Fundamental solutions for water wave animation

This paper investigates the use of fundamental solutions for animating detailed linear water surface waves. We first propose an analytical solution for efficiently animating circular ripples in closed form. We then show how to adapt the method of fundamental solutions (MFS) to create ambient waves interacting with complex obstacles. Subsequently, we present a novel wavelet-based discretization which outperforms the state of the art MFS approach for simulating time-varying water surface waves with moving obstacles. Our results feature high-resolution spatial details, interactions with complex boundaries, and large open ocean domains. Our method compares favorably with previous work as well as known analytical solutions. We also present comparisons between our method and real world examples.

[1]  M. Gross,et al.  A multiscale approach to mesh-based surface tension flows , 2010, ACM Trans. Graph..

[2]  Ronald Fedkiw,et al.  Efficient simulation of large bodies of water by coupling two and three dimensional techniques , 2006, ACM Trans. Graph..

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

[4]  Markus H. Gross,et al.  Lagrangian vortex sheets for animating fluids , 2012, ACM Trans. Graph..

[5]  Dinesh Manocha,et al.  Wave-based sound propagation in large open scenes using an equivalent source formulation , 2013, TOGS.

[6]  K PaiDinesh,et al.  Precomputed acoustic transfer , 2006 .

[7]  Philip J. Morris,et al.  Acoustic Scattering in the Time Domain Using an Equivalent Source Method , 2010 .

[8]  Robert Geist,et al.  Lattice-Boltzmann Water Waves , 2010, ISVC.

[9]  Christopher Wojtan,et al.  High-resolution brittle fracture simulation with boundary elements , 2015, ACM Trans. Graph..

[10]  R. Hiptmair,et al.  Boundary Element Methods , 2021, Oberwolfach Reports.

[11]  Ulrich Rüde,et al.  Animation of open water phenomena with coupled shallow water and free surface simulations , 2006, SCA '06.

[12]  Robert Bridson,et al.  Linear-time smoke animation with vortex sheet meshes , 2012, SCA '12.

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

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

[15]  Ulrich Pinkall,et al.  Filament-based smoke with vortex shedding and variational reconnection , 2010, SIGGRAPH 2010.

[16]  Jörn Loviscach,et al.  A Convolution-Based Algorithm for Animated Water Waves , 2002, Eurographics.

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

[18]  Hao Li,et al.  Tracking surfaces with evolving topology , 2012, ACM Trans. Graph..

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

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

[21]  Dinesh K. Pai,et al.  ArtDefo: accurate real time deformable objects , 1999, SIGGRAPH.

[22]  Petros Koumoutsakos,et al.  Vortex Methods: Theory and Practice , 2000 .

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

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

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

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

[28]  Jernej Barbic,et al.  Interactive editing of deformable simulations , 2012, ACM Trans. Graph..

[29]  R. Coifman,et al.  The fast multipole method for the wave equation: a pedestrian prescription , 1993, IEEE Antennas and Propagation Magazine.

[30]  Ulrich Pinkall,et al.  Filament-based smoke with vortex shedding and variational reconnection , 2010, ACM Trans. Graph..

[31]  Robert Bridson,et al.  Simulating rigid body fracture with surface meshes , 2015, ACM Trans. Graph..

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

[33]  Dinesh Manocha,et al.  Wave-based sound propagation for VR applications , 2014, 2014 IEEE VR Workshop: Sonic Interaction in Virtual Environments (SIVE).

[34]  Stefan Kurz,et al.  The adaptive cross-approximation technique for the 3D boundary-element method , 2002 .

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

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

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

[38]  Seongkyu Lee.  Review: The Use of Equivalent Source Method in Computational Acoustics , 2017 .

[39]  Pixar.  Dynamic Kelvinlets : Secondary Motions based on Fundamental Solutions of Elastodynamics , 2018 .

[40]  Doug L. James,et al.  Regularized kelvinlets , 2017, ACM Trans. Graph..

[41]  Jernej Barbic,et al.  Precomputed acoustic transfer: output-sensitive, accurate sound generation for geometrically complex vibration sources , 2006, ACM Trans. Graph..

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

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

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

[45]  R. Courant,et al.  Methods of Mathematical Physics , 1962 .

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

[47]  Christopher Wojtan,et al.  Liquid surface tracking with error compensation , 2013, ACM Trans. Graph..

[48]  Eitan Grinspun,et al.  Double bubbles sans toil and trouble , 2015, ACM Trans. Graph..

[49]  Christopher Wojtan,et al.  Fast approximations for boundary element based brittle fracture simulation , 2016, ACM Trans. Graph..