???????????

??

????GPU???Shader???????????????????????????????????????????????????

???????????????????????????????????????????????????????????????????????????????????

??????????????

?????????????????????????????????????????????????????????????????????????????????????50???????????????????????

1.        ???????Bump Mapping? [Schachters 1980]

2.        ????Sinusoids Wave?[Max 1981]

3.        ?????Fractal noise?[Perlin 1985]

4.        Gerstner ??Gerstner Wave?[Fournier 1986]

5.        ????????Fast Fourier Transform?[Mastin 1987]

6.        ?????Eulerian approaches?[Kass 1990]

7.        ???????Lagrangian approaches?[Stam 1995]

8.        ??-?????????Hybrid approaches?[Brien 1995]

9.        ???????Fractal Brownian Motion?FBM?[Addison 1996]

10.        ??????Procedural Shape?[Ebert 1999]

11.        ??-???????Spatial -Spectral Approaches? [Thon 2000]

12.        ????????Voxel-Based NSE Solutions? [Yann 2003]

13.        ?????????Vertex Height Map Displacement?[Yuri 2005]

14.        ???????2D Wave Equation?[Nishidate 2005]

15.        ???????Screen Space Mesh?[Muller 2007]

16.        ?????Wave Particles?[Yuksel 2007]

17.        ??????(Vector Displacement Map) [2009]

18.        ????Flow Map?[Vlachos 2010]

19.        ??FFT?????Offline FFT Texture?[Torres 2012]

20.        ??????????bake to flipbook?[Bowles 2017]

21.        ???????Water Wave Packets?[Jeschke 2017]

22.        ????????Water Surface Wavelets?[Jeschke 2018]

23.        ???????Water Wave Simulation?[Grenier 2018]

???????????????????????????????????????????????????????????????????????????

????????????????????????????????????????????????????????????

???????????????????

????????4??????????

??????????????????

????????5????????

?????4????????

???????????????????

??????????????????????????????Skull & Bones???gameplay???

????????????

?????3A????????????????????????????????????????????????

???????????????

?????????????????????

???????QianMo/Water-Rendering-Knowledge-Architecture.png

OK????????

?????????????

??????????????????????????????????????

1.        ????????

• ????Sinusoids Wave?[Max 1981]
• Gerstner ? ?Gerstner Wave? [Fournier 1986]
  

2. ??????

• ????????Fast Fourier Transform?[Mastin 1987]
• ??-???????Spatial -Spectral Approaches?[Thon 2000]
  

3. ??????

• ????????Wave Particles? [Yuksel 2007]
• ???????Water Wave Packets?[Jeschke 2017]
• ???????Water Surface Wavelets?[Jeschke 2018]
  

4. ???????

• ?????Eulerian approaches?[Kass 1990]
• ???????Lagrangian approaches? [Stam 1995]
• ??-?????????Hybrid approaches?[Brien 1995]
  

5. ?????

• ?????????Vertex Height Map Displacement? [Yuri 2005]
• ????Flow Map?[Vlachos 2010]
• ??FFT?????Offline FFT Texture? [Torres 2012]
• ??????????bake to flipbook?[Bowles 2017]
  

6. ????

• ???????Bump Mapping?[Schachters 1980]
• ?????Fractal Noise?[Perlin 1985]
• ???????Fractal Brownian Motion?FBM?[Addison 1996]
• ??????Procedural Shape?[Ebert 1999]
• ????????Voxel-Based Solutions? [Yann 2003]
• ???????2D Wave Equation?[Nishidate 2005]
• ???????Screen Space Mesh?[Muller 2007]
• ???????Water Wave Simulation?[Grenier 2018]
  

??????????????????

4.1 ????????

??????????????????????????????????????????????????????????????

? ??????????????????????????????????????????????????????????????????????????????????https://wikischool.org/divided_light?

?????????????????Sinusoids Wave??Gerstner?(Gerstner Wave)????????????

4.1.1 ????Sinusoids Wave?[Max 1981]

????????????????????Sinusoids Wave??????????????????????????

? Unity??????????Sinusoids Wave????

1981??Max[Max 1981]??????????????????????????????????????????????????????Sinusoids Wave???????t?????x?z???????y = h?x?z?t????????

• ?? ?????
• ??i?????
• ????
• ??????pulsation?
• ????????
  

????Sinusoids Wave?????????????????????????????????Gerstner??

4.1.2 Gerstner ??Gerstner Wave? [Fournier 1986]

??????????Gerstner ??Gerstner Wave?????????????????????????????

? Unity??????Gerstner????

Gerstner ?(Gerstner Wave)?????Trochoidal Wave???????????????????periodic surface gravity waves????????????Gerstner?1802 ????????1863??Ranine????????1986??Fournier???????????

? Gerstner Waves??

? Gerstner Waves???????????

???????ki???Ai????i????i???   ?Gerstner Waves???????

Gerstner Waves????????????????????????????????3A?????Gerstner Wave???????????????Wave Particles????????????3???????Gerstner Wave + Wave Particles??????????

4.2 ??????

4.2.1 ????????Fast Fourier Transform , FFT?[Mastin 1987]

??????????????????????????????????Fast Fourier Transform , FFT?????????????????????????????????????

?1986?[Mastin 1987]???FFT??????????????????2001?Tessendorf??????????Simulating Ocean Water?[Tessendorf 2001]????????????????????????????????

? Unity??????FFT???

??????Fourier transform??????????????????????????????????? ?Fast Fourier Transform?FFT?, ?????O?nlogn??????????????Discrete Fourier transform?DFT??????????????????????????????1805?????????????1965??Cooley?Tukey???????????????????????????FFT??????????????????????????FFT???????????????????????????????FFT??????

FFT??????????N?????????????????????DFT???????? ??????????????????????????DFT????????????????????????????????

??FFT????????????????????????

??FFT??????????????????????spectrum-based?????????????FFT??????????????????????????????????????????????[Tessendorf 2001]???Phillips???????????????????????????????????????FFT?????????????????????displacement map????????????????????????????????????Folding Map?

? ??FFT??????? [NVIDIA 2004]

??FFT????????90????????????????????2000????????????????????????????????????????????????????????????????????Crysis???????????????64 x 64???????????????????512 x 512?????????????????????????????FFT?????????????????????????????????????1997????????????????????????2048 x 2048????????

? ???????????????FFT????????????2048 x 2048???????

4.3 ??????

4.3.1 ?????Wave Particle? [2007]

?????Wave Particle??????Yuksel?2007?[Yuksel 2007]????????????????????????????????????????????????????????????????????????????????

?????Wave Particle???????????????????FFT??????????????????????????????????????????????

? Wave Particle ?????[Yuksel 2007]?

????????????Wave particles?????????????????????????????????????????amplitude?????radius??

???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????

? ?a???b??????????????????????c???d??????????????????????????[Yuksel 2010]?

??????????????????????????????????????????????????????????????????????

? ???????????????????????????[Yuksel 2010]?

???Wave Particles????????????????????

2007?Yuksel?????Wave Particles???????????????????????????3?????????????????3???????????????????????????????????????????????????????????????vector displacement field??

? ?????3????????wave particles?????????? [SIGGRPAPH 2016]

?????4??????????Wave Particles??????????Wave Particles????????

? ?????4???????Wave Particles [SIGGRPAPH 2016]

4.3.2 ???????Water Wave Packets?[SIGGRAPH 2017]

??????Wave Particles?????? Jeschke?Wojtan[2017]?SIGGRAPH 2017??????????theoretical group speed?????????Water wave packets ????????????????????????????????????????????????????????????????????????????????

? ???????Water Wave Packets??paper demo [SIGGRPAPH 2017]

? ???????Water Wave Packets??????

