Generating Flow Fields Variations Using Laplacian Eigenfunctions

  • Syuhei Sato
  • Yoshinori Dobashi
  • Kei Iwasaki
  • Hiroyuki Ochiai
  • Tsuyoshi Yamamoto
Part of the Mathematics for Industry book series (MFI, volume 4)


The visual simulation of fluids has become an important element in many applications, such as movies and computer games. In these applications, large-scale fluid scenes, such as fire in a village, are often simulated by repeatedly rendering multiple small-scale fluid flows. In these cases, animators are requested to generate many variations of a small-scale fluid flow. This chapter presents a method to help animators meet such requirements. Our method enables the user to generate flow field variations from a single simulated dataset obtained by fluid simulation. The variations are generated in both the frequency and spatial domains. Fluid velocity fields are represented using Laplacian eigenfunctions which ensure that the flow field is always incompressible. Using our method, the user can easily create various animations from a single dataset calculated by fluid simulation.


Flow field Variation synthesis Laplacian eigenfunctions Amplitude modulation Resizing simulation space 


  1. 1.
    Bridson R, Hourihan J, Nordenstam M (2007) Curl-noise for procedural fluid flow. ACM Trans Graph 26(3):Article 46Google Scholar
  2. 2.
    Bridson R (2008) Fluid simulation for computer graphics. AK PetersGoogle Scholar
  3. 3.
    Fuller AR, Krishnan H, Mahrous K, Hamann B, Joy KI (2007) Real-time procedural volumetric fire. In: Proceeding of the 2007 symposium on Interactive 3D graphics and games, pp 175–180Google Scholar
  4. 4.
    Lamorlette A, Foster N (2002) Structural modeling of flames for a production environment. ACM Trans Graph 21(3):729–735CrossRefGoogle Scholar
  5. 5.
    Patel M, Taylor N (2005) Simple divergence-free fields for artistic simulation. J Graph GPU Game Tools 10(4):49–60CrossRefGoogle Scholar
  6. 6.
    Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2007) Numerical recipes, 3rd edn: The art of scientific computing. Cambridge University Press, CambridgeGoogle Scholar
  7. 7.
    Witt TD, Lessig C, Fiume E (2012) Fluid simulation using Laplacian eigenfunctions. ACM Trans Graph 31(1):Article 10Google Scholar

Copyright information

© Springer Japan 2014

Authors and Affiliations

  • Syuhei Sato
    • 1
  • Yoshinori Dobashi
    • 2
  • Kei Iwasaki
    • 3
  • Hiroyuki Ochiai
    • 4
  • Tsuyoshi Yamamoto
    • 1
  1. 1.Graduate School of Information Science and TechnologyHokkaido UniversitySapporoJapan
  2. 2.Graduate School of Information Science and TechnologyHokkaido University/JST CRESTSapporoJapan
  3. 3.Wakayama UniversityWakayamaJapan
  4. 4.Institute of Mathematics for IndustryKyushu University/JST CRESTFukuokaJapan

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