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Diaphony of Uniform Samples over Hemisphere and Sphere

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Numerical Analysis and Its Applications (NAA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5434))

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Abstract

The sampling of certain solid angle is a fundamental operation in realistic image synthesis, where the rendering equation describing the light propagation in closed domains is solved. In this work we consider the problem for generation of uniformly distributed random samples over hemisphere and sphere. Using two algorithms we obtain samples in orthogonal spherical triangle and spherical quadrangle. Our aim is to prove uniform distribution of the obtained samples. The importance of the uniformly distributed samples is determined by the effectiveness of the algorithms for numerical solution of the rendering equation. We use numerical characteristic for uniform distribution of points, called diaphony. The diaphony of these samples is calculated numerically. Analysis and comparison of the obtained results are made.

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References

  1. Dimov, I.T., Penzov, A.A., Stoilova, S.S.: Parallel Monte Carlo Sampling Scheme for Sphere and Hemisphere. In: Li, Z., Vulkov, L.G., Waśniewski, J. (eds.) NAA 2004. LNCS, vol. 3401, pp. 148–155. Springer, Heidelberg (2005)

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  2. Dimov, I.T., Penzov, A.A., Stoilova, S.S.: Parallel Monte Carlo Approach for Intgration of the Rendering Equation. In: Li, Z., Vulkov, L.G., Waśniewski, J. (eds.) NAA 2004. LNCS, vol. 3401, pp. 140–147. Springer, Heidelberg (2005)

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  3. Grozdanov, V., Stoilova, S.: On the Theory of b-adic Diaphony. Comp. Ren. Akad. Bul. Sci. 54(3), 31–34 (2001)

    MathSciNet  MATH  Google Scholar 

  4. Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numer. Math. 2, 84–90 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  5. Hellekalek, P., Leeb, H.: Dyadic Diaphony. Acta Arithmetica LXXX(2), 187–196

    Google Scholar 

  6. Keller, A.: Quasi-Monte Carlo Methods in Computer Graphics: The Global Illumination Problem. Lectures in Applied Mathematics 32, 455–469 (1996)

    MathSciNet  MATH  Google Scholar 

  7. Roth, K.: On irregularities of distribution. Mathematika 1, 73–79 (1954)

    Article  MathSciNet  MATH  Google Scholar 

  8. Weyl, H.: Über die Gleichverteilung von Zahlen mod. Eins. Math. Ann. 77(S), 313–352 (1916)

    Article  MATH  Google Scholar 

  9. Zinterhof, P.: Über einige Abschätzungen bei der Approximation von Funktionen mit Gleichverteilungsmethoden. Sitzungsber. Osterr. Akad. Wiss. Math.-Naturwiss. abt II 185, 121–132 (1976)

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

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

    I. T. Dimov & N. Mitev

  2. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 8, 1113, Sofia, Bulgaria

    S. S. Stoilova

Authors
  1. I. T. Dimov
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  2. S. S. Stoilova
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  3. N. Mitev
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Editor information

Editors and Affiliations

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

    Svetozar Margenov

  2. FNSE, Department of Numerical Methods and Statistics, University of Rousse, 8 Studentska str., 7017, Rousse, Bulgaria

    Lubin G. Vulkov

  3. Department of Informatics and Mathematical Modelling, Technical University of Denmark, 2800, Kongens, Lyngby, Denmark

    Jerzy Waśniewski

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Dimov, I.T., Stoilova, S.S., Mitev, N. (2009). Diaphony of Uniform Samples over Hemisphere and Sphere. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2008. Lecture Notes in Computer Science, vol 5434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00464-3_27

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  • DOI: https://doi.org/10.1007/978-3-642-00464-3_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00463-6

  • Online ISBN: 978-3-642-00464-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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