? ???????Water Wave Packets??????

4.3.3 ???????Water Surface Wavelets? [SIGGRAPH 2018]

???[SIGGRAPH 2018]?Jeschke???Water Wave Packets??????????????????Water Surface Wavelets?????????Water Surface Wavelets????????????????????????????????????GPU??????????????????????????????????????????????????????????????????????????????

? Water Surface Wavelets paper Demo [SIGGRPAPH 2018]

? ???????Water Surface Wavelets?????? [SIGGRPAPH 2018]

4.4 ???????

???????????????????????????????????????????????????????????????????????

??????????????????Navier-Stokes???Navier-Stokes Equations,NS????????Navier-Stokes????????????????????????????????????????????????????????????????????????????

Navier-Stokes?????

• ????????fluid velocity vector?
• ??????fluid pressure?
• ??????fluid density?
• ????????kinematic viscosity coefficient?
• ??????gradient differential?
• ????????Laplacian operators?
  

?????Navier-Stokes???????????Eularian Method?????????Lagrangian Method????

• ?????Eularian Method???????????????????????????????????????????????????????????????????????????????????????????????????????
• ???????Lagrangian Method?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????(Smoothed Particle Hydrodynamics?SPH)?????????????????????????????????
  

? ??SPH?????????

? Houdini??????

?????????????????????-?????????Eularian-Lagrangian Hybrid approaches?????????????????????????????????????????????????????

FX Guide?????????????????????????????????????https://www.fxguide.com/fxfeatured/the-science-of-fluid-sims/

????????bake to flipbook???????????????flipbook???????????

4.5 ?????

4.5.1 ????Flow Map?

????Flow Map????????????Vector Field Map??????????????????????????????????UV????VALVE?Vlachos?SIGGRAPH 2010??talk?Water Flow in Portal 2???????????????VALVE?2010????????Houdini???flow map?

? ??Flow Map????? [SIGGRAPH 2010]

? ??Houdini?Flow Map????? [SIGGRAPH 2010]

Flow Map???????????????????????????Flow Map???????????????

? ??Flow Map????? @Unity

? ??Flow Map????? @UDK

Flow Map?????????2D???????????????UV????????????

? ??Flow Map???

Flow Map????????????

1. //get and uncompress the flow vector for this pixel
   
2. float2 flowmap = tex2D( FlowMapS, tex0 ).rg * 2.0f - 1.0f;
   
3. float cycleOffset = tex2D( NoiseMapS, tex0 ).r;
   
4. float phase0 = cycleOffset * .5f + FlowMapOffset0;
   
5. float phase1 = cycleOffset * .5f + FlowMapOffset1;
   
6. 
   
7. // Sample normal map.
   
8. float3 normalT0 = tex2D(WaveMapS0, ( tex0 * TexScale ) + flowmap * phase0 );
   
9. float3 normalT1 = tex2D(WaveMapS1, ( tex0 * TexScale ) + flowmap * phase1 );
   
10. float flowLerp = ( abs( HalfCycle - FlowMapOffset0 ) / HalfCycle );
    
11. float3 offset = lerp( normalT0, normalT1, flowLerp );

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4.5.1.1 Flow Map????????3?Flow Map + Displacement

???Flow Map?????????????????????3???Flow Map + Displacement?

4.5.1.2 Flow Map?????????Flow Map + Distance Fields + Normal Maps

??????????Flow Map + Distance Fields + Normal Maps [GDC 2019, Technical Artist Bootcamp Distance Fields and Shader Simulation Tricks]

4.5.1.3 Flow Map????????4?Flow Map + Wave Particles

???????4???Flow Map + Wave Particles[SIGGRAPH 2016, Rendering Rapids in Uncharted 4]????????????????????????

? ?????4???Flow Map + Wave Particles????flow map??????wave particle grids????????????????????????????????????flow map?????

