Download - Appearance Models for Graphics
Appearance Models for Graphics
COMS 6998-3
Brief Overview of Reflection Models
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Assignments
• E-mail me name, status, Grade/PF. If you don’t do this, you won’t be on class list. [and give me e-mails now]
• Let me know if you don’t receive e-mail by tomorrow
• E-mail me list of papers to present (rank 4 in descending order). Must receive by Fri or you might be randomly assigned.
• Next week, e-mail brief descriptions of proposed projects. Think about this when picking papers
Today
Appearance models
– Physical/Structural (Microfacet: Torrance-Sparrow, Oren-Nayar)
– Phenomenological (Koenderink van Doorn)
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Symmetric Microfacets
Shadowing Masking Interreflection
Brdf of grooves simple: specular/Lambertian
Torrance-Sparrow: Specular Grooves. Specular direction bisects (half-angle) incident, outgoing directions
'( ) ( , ) ( )
4 cos( )cos( )
i i r h
i r
F G Df
Oren-Nayar: Lambertian Grooves.Analysis more complicated. Lambertian plus a correction
Phenomenological BRDF model Koenderink and van Doorn
• General compact representation
• Domain is product of hemispheres
• Same topology as unit disk, adapt basis
– Zernike Polynomials
Paper presentations
• Torrance-Sparrow (Kshitiz)
• Oren-Nayar (Aner)
• Koenderink van Doorn (me, briefly)
Phenomenological BRDF model Koenderink and van Doorn
• General compact representation
• Preserve reciprocity/isotropy if desired
• Domain is product of hemispheres
• Same topology as unit disk, adapt basis
• Outline– Zernike Polynomials– Brdf Representation– Applications
Zernike Polynomials
• Optics, complete orthogonal basis on unit disk using polynomials of radius
• R has terms of degree at least m. Even or odd depending on m even or odd
• Orthonormal, using measure dd
immn
mn eR
nZ )(
1),(
n-|m| even|m|n
Cool Demo: http://wyant.opt-sci.arizona.edu/zernikes/zernikes.htm
|m| 0 1 2
n
0
1
2
n-|m| mustbe even
|m| n
|m| n
|m| n
n-|m| mustbe even
n-|m| mustbe even
n-|m| mustbe even
Hemispherical Zernike Basis
• Measure Disk: Hemisphere: sin()dd
• Set
dd
)2sin(2
dddd )sin(2
)())2sin(2(1
),(
mmn
mn azR
nK
azm=
m>0:cos(m)m=0:sqrt(2)m<0:sin(m)
dd )2cos(2
1
dd )2cos()2sin(
BRDF representation
• Reciprocity: aklmn=amnkl
),(),(),,,( rrmnii
kl
klmnklmnrrii KKaf
BRDF representation
• Reciprocity: aklmn=amnkl
• Isotropy: Dep. only on = |i-r| Expand as a function series of form cos(m[i-r])
• Can define new isotropic functions
• Symmetry (Reciprocity): alnm= anl
m
),(),(),,,( rrmnii
kl
klmnklmnrrii KKaf
)cos())2sin(2())2sin(2(),,( mRARI rmli
mnri
mnl
),,(),,( rimnl
lmn
mnlri Iaf
BRDF Representation: Properties
• First two terms in series
• 5 terms to order 2,14 to order 4, 55 order 8
• Lambertian: First term only
• Retroreflection: ln
• Mirror Reflection: (-1)m ln
• Very similar to Fourier Series
)cos()2sin()2sin(22
2
1
111
000
riI
I
alnm = l0 n0 m0
alnm = ln
alnm = (-1)m ln
Applications
• Interpolating, Smoothing BRDFs• Fitting coarse BRDFs (e.g. CURET).
Authors: Order 2 often sufficient• Extrapolation• Some BRDF models can be exactly
represented (Lambertian, Opik)• Others to low order after filtering/truncation• High-order terms are typically noisy
Discussion/Analysis
• Strong unified foundation
• Spectral analysis interesting in own right
• Ringing!! Must filter
• Don’t handle BRDF features well
• Specularity requires many terms
• Theoretically superior to spherical harmonics but in practice?