research-article

Open access

Water Wave Animation via Wavefront Parameter Interpolation

Authors:

Stefan Jeschke,

Chris WojtanAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 34, Issue 3

Article No.: 27, Pages 1 - 14

https://doi.org/10.1145/2714572

Published: 08 May 2015 Publication History

Abstract

We present an efficient wavefront tracking algorithm for animating bodies of water that interact with their environment. Our contributions include: a novel wavefront tracking technique that enables dispersion, refraction, reflection, and diffraction in the same simulation; a unique multivalued function interpolation method that enables our simulations to elegantly sidestep the Nyquist limit; a dispersion approximation for efficiently amplifying the number of simulated waves by several orders of magnitude; and additional extensions that allow for time-dependent effects and interactive artistic editing of the resulting animation. Our contributions combine to give us multitudes more wave details than similar algorithms, while maintaining high frame rates and allowing close camera zooms.

Supplementary Material

jeschke (jeschke.zip)

Supplemental movie, appendix, image and software files for, Water Wave Animation via Wavefront Parameter Interpolation

Download
868.61 MB

MP4 File (a27.mp4)

Download
67.11 MB

References

[1]

G. B. Airy. 1841. Tides and waves. In Encyclopaedia Metropolitana. B. Fellows, 241--396.

[2]

R. Ando, N. Thuerey, and C. Wotjan. 2013. Highly adaptive liquid simulations on tetrahedral meshes. ACM Trans. Graph. 32, 4, 103:1--103:10.

Digital Library

[3]

P. Bulant and L. Klimes. 1999. Interpolation of ray theory traveltimes within ray cells. Geophys. J. Int. 139, 2, 273--282.

[4]

N. Chentanez and M. Muller. 2010. Real-time simulation of large bodies of water with small scale details. In Proceedings of the ACM SIGGRAPH/EUROGRAPHICS Symposium on Computer Animation (SCA'10). 197--206.

Digital Library

[5]

E. Darles, B. Crespin, D. Ghazanfarpour, and J.-C. Gonzato. 2011. A survey of ocean simulation and rendering techniques in computer graphics. Comput. Graph. Forum 30, 43--60.

[6]

R. G. Dean and R. A. Dalrymple. 1991. Water Wave Mechanics for Engineers and Scientists. World Scientific.

[7]

N. Foster and R. Fedkiw. 2001. Practical animation of liquids. In Proceedings of the Annual ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques (SIGGRAPH'01). 23--30.

Digital Library

[8]

A. Fournier and W. T. Reeves. 1986. A simple model of ocean waves. ACM SIGGRAPH Comput. Graph. 20, 4, 75--84.

Digital Library

[9]

M. N. Gamito and F. K. Musgrave. 2002. An accurate model of wave refraction over shallow water. Comput. Graph. 26, 2, 291--307.

[10]

J.-C. Gonzato and Be Le Saec. 1997. A phenomenological model of coastal scenes based on physical considerations. In Proceedings of the Eurographics Workshop on Computer Animation and Simulation (Eurographics'97). 137--148.

[11]

J.-C. Gonzato and B. Le Aec. 2000. On modelling and rendering ocean scenes. J. Vis. Comput. Anim. 11, 1, 27--37.

[12]

D. Hinsinger, F. Neyret, and M.-P. Cani. 2002. Interactive animation of ocean waves. In Proceedings of the ACM SIGGRAPH/EUROGRAPHICS Symposium on Computer Animation (SCA'02). 161--166.

Digital Library

[13]

M. Kass and G. Miller. 1990. Rapid, stable fluid dynamics for computer graphics. ACM SIGGRAPH Comput. Graph. 24, 49--57.

Digital Library

[14]

T. Keeler and R. Bridson. 2014. Ocean waves animation using boundary integral equations and explicit mesh tracking. In Proceedings of the 13^th ACM SIGGRAPH/EUROGRAPHICS Symposium on Computer Animation (SCA'14).

Digital Library

[15]

H. Lamb. 1895. Hydrodynamics. Cambridge University Press.

[16]

B. R. Levy and J. B. Keller. 1959. Diffraction by a smooth object. Comm. Pure Appl. Math. 12, 1, 159--209.

[17]

F. Losasso, F. Gibou, and R. Fedkiw. 2004. Simulating water and smoke with an octree data structure. ACM Trans. Graph. 23, 3, 457--462.

Digital Library

[18]

G. A. Mastin, P. A. Watterberg, and J. F. Mareda. 1987. Fourier synthesis of ocean scenes. IEEE Comput. Graph. Appl. 7, 3, 16--23.

Digital Library

[19]

J. Mccann and N. S. Pollard. 2008. Real-time gradient-domain painting. ACM Trans. Graph. 27, 3, 93:1--93:7.

Digital Library

[20]

M. Moore and J. Wilhelms. 1988. Collision detection and response for computer animation. ACM SIGGRAPH Comput. Graph. 22, 289--298.

Digital Library

[21]

M. Nielsen and R. Bridson. 2011. Guide shapes for high resolution naturalistic liquid simulation. ACM Trans. Graph. 30, 83.

Digital Library

[22]

M. B. Nielsen, A. Soderstrom, and R. Bridson. 2013. Synthesizing waves from animated height fields. ACM Trans. Graph. 32, 1.

Digital Library

[23]

G. M. Nielson. 1979. The side-vertex method for interpolation in triangles. J. Approx. Theory 25, 4, 318--336.

[24]

J. F. O'Brien and J. K. Hodgins. 1995. Dynamic simulation of splashing fluids. In Proceedings of the IEEE Conference on Computer Animation (CA'95). 198--205.

Digital Library

[25]

J. C. Padrino and D. D. Joseph. 2007. Correction of Lamb's dissipation calculation for the effects of viscosity on capillary-gravity waves. Phys. Fluids 19, 082105.

[26]

D. R. Peachey. 1986. Modeling waves and surf. ACM SIGGRAPH Comput. Graph. 20, 65--74.

Digital Library

[27]

O. Runborg. 2007. Mathematical models and numerical methods for high frequency waves. Comm. Comput. Phys. 2, 5, 827--880.

[28]

J. A. Sethian. 1999. Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science, Vol. 3. Cambridge University Press.

[29]

J. R. Shewchuk. 1996. Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator. In Applied Computational Geometry towards Geometric Engineering, Springer, 203--222.

Digital Library

[30]

Sidefx. 2013. Houdini 13.0 wave layer tank. http://www.sidefx.com/docs/houdini13.0/shelf/wavelayertank.

[31]

A. Soderstrom, M. Karlsson, and K. Museth. 2010. A PML-based nonreflective boundary for free surface fluid animation. ACM Trans. Graph. 29, 5, 136:1--136:17.

Digital Library

[32]

J. Tessendorf. 2004a. Interactive water surfaces. Game Program. Gems 4, 265--274.

[33]

J. Tessendorf. 2004b. Simulating ocean water. In ACM SIGGRAPH Courses.

[34]

N. Thuerey, M. Muller Fischer, S. Schirm, and M. Gross. 2007a. Real-time breaking waves for shallow water simulations. In Proceedings of the IEEE Pacific Graphics Conference (PG'07). 39--46.

Digital Library

[35]

N. Thuerey, F. Saldo, S. Schirm, M. Muller Ischer, and M. Gross. 2007b. Real-time simulations of bubbles and foam within a shallow water framework. In Proceedings of the ACM SIGGRAPH/EUROGRAPHICS Symposium on Computer Animation (SCA'07). 191--198.

Digital Library

[36]

P. Y. Tso and B. A. Barsky. 1987. Modeling and rendering waves: Wave-tracing using beta-splines and reflective and refractive texture mapping. ACM SIGGRAPH Comput. Graph. 6, 3, 191--214.

Digital Library

[37]

B. Ursin. 1982. Quadratic wavefront and traveltime approximations in inhomogeneous layered media with curved interfaces. Geophys. 47, 7, 1012--1021.

[38]

T. Whited. 1980. An improved illumination model for shaded display. Comm. ACM 23, 6, 343--349.

Digital Library

[39]

C. Yuksel, D. H. House, and J. Keyser. 2007. Wave particles. ACM Trans. Graph. 26, 3.

Digital Library

Cited By

Wang GTan SSong GWang S(2025)RETRACTED: Wang et al. Amplitude and Phase Computable Ocean Wave Real-Time Modeling with GPU Acceleration. J. Mar. Sci. Eng. 2022, 10, 1208Journal of Marine Science and Engineering10.3390/jmse1302020013:2(200)Online publication date: 22-Jan-2025
https://doi.org/10.3390/jmse13020200
Huo YXin MLi SZhu XSun CPan BZhang Y(2024)SPH algorithm and its application based on HLLC Approximate Riemann SolverProceedings of the 2024 International Conference on Artificial Intelligence of Things and Computing10.1145/3708282.3708305(123-126)Online publication date: 30-Aug-2024
https://dl.acm.org/doi/10.1145/3708282.3708305
Donatini LVerwilligen JDelefortrie GVantorre MLataire E(2024)Physically accurate real-time synthesis of ocean waves for maritime simulatorsApplied Ocean Research10.1016/j.apor.2023.103866143(103866)Online publication date: Feb-2024
https://doi.org/10.1016/j.apor.2023.103866
Show More Cited By

Index Terms

Water Wave Animation via Wavefront Parameter Interpolation
1. Computing methodologies
  1. Computer graphics
    1. Animation
      1. Physical simulation
    2. Shape modeling
2. Mathematics of computing
  1. Continuous mathematics
    1. Topology
      1. Geometric topology

Recommendations

Empirical directional wave spectra for computer graphics
DigiPro '15: Proceedings of the 2015 Symposium on Digital Production

In this paper, we describe the practical application of several empirically-based, directional ocean wave spectra for use in the Fourier synthesis of animated ocean height fields. We use the Texel MARSEN ARSLOE (TMA) empirical model for the non-...
Water wave packets

This paper presents a method for simulating water surface waves as a displacement field on a 2D domain. Our method relies on Lagrangian particles that carry packets of water wave energy; each packet carries information about an entire group of wave ...
Animation and rendering of complex water surfaces

We present a new method for the animation and rendering of photo-realistic water effects. Our method is designed to produce visually plausible three dimensional effects, for example the pouring of water into a glass (see figure 1) and the breaking of an ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 34, Issue 3

April 2015

152 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2774971

Editor:
Kavita Bala
Cornell University

Issue’s Table of Contents

Copyright © 2015 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 08 May 2015

Accepted: 01 January 2015

Received: 01 September 2014

Published in TOG Volume 34, Issue 3

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article
Research
Refereed

Funding Sources

European Research Council (ERC) Starting
Austrian Science Fund (FWF) project P 24352-N23

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

28
Total Citations
View Citations
1,635
Total Downloads

Downloads (Last 12 months)167
Downloads (Last 6 weeks)18

Reflects downloads up to 16 Feb 2025

Other Metrics

View Author Metrics

Citations

Cited By

Wang GTan SSong GWang S(2025)RETRACTED: Wang et al. Amplitude and Phase Computable Ocean Wave Real-Time Modeling with GPU Acceleration. J. Mar. Sci. Eng. 2022, 10, 1208Journal of Marine Science and Engineering10.3390/jmse1302020013:2(200)Online publication date: 22-Jan-2025
https://doi.org/10.3390/jmse13020200
Huo YXin MLi SZhu XSun CPan BZhang Y(2024)SPH algorithm and its application based on HLLC Approximate Riemann SolverProceedings of the 2024 International Conference on Artificial Intelligence of Things and Computing10.1145/3708282.3708305(123-126)Online publication date: 30-Aug-2024
https://dl.acm.org/doi/10.1145/3708282.3708305
Donatini LVerwilligen JDelefortrie GVantorre MLataire E(2024)Physically accurate real-time synthesis of ocean waves for maritime simulatorsApplied Ocean Research10.1016/j.apor.2023.103866143(103866)Online publication date: Feb-2024
https://doi.org/10.1016/j.apor.2023.103866
Wang XXu YLiu SRen BKosinka JTelea AWang JSong CChang JLi CZhang JBan X(2024)Physics-based fluid simulation in computer graphics: Survey, research trends, and challengesComputational Visual Media10.1007/s41095-023-0368-y10:5(803-858)Online publication date: 27-Apr-2024
https://doi.org/10.1007/s41095-023-0368-y
Chen ZKaufman DSkouras MVouga E(2023)Complex Wrinkle Field EvolutionACM Transactions on Graphics10.1145/359239742:4(1-19)Online publication date: 26-Jul-2023
https://dl.acm.org/doi/10.1145/3592397
Jeschke SWojtan C(2023)Generalizing Shallow Water Simulations with Dispersive Surface WavesACM Transactions on Graphics10.1145/359209842:4(1-12)Online publication date: 26-Jul-2023
https://dl.acm.org/doi/10.1145/3592098
Ramakrishnan VMcGraw T(2023)Water Animation Using Coupled SPH and Wave EquationAdvances in Visual Computing10.1007/978-3-031-47969-4_24(303-314)Online publication date: 16-Oct-2023
https://dl.acm.org/doi/10.1007/978-3-031-47969-4_24
Schreck CWojtan C(2022)Coupling 3D Liquid Simulation with 2D Wave Propagation for Large Scale Water Surface Animation Using the Equivalent Sources MethodComputer Graphics Forum10.1111/cgf.1447841:2(343-353)Online publication date: 24-May-2022
https://doi.org/10.1111/cgf.14478
Liu SYang Z(2022)Virtual water wave simulation with multiple wavenumbersVirtual Reality10.1007/s10055-022-00729-027:2(1221-1231)Online publication date: 7-Dec-2022
https://dl.acm.org/doi/10.1007/s10055-022-00729-0
Huang LQu ZTan XZhang XMichels DJiang C(2021)Ships, splashes, and waves on a vast oceanACM Transactions on Graphics10.1145/3478513.348049540:6(1-15)Online publication date: 10-Dec-2021
https://dl.acm.org/doi/10.1145/3478513.3480495
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

Figures

Tables

Media

View Issue’s Table of Contents