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 trains, as opposed to only a single wave crest. Our approach is unconditionally stable and can simulate high resolution geometric details. This approach also presents a straightforward interface for artistic control, because it is essentially a particle system with intuitive parameters like wavelength and amplitude. Our implementation parallelizes well and runs in real time for moderately challenging scenarios.

[1]  Huamin Wang,et al.  Enriching SPH simulation by approximate capillary waves , 2016, Symposium on Computer Animation.

[2]  Christopher J. Horvath,et al.  Empirical directional wave spectra for computer graphics , 2015, DigiPro.

[3]  Manuel N. Gamito,et al.  An accurate model of wave refraction over shallow water , 2002, Comput. Graph..

[4]  Guy Vandegrift.  The diffraction and spreading of a wavepacket , 2004 .

[5]  Alexander Campbell,et al.  Popular Lectures and Addresses , 2008 .

[6]  Brian A. Barsky,et al.  Modeling and rendering waves: wave-tracing using beta-splines and reflective and refractive texture mapping. , 1987, TOGS.

[7]  Daniel D. Joseph,et al.  Correction of Lamb’s dissipation calculation for the effects of viscosity on capillary-gravity waves , 2007 .

[8]  Cem Yuksel,et al.  Real-time water waves with wave particles , 2010 .

[9]  David R. Basco,et al.  Water Wave Mechanics for Engineers and Scientists , 1985 .

[10]  Joseph B. Keller,et al.  Diffraction by a Smooth Object , 2015 .

[11]  Gary Mastin,et al.  Fourier Synthesis of Ocean Scenes , 1987, IEEE Computer Graphics and Applications.

[12]  Markus H. Gross,et al.  Eurographics/ Acm Siggraph Symposium on Computer Animation (2007) Real-time Simulations of Bubbles and Foam within a Shallow Water Framework , 2022 .

[13]  Hilko Cords,et al.  Moving with the Flow: Wave Particles in Flowing Liquids , 2008, J. WSCG.

[14]  J. Francis.  Tides and Waves , 1969, Nature.

[15]  Gavin S. P. Miller,et al.  Rapid, stable fluid dynamics for computer graphics , 1990, SIGGRAPH.

[16]  Djamchid Ghazanfarpour,et al.  A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics , 2011, Comput. Graph. Forum.

[17]  Robert Bridson,et al.  Synthesizing waves from animated height fields , 2013, ACM Trans. Graph..

[18]  Derek Nowrouzezahrai,et al.  Surface turbulence for particle-based liquid simulations , 2015, ACM Trans. Graph..

[19]  R. Liboff.  Introductory quantum mechanics , 1980 .

[20]  Marie-Paule Cani,et al.  Interactive animation of ocean waves , 2002, SCA '02.

[21]  Bertrand Le Saëc,et al.  A phenomenological model of coastal scenes based on physical considerations , 1997, Computer Animation and Simulation.

[22]  Robert Bridson,et al.  Guide shapes for high resolution naturalistic liquid simulation , 2011, ACM Trans. Graph..

[23]  D. Peregrine.  A Modern Introduction to the Mathematical Theory of Water Waves. By R. S. Johnson. Cambridge University Press, 1997. xiv+445 pp. Hardback ISBN 0 521 59172 4 £55.00; paperback 0 521 59832 X £19.95. , 1998, Journal of Fluid Mechanics.

[24]  Jessica K. Hodgins,et al.  Dynamic simulation of splashing fluids , 1995, Proceedings Computer Animation'95.

[25]  Theodore Kim,et al.  Dispersion kernels for water wave simulation , 2016, ACM Trans. Graph..

[26]  J Pedlowsky,et al.  Waves in the ocean and atmosphere : introduction to wave dynamics , 2004 .

[27]  Jihun Yu,et al.  Explicit Mesh Surfaces for Particle Based Fluids , 2012, Comput. Graph. Forum.

[28]  J. Breeding.  Velocities and refraction laws of wave groups: A verification , 1978 .

[29]  D. House,et al.  Wave particles , 2007, SIGGRAPH 2007.

[30]  Darwyn R. Peachey,et al.  Modeling waves and surf , 1986, SIGGRAPH.

[31]  Turner Whitted,et al.  An improved illumination model for shaded display , 1979, CACM.

[32]  Bruce J. Schachter.  Long crested wave models , 1980 .

[33]  J. Synge,et al.  Water Waves and Hydrons: The term "hydron" is proposed for fictitious particles that travel with the group velocity of waves. , 1962, Science.

[34]  Matthias Müller,et al.  Real-time simulation of large bodies of water with small scale details , 2010, SCA '10.

[35]  Guillaume Abadie,et al.  Advances in real-time rendering in games , 2018, ACM SIGGRAPH 2018 Courses.

[36]  Bernard Le Mehaute,et al.  Gravity–capillary rings generated by water drops , 1988, Journal of Fluid Mechanics.

[37]  G. Birkhoff,et al.  Quantum mechanics and asymptotic series , 1933 .

[38]  Stefan Jeschke,et al.  Water Wave Animation via Wavefront Parameter Interpolation , 2015, ACM Trans. Graph..

[39]  J. Tessendorf.  Simulating Ocean Water , 2004 .

[40]  M. Gross,et al.  A multiscale approach to mesh-based surface tension flows , 2010, SIGGRAPH 2010.

[41]  Theodore Kim,et al.  Closest point turbulence for liquid surfaces , 2013, TOGS.

[42]  Christof Rezk Salama,et al.  GPU-Based Monte-Carlo Volume Raycasting , 2007, 15th Pacific Conference on Computer Graphics and Applications (PG'07).

[43]  Markus H. Gross,et al.  Real-time Breaking Waves for Shallow Water Simulations , 2007, 15th Pacific Conference on Computer Graphics and Applications (PG'07).

[44]  Robert Bridson,et al.  Ocean waves animation using boundary integral equations and explicit mesh tracking , 2014, SCA '14.

[45]  Alain Fournier,et al.  A simple model of ocean waves , 1986, SIGGRAPH.

[46]  Eitan Grinspun,et al.  Surface-only liquids , 2016, ACM Trans. Graph..

[47]  L. Chambers.  Linear and Nonlinear Waves , 2000, The Mathematical Gazette.

[48]  David Finkelstein,et al.  Introductory Quantum Mechanics and Quantum Mechanics , 1993 .