Tracking, Correcting and Absorbing Water Surface Waves

Computer graphics is an extremely exciting field for two reasons. On the one hand, there is a healthy injection of pragmatism coming from the visual effects industry that want robust algorithms that work so they can produce results at an increasingly frantic pace. On the other hand, they must always try to push the envelope and achieve the impossible to wow their audiences in the next blockbuster, which means that the industry has not succumb to conservatism, and there is plenty of room to try out new and crazy ideas if there is a chance that it will pan into something useful. Water simulation has been in visual effects for decades, however it still remains extremely challenging because of its high computational cost and difficult art-directability. The work in this thesis tries to address some of these difficulties. Specifically, we make the following three novel contributions to the state-of-the-art in water simulation for visual effects.

[1]  Dennis DeTurck,et al.  Vector Calculus and the Topology of Domains in 3-Space , 2002, Am. Math. Mon..

[2]  Hans-Peter Seidel,et al.  Animation cartography—intrinsic reconstruction of shape and motion , 2012, TOGS.

[3]  Eitan Grinspun,et al.  Multimaterial mesh-based surface tracking , 2014, ACM Trans. Graph..

[4]  Fang. Q. Hu On the construction of PML absorbing boundary condition for the non-linear Euler equations , 2006 .

[5]  Chang-Hun Kim,et al.  Discontinuous fluids , 2005, ACM Trans. Graph..

[6]  Keenan Crane,et al.  Robust fairing via conformal curvature flow , 2013, ACM Trans. Graph..

[7]  Lingling Wu,et al.  A simple package for front tracking , 2006, J. Comput. Phys..

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

[9]  Ken Museth,et al.  VDB: High-resolution sparse volumes with dynamic topology , 2013, TOGS.

[10]  Matthias Müller-Fischer,et al.  Liquid simulation with mesh-based surface tracking , 2011, SIGGRAPH '11.

[11]  Ben Houston,et al.  The tar monster: creating a character with fluid simulation , 2004, SIGGRAPH '04.

[12]  M. Gross,et al.  Deforming meshes that split and merge , 2009, SIGGRAPH 2009.

[13]  Jean-Pierre Berenger,et al.  A perfectly matched layer for the absorption of electromagnetic waves , 1994 .

[14]  Yizhou Yu,et al.  Taming liquids for rapidly changing targets , 2005, SCA '05.

[15]  James F. O'Brien,et al.  A texture synthesis method for liquid animations , 2006, SCA '06.

[16]  Ryan Schmidt,et al.  On the velocity of an implicit surface , 2011, TOGS.

[17]  Eftychios Sifakis,et al.  A parallel multigrid Poisson solver for fluids simulation on large grids , 2010, SCA '10.

[18]  Leonidas J. Guibas,et al.  Dynamic geometry registration , 2007, Symposium on Geometry Processing.

[19]  Nipun Kwatra,et al.  Texturing Fluids , 2006, IEEE Transactions on Visualization and Computer Graphics.

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

[21]  C. Bogey,et al.  Low-dissipation and low-dispersion fourth-order Runge–Kutta algorithm , 2006 .

[22]  Hyeongseok Ko,et al.  A practical simulation of dispersed bubble flow , 2010 .

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

[24]  Andrew Lewis,et al.  Model reduction for real-time fluids , 2006, SIGGRAPH '06.

[25]  Mark J. Stock,et al.  Impact of a vortex ring on a density interface using a regularized inviscid vortex sheet method , 2008, J. Comput. Phys..

[26]  Yongning Zhu,et al.  Animating sand as a fluid , 2005, SIGGRAPH 2005.

[27]  Fang Q. Hu,et al.  Absorbing boundary conditions for nonlinear Euler and Navier-Stokes equations based on the perfectly matched layer technique , 2008, J. Comput. Phys..

[28]  Patrick Joly,et al.  Stability of perfectly matched layers, group velocities and anisotropic waves , 2003 .

[29]  Jessica K. Hodgins,et al.  Flow-based video synthesis and editing , 2004, SIGGRAPH 2004.

[30]  Matthias Müller,et al.  Fast and robust tracking of fluid surfaces , 2009, SCA '09.

[31]  Marcel Campen,et al.  Exact and Robust (Self‐)Intersections for Polygonal Meshes , 2010, Comput. Graph. Forum.

[32]  Robert Bridson,et al.  Detailed water with coarse grids , 2014, ACM Trans. Graph..

[33]  Ronald Fedkiw,et al.  Animation and rendering of complex water surfaces , 2002, ACM Trans. Graph..

[34]  Leonidas J. Guibas,et al.  Robust single-view geometry and motion reconstruction , 2009, ACM Trans. Graph..

[35]  Martti Mäntylä,et al.  Introduction to Solid Modeling , 1988 .

[36]  N Thuerey,et al.  Detail-preserving fluid control , 2009, SCA '06.

[37]  Anthony J. Yezzi,et al.  Texture transfer during shape transformation , 2005, TOGS.

[38]  Ronald Fedkiw,et al.  A novel algorithm for incompressible flow using only a coarse grid projection , 2010, ACM Trans. Graph..

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

[40]  Fabrice Neyret,et al.  Simulation of smoke based on vortex filament primitives , 2005, SCA '05.

[41]  Bo Zhu,et al.  Codimensional Non-Newtonian Fluids , 2016 .

[42]  T. Colonius,et al.  A VORTEX PARTICLE METHOD FOR COMPRESSIBLE FLOWS , 2001 .

[43]  Christopher Wojtan,et al.  A Practical Method for High‐Resolution Embedded Liquid Surfaces , 2016, Comput. Graph. Forum.

[44]  Ronald Fedkiw,et al.  Level set methods and dynamic implicit surfaces , 2002, Applied mathematical sciences.

[45]  Bonni J. Dichone,et al.  Boundary Conditions for Fluid Mechanics , 2017 .

[46]  Ken Museth,et al.  Non-reflective boundary conditions for incompressible free surface fluids , 2009, SIGGRAPH '09.

[47]  James F. O'Brien,et al.  A semi-Lagrangian contouring method for fluid simulation , 2006, ACM Trans. Graph..

[48]  Jihun Yu,et al.  Reconstructing surfaces of particle-based fluids using anisotropic kernels , 2010, SCA '10.

[49]  Hyeong-Seok Ko,et al.  Stretching and wiggling liquids , 2009, ACM Trans. Graph..

[50]  R. Palais An Introduction to Wave Equations and Solitons , 2000 .

[51]  Sang Il Park,et al.  Vortex fluid for gaseous phenomena , 2005, SCA '05.

[52]  F. Hu A Stable, perfectly matched layer for linearized Euler equations in unslit physical variables , 2001 .

[53]  G. Turk,et al.  Fast viscoelastic behavior with thin features , 2008, SIGGRAPH 2008.

[54]  James F. O'Brien,et al.  A method for animating viscoelastic fluids , 2004, SIGGRAPH 2004.

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

[56]  Kaj Madsen,et al.  Methods for Non-Linear Least Squares Problems (2nd ed.) , 2004 .

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

[58]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

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

[60]  Jonathan Gagnon,et al.  Dynamic lapped texture for fluid simulations , 2016, The Visual Computer.

[61]  Greg Turk,et al.  Blending liquids , 2014, ACM Trans. Graph..

[62]  Jos Stam,et al.  Stable fluids , 1999, SIGGRAPH.

[63]  Ronald Fedkiw,et al.  Visual simulation of smoke , 2001, SIGGRAPH.

[64]  Eugene Fiume,et al.  Fluid simulation using Laplacian eigenfunctions , 2012, TOGS.

[65]  Christopher Wojtan,et al.  A stream function solver for liquid simulations , 2015, ACM Trans. Graph..

[66]  Steven G. Johnson,et al.  Notes on Perfectly Matched Layers (PMLs) , 2021, ArXiv.

[67]  Robert Bridson,et al.  Matching fluid simulation elements to surface geometry and topology , 2010, ACM Transactions on Graphics.

[68]  Radu Horaud,et al.  TransforMesh : A Topology-Adaptive Mesh-Based Approach to Surface Evolution , 2007, ACCV.

[69]  R. Fedkiw,et al.  USING THE PARTICLE LEVEL SET METHOD AND A SECOND ORDER ACCURATE PRESSURE BOUNDARY CONDITION FOR FREE SURFACE FLOWS , 2003 .

[70]  Xiangmin Jiao,et al.  Face offsetting: A unified approach for explicit moving interfaces , 2007, J. Comput. Phys..

[71]  Ali M. Malkawi,et al.  Adaptive Localization Method: An Approach to Real Time Airflow Simulation and Immersive Visualization , 2007 .