iBet uBet web content aggregator. Adding the entire web to your favor.
iBet uBet web content aggregator. Adding the entire web to your favor.



Link to original content: https://unpaywall.org/10.1007/978-3-7091-6344-3_12
An Accurate Model of Wave Refraction Over Shallow Water | SpringerLink
Skip to main content

An Accurate Model of Wave Refraction Over Shallow Water

  • Conference paper
Computer Animation and Simulation 2000

Part of the book series: Eurographics ((EUROGRAPH))

Abstract

A computer model of wave refraction is desirable, in the context of landscape modeling, to generate the familiar wave patterns seen near coastlines. In this article, we present a new method for the calculation of shallow water wave refraction. The method is more accurate than previously existing methods and provides realistic wave refraction effects. We resort to Fermat’s principle of the shortest path and compute the propagation of wavefronts over an arbitrary inhomogeneous medium. The propagation of wavefronts produces a phase map for each terrain. This phase map is then coupled with a geometric model of waves to generate a heightfield representation of the sea surface.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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 EPUB and 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Arthur, R., Munk, W., and Isaacs, J. The direct construction of wave rays. Trans. Am. Geophys. Un. 33, 6 (1952), 855–865.

    Google Scholar 

  2. Benamou, J.-D. Multivalued solution and viscosity solutions of the eikonal equation. Tech. Rep. 3281, INRIA Rocquencourt, October 1997. available at http: //www.inria.fr/RRRT/RR-3281.html.

    Google Scholar 

  3. Biesel, F. Study of wave propagation in water of gradually varying depth. In Gravity Waves. 1952, pp. 243-253. U.S. National Bureau of Standards Circular.

    Google Scholar 

  4. Born, M., and Wolf, E. Principles of Optics: electromagnetic theory of propagation, interference and diffraction of light. Cambridge University Press, Cambridge, UK, 1997.

    Google Scholar 

  5. Campion, D., and Brewer, A. The Book of Waves: Form and Beauty on the Ocean, third ed. Roberts Rinehart Pub., December 1997. ISBN 157098168X.

    Google Scholar 

  6. Chen, J. X., da Vitoria Lobo, N., Hughes, C. E., and Moshell, J. M. Real-Time fluid simulation in a dynamic virtual environment. IEEE Computer Graphics & Applications 17, 3 (May-June 1997), 52–61. ISSN 0272-1716.

    Article  Google Scholar 

  7. Coxeter, H. S. M. Introduction to Geometry. Wiley, New York, 1961.

    Google Scholar 

  8. Foster, N., and Metaxas, D. Realistic animation of liquids. Graphical Models and Image Processing 58, 5 (1996), 471–483.

    Article  Google Scholar 

  9. Fournier, A., and Reeves, W. T. A simple model of ocean waves. In Computer Graphics (SIGGRAPH’ 86 Proceedings) (Aug. 1986), D. C. Evans and R. J. Athay, Eds., vol. 20, pp. 75–84.

    Article  Google Scholar 

  10. Gamito, M. N., and Musgrave, F. K. Non-height field rendering, available at http: //www.wizardnet.com/musgrave/sundry.html.

    Google Scholar 

  11. Gelfand, I. M., and Fomin, S. V. Calculus of Variations, rev. english ed. Prentice-Hall, Englewood Cliffs, N.J., 1963.

    Google Scholar 

  12. Gonzato, J.-C., and le Saec, B. A phenomenological model of coastal scenes based on physical considerations. In Computer Animation and Simulation’ 97 (1997), D. Thalmann and M. van de Panne, Eds., Eurographics Association, Springer Computer Science, pp. 137-148. ISBN 3-211-83048-0.

    Google Scholar 

  13. Hindmarsh, A. C. Odepack: A systematized collection of ode solvers. In Scientific Computing, R. S. Stepleman, Ed. North-Holland, Amsterdam, 1983, pp. 55-64. Package available at www.netlib.org.

    Google Scholar 

  14. Kass, M., and Miller, G. Rapid, stable fluid dynamics for computer graphics. In Computer Graphics (SIGGRAPH’ 90 Proceedings) (Aug. 1990), F. Baskett, Ed., vol. 24, pp. 49–57.

    Article  Google Scholar 

  15. Kinsman, B. Wind Waves. Dover, 1984.

    Google Scholar 

  16. LE Méhauté, B. An Introduction to Hydrodynamics and Water Waves. Springer-Verlag, New York, 1976.

    Google Scholar 

  17. Lewis, J.-P. Algorithms for solid noise synthesis. In Computer Graphics (SIGGRAPH’ 89 Proceedings) (July 1989), J. Lane, Ed., vol. 23, pp. 263–270.

    Article  Google Scholar 

  18. Mastin, G. A., Watterberg, P. A., and Mareda, J. F. Fourier synthesis of ocean scenes. IEEE Computer Graphics and Applications 7, 3 (Mar. 1987), 16–23.

    Article  Google Scholar 

  19. Max, N. L. Vectorized procedural models for natural terrain: Waves and islands in the sunset. In Computer Graphics (SIGGRAPH’ 81 Proceedings) (Aug. 1981), vol. 15, pp. 317–324.

    Article  Google Scholar 

  20. Peachey, D. R. Modeling waves and surf. In Computer Graphics (SIGGRAPH’ 86 Proceedings) (Aug. 1986), D. C. Evans and R. J. Athay, Eds., vol. 20, pp. 65–74.

    Article  Google Scholar 

  21. Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. Numerical Recipes in C: The Art of Scientific Computing (2nd ed.). Cambridge University Press, Cambridge, 1992. ISBN 0-521-4310

    Google Scholar 

  22. Schachter, B. J. Long crested wave models. Computer Graphics and Image Processing 12 (1980), 187–201.

    Article  Google Scholar 

  23. Tessendorf, J. Simulating ocean water. In Simulating Nature: From Theory to Applications (1999), D. S. Ebert, Ed., no. 26 in SIGGRAPH 99 Course Notes.

    Google Scholar 

  24. TS’O, P. Y., and Barsky, B. A. Modeling and rendering waves: Wave-tracing using beta-splines and reflective and refractive texture mapping. ACM Transactions on Graphics 6, 3 (1987), 191–214.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Wien

About this paper

Cite this paper

Gamito, M.N., Musgrave, F.K. (2000). An Accurate Model of Wave Refraction Over Shallow Water. In: Magnenat-Thalmann, N., Thalmann, D., Arnaldi, B. (eds) Computer Animation and Simulation 2000. Eurographics. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6344-3_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-6344-3_12

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83549-4

  • Online ISBN: 978-3-7091-6344-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics