Transcript Spherical Harmonic Lighting of Wavelength

Spherical Harmonic Lighting of
Wavelength-dependent
Phenomena
Clifford Lindsay, Emmanuel Agu
Worcester Polytechnic Institute
(USA)
Introduction
 Modeling of Light Interference As A BRDF
 Compactly Store Surface Response and
Hemispheric Light Contribution In Terms Of Spherical
Harmonic Coefficients
 Evaluation of Light And Reflection Is Done on GPU
 Working With Spectral Color Space Instead of RGB
Spherical Harmonics
y  ,  
Spherical harmonics is a set of
basis functions defined in
spherical coordinates
m
l
4
ci 
N
We can use spherical
harmonics to approximate the
original, where ci is a vector of
SH coefficient
We can then use
these coefficients to
reconstruct an
approximation to the
original signal
N
 c B x  
i 1
i
i
 f x y x 
N
j 1
j
i
j
Interference
Factors that Affect Light Interference:
 Refractive index and thickness of the thin film
 Refractive indices of the media 1 & 2
 Incident Angle  and incident SPD (Spectral Power Distribution)
Spectral BRDF
Just Like Regular BRDFs (but different)
 Rendering equation
 Function of 4 angles (incident, reflection)
 Conservative
f ( s,  )   4 R f ( ,  ) sin (
2
s
2

What’s Different?
 Different Color Interaction
 Different Material Interaction
 Different Viewer Interaction (non-reciprocal)
w cost )
Previous Work in S.H.
 Diffuse Reflection Maps, Hanrahan, Ramamoorthi, 2001
 Physically Based BRDFs, Westin 1992
 Isotropic BRDFs with SH Maps, Hanrahan, Ramamoorthi, 2002
 Arbitrary BRDFs, Kautz et al, 2002
 Radiance Transfer, Glossy Surfaces, Self-shadow,
and Interreflection, Sloan et al, 2002
Our Approach
Two Stage Approach:
1. Pre-computation


Ls  Li
f ( s,  )  f i0 in
2. Render
n2

L
i 0
i
fi
Pre-computation
Total Light Contribution:
 Set of coefficients approximating total light contribution
 L0 
Ls    
 Li 
BRDF Response:
 Texture map based all possible view vectors
V
c0,0  cn ,0 


f ( s,  )      
 c0,i  cn ,i 
GPU
Rendering:
V,T,B
Index Texture Map Based on view V
Vertex
Processor
 Summing the coefficients for
final contribution
 Add ambient, diffuse, Fresnel
for additional realism
Texture Map, fi
Uniform Var, Li
Fragment
Processor
n2
L
i 0
i
fi
Conclusion
 Real-time rendering of complex materials
previously available to offline renderers (ray
tracers)
 Data and Data structures that are GPU friendly
 Evaluation of Spherical Harmonics is a linear
operation
 Increased realism with Image Based Lighting and
accurate BRDFs with GPU acceleration
Results