Computer graphics & visualization Global Illumination Effects

computer graphics & visualization

How to make a PIXAR movie

Global Illumination Effects


Global Illumination EffectsChristian A. Wiesner

Motivation• Realistic illumination of the scene



Motivation• Soft shadows



Motivation• Subsurface scattering



Motivation• Many algorithms exist– Photon mapping– Ambient Occlusion– …

• Common goal: Solving parts of the Rendering Equation



Problems• Scene changes -> New computation• Still not possible in real-time• Uses Raytracing or Radiosity

Already explainedGoing to be explained now



Photons• Have energy

• h: Planck constant• v: Frequency of light

hvE



Radiometric QuantitiesRadiant energy J

Radiant power W

Irradiance W/m²

Radiosity W/m²

Radiant intensity W/sr

dt

dQ

dA

dE

dA

dB

d

dI

Q



Radiance

cos²

dAd

dL

• θ: angle between surface‘s normal and ω• cosθ: Lambertian law• Constant along a ray



Irradiance



BRDF

iiii

rrrir dxL

xdLxf

cos),(

),(),,(

Bidirectional reflectance distribution function

How much light is reflected



Reflection Equation

iiiirirrr dxLxfxL

cos),(),,(),(

Integrate over the hemisphere



Rendering Equation

Sy

yirirrer dAyxGyxVyLxfxLxL

),(),(),(),,(),(),(

Radiance

Emitted light

Surfaces

BRDF

Visibility

Geometry factor



Radiosity• Ideal diffuse reflection can be simulated with

Radiosity• Uses finite elements• Introduced by Goral et al.



Radiosity• Origin: Thermal heat transfer• Developed in 1984, still in use• Modelling of diffuse lighting– Doesn‘t account for specular lighting– Independent of viewer– Therefore: Stays constant in constant scene



Radiosity Equation

j

ijjieii FBBB

RadiosityEmissivity

Reflectivity Form factor

Sy

yirirrer dAyxGyxVyLxfxLxL

),(),(),(),,(),(),(

constant



Form Factors

i jA A

ijji

iij dAdA

rAF

²

coscos1



Form Factors



Nusselt Analog• Simple geometric analog for calculating form

factors

B B

AFij

A



Hemicube Algorithm• Hemicube instead of hemisphere



Hemicube Algorithm• Idea:– Precompute delta form factors analytically– Count covered pixels– Sum up covered delta form factors to the true form

factor

q

qij FF



Hemicube Example



Hemicube Algorithm on GPU• Use projection center as viewport• Use current face as viewing plane• Do the rendering• Grab the colour buffer (IDs of patches)• Count coloured pixels• Visibility test performed by depth test



Radiosity Algorithm• Compute form factors• Solve linear equation system

for i = 1, … , nj

ijjieii FBBB

nnnnnnnnn

n

n

E

E

E

B

B

B

FFF

FFF

FFF

2

1

2

1

21

22222212

11121111

1

1

1

)1( T



Von Neumann Series

...

...

...

²

)3()2()1()0(

3210

BBBB

ETETETET

BTTEETBEB

0 Bounces 1 Bounce 2 Bounces 3 Bounces



Jacobi Iteration



Shooting / Gathering

N

j

kjijii

ki BFEB

X

X

X

XXXXX

1

)()1( )(

N

j

kj ij i i

kiB F E B

X

X

X

X

X

X

X

X

X

X

1

) ( ) 1 () (



Radiosity Result



Radiosity vs. Ray Tracing



Radiosity Conclusion• Old, but still in use• Used for simulating diffuse lighting• Result can be used in combination with other GI

algorithms



Ambient Occlusion Motivation• Ambient term constant in Phong model• Not very realistic• Idea: Compute occlusion of each face



Ambient Occlusion• Result: Occluded areas appear darker than

brigther ones• Multiply with usual Phong model• 2 possibilities:– Screen space– Object space



Screen Space Ambient Occlusion• Can be completely done on GPU• No preprocessing• Independent of scene complexity• Idea: Instead of performing full raytracing use

occlusion information from z-buffer



Screen Space Ambient Occlusion• Take 3D samples around each point• Determine occlusion of each point by testing

against the depth buffer• Far samples with less influence• Use blurring for smooth results



Screen Space Ambient Occlusion



Object Space Ambient Occlusion• Define surface element as an oriented disk• Use Heron‘s formula ,• Store position, normal and area in texture for

pixel shader

))()(( csbsass 2

cbas



Object Space Ambient Occlusion• Compute accessibility value ateach element (% of hemisphere)• Approximation based on thesolid angle of an oriented disk

• Strongly dependent on scenecomplexity

²

)cos4,1max(cos1

rA

r RE



Object Space Ambient Occlusion



Ambient Occlusion Results



Ambient Occlusion Results



Ambient Occlusion Conclusion• Can be preprocessed for each object• Used in the current version of PIXAR‘s

RenderMan



Outlook• Faster computation– Cheaper– Artists can see results faster

• More realistic lighting



Conclusion• Very important for any animated movie• Computation time not too important



Thanks for your attention!

Documents

Computer graphics & visualization Global Illumination Effects