Skip to main content
SpringerLink
Log in
Book cover

International Conference on Large-Scale Scientific Computing

LSSC 2007: Large-Scale Scientific Computing pp 670–678Cite as

Surface Reconstruction and Lagrange Basis Polynomials

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4818))

Abstract

Surface reconstruction, based on line integrals along segments of the unit disk is studied. Various methods concerning with this problem are known. We consider here interpolation over regular schemes of chords by polynomials. We find the interpolant in Lagrange form and investigate some properties of Lagrange basis polynomials. Numerical experiments for both surface and image reconstruction are presented.

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

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. Bojanov, B., Georgieva, I.: Interpolation by bivariate polynomials based on Radon projections. Studia Math. 162, 141–160 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bojanov, B., Petrova, G.: Numerical integration over a disc. A new Gaussian cubature formula. Numer. Math. 80, 39–59 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bojanov, B., Petrova, G.: Uniqueness of the Gaussian cubature for a ball. J. Approx. Theory 104, 21–44 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bojanov, B., Xu, Y.: Reconstruction of a bivariate polynomials from its Radon projections. SIAM J. Math. Anal. 37, 238–250 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Davison, M.E., Grunbaum, F.A.: Tomographic reconstruction with arbitrary directions. Comm. Pure Appl. Math. 34, 77–120 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  6. Georgieva, I., Ismail, S.: On recovering of a bivariate polynomial from its Radon projections. In: Constructive Theory of Functions, pp. 127–134. Marin Drinov Academic Publishing House, Sofia (2006)

    Google Scholar 

  7. Georgieva, I., Uluchev, R.: Smoothing of Radon projections type of data by bivariate polynomials. In: J. Comput. Appl. Math. (to appear)

    Google Scholar 

  8. Hakopian, H.: Multivariate divided differences and multivariate interpolation of Lagrange and Hermite type. J. Approx. Theory 34, 286–305 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  9. John, F.: Abhängigkeiten zwischen den Flächenintegralen einer stetigen Funktion. Math. Anal. 111, 541–559 (1935)

    Article  MATH  Google Scholar 

  10. Marr, R.: On the reconstruction of a function on a circular domain from a sampling of its line integrals. J. Math. Anal. Appl. 45, 357–374 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  11. Natterer, F.: The Mathematics of Computerized Tomography. Classics in Applied Mathematics 32 (2001)

    Google Scholar 

  12. Pickalov, V., Melnikova, T.: Plasma Tomography, Nauka, Novosibirsk (1995) (in Russian)

    Google Scholar 

  13. Radon, J.: Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten. Ber. Verch. Sächs. Akad. 69, 262–277 (1917)

    MATH  Google Scholar 

  14. Solmon, D.C.: The X-ray transform. J. Math. Anal. Appl. 56(1), 61–83 (1976)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl. 8, Sofia, 1113, Bulgaria

    Irina Georgieva

  2. Department of Mathematics and Informatics, University of Transport, 158 Geo Milev Str., Sofia, 1574, Bulgaria

    Rumen Uluchev

Authors
  1. Irina Georgieva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rumen Uluchev
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl. 25A, 1113, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25-A, 1113, Sofia, Bulgaria

    Svetozar Margenov

  3. Department of Informatics and Mathematical Modelling, Technical University of Denmark, Richard Petersen Plads, Building 321, DK-2800, Kongens Lyngby, Denmark

    Jerzy Waśniewski

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Georgieva, I., Uluchev, R. (2008). Surface Reconstruction and Lagrange Basis Polynomials. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2007. Lecture Notes in Computer Science, vol 4818. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78827-0_77

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-78827-0_77

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78825-6

  • Online ISBN: 978-3-540-78827-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation