Simulation and Rendering of Real-Time Breaking Waves

1
Simulation and Rendering of Real-Time Breaking
Waves

• Adam Lake, David Reagin, John Van Drasek
• Intel Software Solutions Group (SSG)
• Modern Game Technologies Project
• 2/27/2005

2
Motivation
We arrive at the truth, not by the reason only, but also by the heart. -- Blaise Pascal

• Great real-time results for deep ocean but what
  about close to shore?
• Sum of Sines Isidoro02, Finch04
• Tessendorf, etc. Tessendorf01
• Little work on breaking waves in computer
  graphics!
• Animation and Control of Breaking Waves
  Mihalef04
• Navier Stokes and store
• None emphasize real-time breaking waves

3
Getting water right requires

• Geometry
• Overall shape must be correct
• Shading
• Lighting and shading
• Additional Geometry/Texture
• Capillary waves, foam, etc. must be modeled

4
Goal

• Get the geometric solution to look right
• Shading and additional geometry are areas of
  future work
• Good candidates for vertex and pixel shaders
• If geometry is correct, not as important to
  interact with shading and lighting values

5
Basic Algorithm

• 3 passes over 2D Grid
• Deep Wave Simulation
• Shallow Wave Simulation
• Curling of Wave
• Classify portions of waveform
• Modify shape based on this classification
• Curling breaks height field

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Part I of III Deep Ocean Simulation
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Deep Ocean Simulation

• Based on Sum of Sines approach of Finch04,
  Isodoro02
• Summation of N waves to simulate Ocean Surface
  (N4 for us)
• 4 good candidate for SSE optimization!!
• x dependent upon wind direction, velocity,
  wavelength of wave

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Normal Generation

• 2 techniques
• Derivates as presented in Finch04
• Good for GPU implementations
• Possible to make faster with trig lookup tables
• Compute face normals, then average
• Faster than Option 1 on CPU implementations
• Must use neighbor list to get performance
• Brute force method was painfully slow!

9
Wave Speed and Wavelength Relationship for Deep
Ocean Waves
Eqn. from Garrison02
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Wavelength to Velocity Relationship for Deep Waves
Figure from Garrison02
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Deep Ocean Wave Demo
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Nature vs. Your Next Big Hit

• Even these functions are on average, many
  parameters can effect wavelength, velocity,
  direction, etc.
• While in nature there are observed
  relationshipsthe model gives user control over
  surface parameters
• Ignoring these relationships is fine to tune your
  deep ocean for your environment

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Threading Lake05

• Task Level Decomposition
• Thread A Simulated Game Workload
• Thread B Compute Wave

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Performance with threading
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Part II of III Shallow Wave Simulation
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Breaking Waves
Image from Seafriends.
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Shallow Wave Observations

• Same variables as deep wave
• Wavelength, steepness, velocity,
• Wavelength
• Decreases as we approach shore
• Specifically, at a depth of ½ wavelength
• Steepness
• Increases as we approach shore
• Fix velocity to maintain phase
• Recall wavelength and speed are dependent
• If you dont do this waves will be incorrect
• Adjust height
• Attempt to preserve water column as it collapses

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Shallow Wave Algorithm

• Input position, wavelength, steepness,
  position, distance to shore, sealevel, and
  distance to ocean floor as input
• Output New vertex position in shallow wave
  simulation
• For each point,
• Determine Deep Ocean wave position from Section
  I.
• Based on this position
• Adjust wavelength
• Wavelength varies linearly from lamba to ½ lambda
  in our example
• Adjust Steepness
• In our example steepness varies from x to y in
  our demo
• Fix Velocity to Maintain phase
• For velocity solve
• Adjust Height as it attempts to maintain water
  column
• Collapse of water column is what causes break
• Calculate new position using modified values as
  input to deep ocean simulation equation!

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Shallow wave speed and wavelength relationship
Eqn. from Garrison02
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Shallow Waves demo!
Image from Seafriends04
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Part III of III Breaking Waves!
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Breaking Waves
Image from Seafriends.
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Types of Breaking Waves
Image from Mead03
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Side view of breaking wave
Image from Miller76
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Side view of breaking wave after collapse
Image from Miller76
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Breaking Waves

• When waves reach a point that the wavelength is a
  factor of 1/7 of waveheight, the wave breaks
  Seafriends.
• Dependent on slope, composition, wind velocity,
  etc.
• In our implementation, user can vary parameters

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The Vortex
Image from Mead03.
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Vortex Ratio

• Ratio of length to width in practice is often
  between 1.73 and 4.43 Mead03.

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Cubic form of vortex

• Cubic form of Vortex is expressed as
  Longuet-Higgins82

Note Not actually needed for implementation!
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Classification of surfing wave breaking Intensity
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Breaking Algorithm

• Input is positions from shallow wave simulation
• Pass 3 of the algorithm
• Pass 1 deep wave
• Pass 2 shallow wave
• Pass 3 curling

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Breaking Algorithm Overview

• For every timestep t
• Move vortex forward as wave moves forward
• For each vertex
• Classify based on type
• Project point towards vortex based on type,
  height, and distance to shoreline

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Wave Breaking Algorithm

• Classify vertex state
• TOP, BACK, FRONT, FLAT
• Floating point gotchas, especially FLAT!

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So, how do we approximate this shape?
Image from Mead03.
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Vortex Approximation

• Using 2D Circle as attractor
• Pulls vertices based on
• Distance from shore
• Height from sealevel
• Desired vortex shape
• Sphere moves towards sealevel as we move into
  shore
• Sphere decreases in size as we move toward shore

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Image of Vortex Sizes, etc.
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Wave Breaking Algorithm

• Switch(vertex_state)
• TOP or FRONT
• Obtain 2D Circle Position
• Midpoint between FRONT of back wave and BACK of
  front wave
• To simulate Vortex, project towards circle based
  on vertex height
• BACK
• Interpolate to remove gap
• FLAT
• Nothing

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Results 1/3
Only showing FRONT and TOP
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Results 2/3
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Results 3/3
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Breaking Wave Demo!
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Areas of Future Work

• Work in Progress
• Lighting and shading
• Foam
• Interaction with outside environment
• Modify ocean floor
• Ready but not complete
• Model is not restricted to waves coming in
  straight ondemonstrate this
• Stage IV In the surf

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Acknowledgements

• Kim Pallister and Pete Baker for giving the
  resources and time to work on this project.
• Jacob Anderson (jwa_at_beyond-ordinary.com) at
  Beyond Ordinary Software Solutions for useful
  pointers and early discussion.
• Discussions with Dean Macri on vortex simulation.
• Useful discussions with Stephen Junkins, Allen
  Hux, Kim Pallister, William Hachfeld_at_SGI.
• Allison Knowles for title, poster, and
  acknowledgement photographs.

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References 1 of 2

• Black98 Black, K. P., J. A. Hutt S. T. Mead,
  1998. Narrowneck Reef Report 2 Surfing Aspects.
  Technical Report prepared for the Gold Coast City
  Council, June,1998.
• Cohen98 Aaron Cohen and Mike Woodring. Win32
  Multithreaded Programming. OReilly and
  Associates. 1998.
• Gomez00 Miguel Gomez. Interactive Simulation of
  Water Surfaces. Game Programming Gems 1. Edited
  by Mark Deloura. Pages 187-194.
• Finch04 Mark Finch. Effective Water Simulation
  from Physical Models. GPU Gems Programming
  Techniques, Tips, and Tricks for Real-Time
  Graphics. Edited by Randima Fernando. Pages 5-29.
  2004.
• Garrison02 Tom Garrison. Oceanography An
  Invitation to Marine Science. Wadsworth/Thomson
  Learning. 2002. http//www.seafriends.org.nz/ocea
  no/waves.htm
• Giancoli85 Douglas Giancoli. Physics,
  Principles with Application, 2nd edition.
  Prentice Hall, Inc. 1985.
• Isidoro02 John Isidoro, Alex Vlachos, and Chris
  Brennan. Rendering Ocean Water. Direct3D ShaderX
  Vertex and Pixel Shader Tips and Tricks. Pages
  347-356. 2002.
• IMDB04 Credits for Titanic. http//us.imdb.com/t
  itle/tt0120338/.
• Lake05 Adam Lake and David Reagin. Real-Time
  Deep Ocean Wave Simulation On Multi-Threaded
  Architectures. Intel developer services
  www.intel.com/ids .
• Longuet-Higgins76 M.S. Longuet-Higgins,E.D.
  Cokelet. The Deformation of Steep Surface Waves
  on Water. I. A Numerical Method of Computation.
  Proceedings of the Royal Society of London.
  Series A, Mathematical and Physical Sciences,
  Vol. 350, No. 1660 (Jul 30, 1976), 1-26.

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References 2 of 2

• Longuet-Higgins80 M.S. Longuet-Higgins, A
  Technique for Time-Dependent Free-Surface Flows.
  Proceedings of the Royal Society of London.
  Series A, Mathematical and Physical Sciences,
  Vol. 371, No. 1747, Aug. 4, 1980. Pages 441-451.
• Longuet-Higgins82 M.S. Longuet-Higgins.
  Parametric Solutions for Breaking Waves. J.
  Fluid Mechanics, 1982, vol. 121, pp. 403-424.
• Mead03 Shaw Mead. Keynote Address Surfing
  Science. Proceedings of the 3red International
  Surfing Reef Symposium, Raglan, New Zealand.
  June 22-25, 2003. P. 1-36.
• Mihalef04 Viorel Mihalef, Dimitris Metaxas,
  Mark Sussman. Animation and Control of Breaking
  Waves. Eurographics/ACM SIGGRAPH Symposium on
  Computer Animation, 2004.
• Miller76 Miller R.L. Role of Vortices in Surf
  Zone prediction sedimentation, and wave forces.
  Beach and Nearshore sedimentation, pp. 92-114,
  1976, Tulsa, Oklahoma. Soc. Of Economic
  Paleontologists and Mineralogists.
• Miller76 Miller R.L..
• Mead Shaw Mead and Kerry Black. Predicting the
  Breaking Intensity of Surfing Waves. Special
  Issue of the Journal of Coastal Research on
  Surfing (in press). Pages 103-130.
  www.asrltd.co.nz/Paper4Web.pdf .
• Schneider01 Jens Schneider and Rudiger
  Westermann. Towards Real-Time Visual Simulation
  of Water Surfaces. VMV 2001, Stuttgart, Germany,
  Nov. 21-23, 2001.
• Tessendorf01 Simulating Ocean Water.
  SIGGRAPH2001 Course Notes. 2001.
• QuickMath04 http//www.quickmath.com/. November
  4, 2004.

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Backup
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• Irribarren Numbercite
• B is slope
• Hb/Linf ratio of wave height to wavelength

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Wave Energy as a function of Period
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• When each vertex of wave reaches breaking point
• Classify vertex as FRONT, BACK, BOTTOM, TOP of
  waveform
• FRONT, BOTTOM and TOP are projected towards
  virtual sphere to create vortex
• As wave approaches shore
• Sphere decreases in size as wave approaches
  shore.
• Vertices increase their attraction to sphere
• BACK are projected to create natural arc on back
  of wave

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Breaking

• Takes as input the shallow wave that reaches the
  breaking point
• Curl front of waveform to simulate crash
• Back follows

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Velocity and wavelength are related
Image from Seafriends