Simulation and Rendering of RealTime Breaking Waves
Adam Lake, David Reagin, John Van Drasek
Intel Software Solutions Group (SSG)
Modern Game Technologies Project
2/27/2005
“We arrive at the truth, not by the reason only, but
also by the heart.” -- Blaise Pascal
Motivation
• 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
Getting water right requires…
• Geometry
– Overall shape must be correct
• Shading
– Lighting and shading
• Additional
Geometry/Texture
– Capillary waves, foam, etc. must be
modeled
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
Basic Algorithm
3 passes over 2D Grid:
I.
II.
III.
Deep Wave Simulation
Shallow Wave Simulation
Curling of Wave
–
–
–
Classify portions of waveform
Modify shape based on this classification
Curling breaks ‘height field’
Part I of III: Deep Ocean
Simulation
Deep Ocean Simulation
• Based on Sum of Sines approach of [Finch04],
[Isodoro02]:
 sin( x)  1 
f ( x) amplitude  

2


steepness
• Summation of N waves to simulate Ocean
Surface (N==4 for us)
– 4 good candidate for SSE optimization!!
• x dependent upon wind direction, velocity,
wavelength of wave
.
Normal Generation…
2 techniques:
1.
Derivates as presented in [Finch04]
•
•
2.
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!
Wave Speed and Wavelength
Relationship for Deep Ocean
Waves
speed 
g  wavelength
 1.25 wavelength
2
Eqn. from [Garrison02]
Wavelength to Velocity
Relationship for Deep Waves
Figure from [Garrison02]
Deep Ocean Wave Demo…
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
relationships…the model gives user
control over surface parameters
• Ignoring these relationships is fine to
tune your deep ocean for your
environment
Threading [Lake05]
– Task Level Decomposition
• Thread A: Simulated Game Workload
• Thread B: Compute Wave
Performance with threading
DP vs UP Performance
700
90.00%
80.00%
600
70.00%
500
50.00%
300
40.00%
FPS
400
30.00%
200
20.00%
100
10.00%
0
0.00%
No WorkloadWorkloadWorkload No WorkloadWorkloadWorkload No WorkloadWorkloadWorkload
workload
1
2
3
workload
1
2
3
workload
1
2
3
40x40 Mesh
80x80 Mesh
UP FPS
DP FPS
140x140 Mesh
Speedup
Speedup
60.00%
Part II of III: Shallow Wave
Simulation
Breaking Waves
Image from [Seafriends].
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 don’t do this waves will be incorrect
• Adjust height
– Attempt to preserve water column as it collapses
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,
1.
2.
Determine Deep Ocean wave position from Section I.
Based on this position:
1.
2.
3.
4.
3.
Adjust wavelength
1.
Wavelength varies linearly from lamba to ½ lambda in our example
1.
In our example steepness varies from x to y in our demo
1.
For velocity solve
1.
Collapse of water column is what causes break
Adjust Steepness
Fix Velocity to Maintain phase
Adjust Height as it attempts to maintain water column
Calculate new position using modified values as input to deep ocean simulation equation!
Shallow wave speed and
wavelength relationship
speed  gravity  depth  3.1 depth
Eqn. from [Garrison02]
Shallow Waves demo!
Image from [Seafriends04]
Part III of III: Breaking Waves!
Breaking Waves
Image from [Seafriends].
Types of Breaking Waves
Image from [Mead03]
Side view of breaking wave
Image from [Miller76]
Side view of breaking wave after
collapse
Image from [Miller76]
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
The Vortex
Image from [Mead03].
Vortex Ratio
• Ratio of length to width in practice
is often between 1.73 and 4.43
[Mead03].
Cubic form of vortex
• Cubic form of Vortex is expressed
as [Longuet-Higgins82]:
Note: Not actually needed for implementation!
Classification of surfing wave
breaking Intensity
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
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’
Wave Breaking Algorithm
• Classify vertex state:
– [TOP, BACK, FRONT, FLAT]
– Floating point gotchas, especially FLAT!
2D Slice of Shallow Wave Vertex Positions
0.14
TOP
0.12
Height
0.1
FRONT
0.08
0.06
BACK
0.04
BOTTOM
0.02
0
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79
Vertex Number
So, how do we approximate this
shape?
Image from [Mead03].
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
Image of Vortex Sizes, etc.
Wave Breaking Algorithm
•
Switch(vertex_state):
–
TOP or FRONT:
1.
Obtain 2D Circle Position:
•
2.
–
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
Results [1/3]
100% of Calculated Radius
0.14
0.12
0.1
0.08
Series2
0.06
0.04
0.02
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Only showing FRONT and TOP
0.8
Results [2/3]
75% of Calculated Radius
0.14
0.12
0.1
0.08
Series2
0.06
0.04
0.02
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Results [3/3]
25% of Calculated Radius
0.12
0.1
0.08
0.06
Series2
0.04
0.02
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Breaking Wave Demo!
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 on…demonstrate this
• Stage IV: In the surf…
Acknowledgements
• Kim Pallister and Pete Baker for giving
the resources and time to work on
this project.
• Jacob Anderson (jwa@beyondordinary.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@SGI.
• Allison Knowles for title, poster, and
acknowledgement photographs.
References [1 of 2]
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•
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[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. O’Reilly 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/oceano/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/title/tt0120338/.
[Lake05] Adam Lake and David Reagin. Real-Time Deep Ocean Wave Simulation On MultiThreaded 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.
References [2 of 2]:
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[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.
Backup
• Irribarren Number[cite]:
– B is slope
– Hb/Linf = ratio of wave height to wavelength
Wave Energy as a function of
Period
•
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
I.
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Wav
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Sim
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II.
Shal
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Wav
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Sim
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S
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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
Velocity and wavelength are related
Image from [Seafriends]