????????4??Flow + Wave Particles?????

1. timeInt = time / (2.0 * interval)  
   
2. float2 fTime = frac(float2(timeInt, timeInt * .5)  
   
3. posA = pos.xz - (flowDir/2) * fTime.x * flowDir  
   
4. posB = pos.xz - (flowDir/2) * fTime.y * flowDir  
   
5. gridA0 = waveParticles(posA.xz, freq0,scale0)  
   
6. gridA1 = waveParticles(posA.xz, freq1,scale1)  
   
7. �  
   
8. gridB0 = waveParticles(posB.xz, freq2,scale0)  
   
9. gridB1 = waveParticles(posB.xz, freq3,scale1)  
   
10. �
    
11. 
    
12. float3 pos0 = gridA0 + gridA1 + gridA2 + gridA3  
    
13. float3 pos1 = gridB0 + gridB1 + gridB2 + gridB3  
    
14. pos = blend(pos0, pos1, abs((2*frac(timeInt)-1)))  
    
15. pos.y += heightMap.eval(uv)
    

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4.5.2 ??FFT?????Offline FFT Texture?

??FFT???Offline FFT Texture???????????3???????[Torres 2012]???????????????FFT??????????????????????????????vector displacement maps????????????FFT????????????????????tiling?

? ????FFT????????4??????

? ????FFT????????3??????

4.6 ????

????5??????????????????????????????

• ???????Bump Mapping?[Schachters 1980]
• ???????Fractal Brownian Motion?FBM?[Addison 1996]
• ?????Procedural Shape?[Ebert 1999]
• ?????Fractal Noise?[Gonzato 2000]
• ????????Voxel-Based Solutions? [Yann 2003]
• ???????Screen Space Mesh?[Muller 2007]
• ???????Vector Displacement Map?[2009]
  

??????????Bump Mapping???????????????????????????????????????????????????????????????????????????????

??????Fractal Noise??????????????Perlin???????????????????????

???????Vector Displacement Map???????????????????????????????????????

? ????????????Vector Displacement Map? @Arnold Render

? ?????????Vector Displacement Map?????? @Arnold Render

??????????????????paper???????????????

????????????SIGGRAPH 2017? ,Crest Ocean System??????????Procedural Shape???????????????????????

????????????

???????????

???????Shading???????????????????????????????

????????????????????????????????????????????????????????????????Sub-Surface Scattering, SSS???????????????????????????BSSRDF?Bidirectional Surface Scattering Reflectance Distribution Function???????????????

???????????BSSRDF???????????????????????????????????????????

?????3??2012?SIGGRAPH????????????????????????????

???????????????????

• ????Diffuse?
• ?????Specular?
• ?????Normal Map?
• ???Reflection?
• ????Translucency?
  

• ???????????Depth Based LUT Approach?
• ??????Subsurface Scattering?
  

• ???Foam/WhiteCap?
  

• ?????Flow?
• ?????Underwater Haze?
  

????????????????????????????????????Flow????????????????

????????????????Translucency?????Foam/WhiteCap??????????

5.1 ??????Translucency??????

????????Translucency??????????????????????????

• LUT???Look-Up-Table Approach?
• ??????????Sub-Surface Scattering,SSS Approximation Approach??
• ?????? ????LUT???????????????????????????????3?
  

5.1.1 ???????????Depth Based LUT Approach?

Depth Based-LUT?????????????????????????????????/??LUT?Absorb/Scatter LUT?????????????????????????????

?????????????????????????????????????

? ????????????????????????

5.1.2 ??????????Sub-Surface Scattering Approximation Approach?

?????????????????Sub-Surface Scattering?SSS??????????????????

• [SIGGRAPH 2019] Crest Ocean System?????????SSS???
• [GDC 2011] ?????Fast SSS???
  

? ??????????????

5.1.2.1 [SIGGRAPH 2019] Crest Ocean System?????????SSS??

