Convergent Adaptive Normal Multi-scale Transforms

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6920))

Abstract

In this paper we introduce a family of globally well-posed and convergent normal multi-scale transforms with high-order detail decay rate for smooth curves, based on adaptivity. For one of the members in the family, we propose a concrete algorithm what the adaptive criteria should be, and provide numerical evidence for the implementation. We compare the performance of our algorithm with other normal multi-scale transforms.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baraniuk, R., Janssen, M., Lavu, S.: Multiscale approximation of piecewise smooth two-dimensional functions using normal triangulated meshes. Appl. Comput. Harm. Anal. 19, 92–130 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. Binev, P., Dahmen, W., DeVore, R.A., Dyn, N.: Adaptive approximation of curves. In: Approximation Theory, pp. 43–57. Acad. Publ. House, Sofia (2004)

    Google Scholar 

  3. Daubechies, I., Runborg, O., Sweldens, W.: Normal multiresolution approximation of curves. Constr. Approx. 20, 399–462 (2005)

    MathSciNet  MATH  Google Scholar 

  4. Dyn, N., Floater, M., Hormann, K.: Four-point curve subdivision based on iterated chordal and centripetal parameterizations. Comp. Aided Geom. Design 26, 279–286 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Friedel, I., Khodakovsky, A., Schröder, P.: Variational normal meshes. ACM Trans. Graph. 23, 1061–1073 (2004)

    Article  Google Scholar 

  6. Guskov, I., Vidimce, K., Sweldens, W., Schröder, P.: Normal meshes. In: Computer Graphics Proceedings (Siggraph 2000), pp. 95–102. ACM Press, New York (2000)

    Google Scholar 

  7. Harizanov, S., Oswald, P.: Stability of nonlinear subdivision and multiscale transforms. Constr. Approx. 31, 359–393 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Harizanov, S., Oswald, P., Shingel, T.: Normal multi-scale transforms for curves. Found. Comput. Math. (2009) (submitted)

    Google Scholar 

  9. Khodakovsky, A., Guskov, I.: Compression of normal meshes. In: Geometric Modeling for Scientific Visualization, pp. 189–207. Springer, Berlin (2003)

    Google Scholar 

  10. Lavu, S., Choi, H., Baraniuk, R.: Geometry compression of normal meshes using rate-distortion algorithms. In: Eurographics/ACM Siggraph Symposium on Geometry Processing, pp. 52–61. RWTH Aachen (2003)

    Google Scholar 

  11. Marinov, M., Dyn, N., Levin, D.: Geometrically controlled 4-point interpolatory schemes. In: Dodgson, N., Floater, M., Sabin, M. (eds.) Advances in Multiresolution for Geometric Modelling, pp. 301–315. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  12. Oswald, P.: Normal multi-scale transforms for surfaces. This Proceedings (submitted)

    Google Scholar 

  13. Runborg, O.: Introduction to normal multiresolution analysis. In: Samelson, K. (ed.) Multiscale Methods in Science and Engineering. LNCS, vol. 44, pp. 205–224. Springer, Heidelberg (2005)

    Google Scholar 

  14. Runborg, O.: Fast interface tracking via a multiresolution representation of curves and surfaces. Commun. Math. Sci. 7, 365–389 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  15. Sabin, M., Dodgson, N.: A circle-preserving variant of the four-point subdivision scheme. In: Dahlen, M., Morken, K., Schumaker, L.L. (eds.) Mathematical Methods for Curves and Surfaces: Tromso 2004, pp. 275–286. Nashboro Press (2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Harizanov, S. (2012). Globally Convergent Adaptive Normal Multi-scale Transforms. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2010. Lecture Notes in Computer Science, vol 6920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27413-8_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-27413-8_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27412-1

  • Online ISBN: 978-3-642-27413-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics