Making Procedural Water Waves Boundary‐aware

The “procedural” approach to animating ocean waves is the dominant algorithm for animating larger bodies of water in interactive applications as well as in off‐line productions — it provides high visual quality with a low computational demand. In this paper, we widen the applicability of procedural water wave animation with an extension that guarantees the satisfaction of boundary conditions imposed by terrain while still approximating physical wave behavior. In combination with a particle system that models wave breaking, foam, and spray, this allows us to naturally model waves interacting with beaches and rocks. Our system is able to animate waves at large scales at interactive frame rates on a commodity PC.

[1]  Leonidas J. Guibas,et al.  Shape google: Geometric words and expressions for invariant shape retrieval , 2011, TOGS.

[2]  KassMichael,et al.  Rapid, stable fluid dynamics for computer graphics , 1990 .

[3]  Bedrich Benes,et al.  Interactive terrain modeling using hydraulic erosion , 2008, SCA '08.

[4]  Donald H. House,et al.  Wave particles , 2007, ACM Trans. Graph..

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

[6]  James F. O'Brien,et al.  Eurographics/acm Siggraph Symposium on Computer Animation (2007) Liquid Simulation on Lattice-based Tetrahedral Meshes , 2022 .

[7]  N. Chentanez,et al.  Water surface wavelets , 2018, ACM Trans. Graph..

[8]  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.

[9]  Matthias Müller,et al.  Solid simulation with oriented particles , 2011, ACM Trans. Graph..

[10]  Guan-Yu Chen,et al.  Theoretical analysis of surface waves shoaling and breaking on a sloping bottom. Part 2: Nonlinear waves , 2006 .

[11]  Markus H. Gross,et al.  Robust and Efficient Wave Simulations on Deforming Meshes , 2008, Comput. Graph. Forum.

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

[13]  FournierAlain,et al.  A simple model of ocean waves , 1986 .

[14]  Jan Bender,et al.  Smoothed Particle Hydrodynamics Techniques for the Physics Based Simulation of Fluids and Solids , 2020, Eurographics.

[15]  Michiel van de Panne,et al.  A numerically efficient and stable algorithm for animating water waves , 2002, The Visual Computer.

[16]  Austria,et al.  Errata for Wave Curves: Simulating Lagrangian water waves on dynamically deforming surfaces , 2020 .

[17]  Ronald Fedkiw,et al.  A new grid structure for domain extension , 2013, ACM Trans. Graph..

[18]  Richard Keiser,et al.  Multiresolution particle-based fluids , 2006 .

[19]  Stefan Jeschke,et al.  Water wave packets , 2017, ACM Trans. Graph..

[20]  Markus H. Gross,et al.  SPH Based Shallow Water Simulation , 2011, VRIPHYS.

[21]  Rüdiger Westermann,et al.  Large-Scale Liquid Simulation on Adaptive Hexahedral Grids , 2014, IEEE Transactions on Visualization and Computer Graphics.

[22]  Jim X. Chen,et al.  Toward Interactive-Rate Simulation of Fluids with Moving Obstacles Using Navier-Stokes Equations , 1995, CVGIP Graph. Model. Image Process..

[23]  HarmonDavid,et al.  Interference-aware geometric modeling , 2011 .

[24]  Huamin Wang,et al.  Eurographics/ Acm Siggraph Symposium on Computer Animation (2007) Solving General Shallow Wave Equations on Surfaces , 2022 .

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

[26]  Jostein R. Natvig,et al.  Visual simulation of shallow-water waves , 2005, Simul. Model. Pract. Theory.

[27]  Eftychios Sifakis,et al.  Power diagrams and sparse paged grids for high resolution adaptive liquids , 2017, ACM Trans. Graph..

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

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

[30]  Robert Bridson,et al.  Fluid Simulation for Computer Graphics , 2008 .

[31]  Chris Wojtan,et al.  Fundamental solutions for water wave animation , 2019, ACM Trans. Graph..

[32]  Bertrand Le Saëc,et al.  On modelling and rendering ocean scenes , 2000, Comput. Animat. Virtual Worlds.

[33]  Miles Macklin,et al.  Position based fluids , 2013, ACM Trans. Graph..

[34]  Christopher Wojtan,et al.  Highly adaptive liquid simulations on tetrahedral meshes , 2013, ACM Trans. Graph..

[35]  Olga Sorkine-Hornung,et al.  Interference-aware geometric modeling , 2011, ACM Trans. Graph..

[36]  Eugene Zhang,et al.  Interactive Tensor Field Design and Visualization on Surfaces , 2007, IEEE Transactions on Visualization and Computer Graphics.

[37]  Bertrand Le Saëc,et al.  On modelling and rendering ocean scenes , 2000 .

[38]  H. Hsu,et al.  Theoretical analysis of surface waves propagation on sloping bottoms: Part 1 , 2005 .

[39]  Soonhung Han,et al.  Solving the Shallow Water equations using 2D SPH particles for interactive applications , 2010, The Visual Computer.

[40]  R PeacheyDarwyn.  Modeling waves and surf , 1986 .

[41]  F. Biesel.  Study of wave propagation in water of gradually varying depth , 1952 .

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

[43]  Markus H. Gross,et al.  Two-scale particle simulation , 2011, ACM Trans. Graph..

[44]  Ronald Fedkiw,et al.  Simulating water and smoke with an octree data structure , 2004, ACM Trans. Graph..

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