??Crest Ocean System??????????SSS?????????

• ?????????????????????
• ??FFT???????????????????mask
• ????????????mask????????????????????????????????????
• ?????Displacement???????????????????????????????
  

????????????

1. float v = abs(i_view.y);
   
2. 
   
3. half towardsSun = pow(max(0., dot(i_lightDir, -i_view)),_SubSurfaceSunFallOff);
   
4. 
   
5. half3 subsurface = (_SubSurfaceBase + _SubSurfaceSun * towardsSun) *_SubSurfaceColour.rgb * _LightColor0 * shadow;
   
6. 
   
7. subsurface *= (1.0 - v * v) * sssIndensity;
   
8. 
   
9. col += subsurface;

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? ?Crest Ocean System????????????????

? ??????Sea of Thieves?????????????????

? ??????Sea of Thieves?????????????????

5.1.2.2 [GDC 2011] ?????Fast SSS??

[GDC 2011]??Frostbite?????Fast Approximating Subsurface Scattering????????????????

????????????

5.2 ???????

???Foam????????????Whitecap?White Water??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????

? ??????

??????????????????????????????????????????????????????

?????????????????????????

• ???????dynamic texture?
• ???????particle system?
  

???????????????

• ????
• ????
• ????
  

????????????????????????

• ?????????[Tessendorf 2001]
• ??Saturate??????? [GPU Gems 2]
• ?????????? [Tessendorf 2001]
• ?????? [Akinci 2013]
• ????????? [Kozin 2018][Sea of Thieves]
• ?????????? [GDC 2018][Far Cry 5]
  

?????????????????

5.2.1 ?????[Tessendorf 2001] ??????????

Tessendorf?????????paper?Simulating Ocean Water?[Tessendorf 2001]??????????????Jacobian??????????????????????????????????????????Folding Map???

??????War Thunder?????CGDC 2015??????????????????M???????????????M~0.3...05?

? ??????War Thunder???????????M???????????? [CGDC 2015]

?????????Sea of Thieves?????SIGGRPAPH 2018???????????????????????????????????Progressive Blur???????noisy????????????????

? ??????????????? + ?????Progressive Blur?????????

5.2.2 ?????[GPU Gems 2] ??Saturate?????

?GPU Gems 2??????????????????????????????????H0????????????????????????????

• ???   ?????????? ??????   ??????
• ?????????????????????????????????????????????????????????
• ??????????????????????????????
  

5.2.3 ?????[2012]?????3???Multi Ramp Map???

?????3??????????????????

• ?????????????????????????????
• ???????Perlin???????????????????????????
• ????????????R?G?B??????????????????????ramp???????????????????????????????????????????????ramp????????????????
  

5.2.4 ?????[SIGGRAPH 2018]???????????????????

??????Sea of Thieves?????SIGGRPAPH 2018?talk????????????????????

• ????top-down?????????????????????????????mask???
  

half4 foamMask = 1 - saturate(_FoamThickness* (depth - i.screenPos.w )) ;

• ????foamMask???texture?blend?
• ???????????????????mask??????progressively blur??????????????
  

? ??????Sea of Thieves????????

? ??????Sea of Thieves????????

5.2.5 ????&?????[GDC 2018]?????5???????????

GDC 2018??????5?????????????????????????????????Noise?????????????offset??Flow Map?????????????????Signed Distance Field?SDF??????????????????????????????

???????????????

????2019??????3A????????????&?????????????????????

???????????????????????????????????????

6.1 Crest Ocean System

Crest Ocean System?Unity???????????????????SIGGRAPH?SIGGRAPH 2017?SIGGRAPH 2019??????????

???????https://github.com/crest-ocean/crest

demo???https://www.youtube.com/watch?v=ekng3c43Y1E

????????Crest Ocean System??????LWRP?????https://assetstore.unity.com/pac ... tem-lwrp-urp-141674

6.2 CryEngine????

????GPU?????????????CryEngine???????????????????????????????????????????CryEngine????????

???????https://github.com/CRYTEK/CRYENGINE/CryFX/Water.cfx

demo???https://www.youtube.com/watch?v=tZthI6M07iM

6.3 UE4 Dynamic Water Project

Dynamic Water Project ?Unreal???????????????????????????????????

???????marvelmaster/UE4_Dynamic_Water_Project

6.4 Ceto Ocean system

Ceto ?Unity??????????????????

???????https://github.com/Scrawk/Ceto

6.5 NVIDIA UE4 WaveWorks

GDC 2017??NVIDIA?Unreal Engine?????WaveWorks?????Unreal Engine 4.15?????????

???????https://github.com/NvPhysX/UnrealEngine/tree/WaveWorks

demo???https://www.youtube.com/watch?v= ... p;index=11&t=0s

6.6 Unity LWRP BoatAttack

BoatAttack?Unity?2018?5?13??????LWRP??????????????????????????????????Unity???????????????

???????https://github.com/Verasl/BoatAttack

demo???https://www.youtube.com/watch?v=7v9gZK9HqqI

????

??????????????????????????????????????????????????????????????????????

??????????????????

???????QianMo/Water-Rendering-Knowledge-Architecture.png

???GitHub?

???????????GPU???Shader???????????????GPU???Shader???????????????Game-Programmer-Study-Notes??GitHub Repo??

???GitHub??????

QianMo/Game-Programmer-Study-Notesgithub.com

Reference:


[1] FX Guide 2012, Assassins Creed III The tech behind or beneath the action, https://www.fxguide.com/fxfeatur ... beneath-the-action/
[2] SIGGRAPH 2001, Tessendorf J. Simulating ocean water[J]. Simulating nature: realistic and interactive techniques.
[3] SIGGPRAPH 2019, Multi-resolution Ocean Rendering in Crest Ocean System
[4] GDC 2008, Fast Water Simulation for Games
[5] GDC 2012, Water Technology of Uncharted
[6] GDC 2018, Water Rendering in FarCry 5
[7] Jeschke S, Wojtan C. Water wave packets[J]. ACM Transactions on Graphics (TOG), 2017
[8] 2010, Yuksel C. Real-time water waves with wave particles[M]. Texas A&M University
[9] SIGGRAPH 2016, Rendering rapids in Uncharted 4
[10] GDC 2019, Technical Artist Bootcamp Distance Fields and Shader Simulation Tricks
[11] https://zhuanlan.zhihu.com/p/21573239
[12] SIGGRAPH 2010, Water Flow in Portal 2
[13] GPU Gems2, Using Vertex Texture Displacement for Realistic Water Rendering
[14] SIGGRAPH 2013, Oceans on a Shoestring Shape Representation, Meshing and Shading
[15] SIGGRAPH 2018, The Technical Art of Sea of Thieves
[16] GDC 2015, An Introduction to Realistic Ocean Rendering through FFT
[17] CGDC 2015, Ocean simulation and rendering in War Thunder
[18] NVIDIA 2004, Ocean Surface Simulation nvidia
[19] SIGGRAPH Asia 2012, Real-time Animation and Rendering of Ocean Whitecaps
[20] TOG 2017, Water Wave Packets
[21] NVIDIA 2004, Ocean Surface Simulation nvidia
[22] GDC 2017, From Shore to Horizon Creating a Practical Tessellation Based Solution
[23] https://www.tek.com/fft
[24] https://www.youtube.com/watch?v=hzw-NOKeSRY
[25] https://www.youtube.com/watch?v=iBBQzs-7Ac4
[26] https://www.fxguide.com/fxfeatured/the-science-of-fluid-sims/
[27] https://graphicsrunner.blogspot. ... sing-flow-maps.html
[28] ??????????

??????
?????https://zhuanlan.zhihu.com/p/95917609