1. Previous lecture Reflectance I BRDF, BTDF, BSDF Ideal specular model
Ideal diffuse (Lambertian) model
Phong
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

2. Microfacet Reflectance Models
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

3. Outline Microfacet models Lafortune’s model Two layer models Diffuse
Oren-Nayar
Specular
Torrance-Sparrow
Blinn
Ashikhmin-Shirley (anisotropic)
Ward
Schlick
Lafortune’s model
Two layer models
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

4. Microfacet Models (Text ch. 9.4)
Model surface as set of polygonal facets
Capture surface roughness effects
Microfacets can be diffuse or specular
Use facet distribution to model roughness
Statistical model of microscopic effects gives macroscopic appearance
More realistic, particularly at high incidence angles
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5. Basic microfacet modeling
Surface normal distribution
How the surface normals of the facets are distributed about the macroscopic normal
Facet BRDF
Are the facets diffuse or specular?
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

6. Microscopic geometry Masking – viewer can’t see a microfacet
Shadowing – light can’t see a microfacet
Interreflection – light off one facet hits another
Aim is to capture these effects as efficiently as possible
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

7. Oren-Nayar model (Text ch. 9.4.1)
Model facet distribution as Gaussian with s.d.  (radians)
Facet BRDF is Lambertian
Resulting model has no closed form solution, but a good approximation
Sample using cosine-weighted sampling in hemisphere
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

8. Oren-Nayar effects Lambertian Oren-Nayar
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

9. Torrance-Sparrow (Text ch. 9.4.2)
Specular BRDF for facets
Arbitrary (in theory) distribution of facet normals
Additional term for masking and shadowing
Explicit Fresnel term
Half vector – facet orientation to produce specular transfer n i h o
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

10. Torrance-Sparrow BRDF
G(o , i) handles microfacet geometry
D(h) is the microfacet orientation distribution evaluated for the half angle
Changing this changes the surface appearance
Fr(o) is the Fresnel reflection coefficient
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

11. Geometry term Masking: Shadowing: Together:
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

12. Blinn’s microfacet distribution
Parameter e controls “roughness”
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

13. Sampling Blinn’s model (Text ch. 15.5.1)
Sampling from a microfacet BRDF tries to account for all the terms: G, D, F, cos
But D provides most variation, so sample according to D
The sampled direction is completely determined by halfway vector, h, so sample that
Then construct reflection ray based upon it
So how do we sample such a direction …
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

14. Blinn sampling continued
Need to sample spherical coords: , 
Book has details, and probably an error on page 684
Complication: We need to return the probability of choosing i, but we have the probability of choosing h
Simple conversion term
We need to construct the reflection direction about an arbitrary vector …
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

15. Arbitrary reflection
Coordinate system is not nicely aligned, so use construction
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

16. Anisotropic microfacet distributions
Parameters for x and y direction roughness, where x and y are the local BRDF coordinate system on the surface
Gives the reference frame for 
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

17. Sampling anisotropic distribution
Sampling is discussed in section of the text
Similar to Blinn but with different distribution
Note that there are 4 symmetric quadrants in the tangent plane
Sample in a single quadrant, then map to one of 4 quadrants
Take care to maintain stratification 1
1st
2nd
3rd
4th
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

18. Ward’s isotropic model
“the simplest empirical formula that will do the job”
Leaves out the geometry and Fresnel terms
Makes integration and sampling easier
3 terms, plus some angular values:
d is the diffuse reflectance
s is the specular reflectance
 is the standard deviation of the micro-surface slope
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

19. Ward’s anisotropic model
For surfaces with oriented grooves
2 terms for anisotropy:
x is the standard deviation of the surface slope in the x direction
y is the standard deviation of the surface slope in the y direction
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

20. Sampling Ward’s model Take 1 and 2 and transform to get h and h:
Only samples one quadrant, use same trick as before to get all quadrants
Not sure about correct normalization constant for solid angle measure
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

21. Schlick’s model (Schlick 94)
Empirical model well suited to sampling
Two parameters:
, a roughness factor (0 = Specular, 1 = Lambertian)
, an anisotropy term, (0 perfectly anisotropic, 1 = isotropic)
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

22. Schlick’s model Facet Distribution: Geometry Terms:
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

23. Putting it together Term to account for inter-reflection
Not a Torrance-Sparrow model
As before, sample a half vector:
Only samples in 1 quadrant
Use trick from before
Normalization not given
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

24. More to it than that
Both Ward and Schlick’s original papers define complete reflectance, including diffuse and pure specular components
PBRT calls these materials, because they are simply linear sums of individual components
Schlick’s paper also includes a way to decide how to combine the diffuse, specular and glossy terms based on the roughness
Both Ward and Schlick discuss sampling from the complete distribution
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

25. Phong reloaded
The Phong model can be revised to make it physically reasonable – energy conserving and reciprocal
In canonical BRDF coordinate system (z axis is normal)
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

26. Oriented Phong
Define an orientation vector – the direction in which the Phong reflection is strongest
For standard Phong, o=(-1,-1,1)
To get “off specular” reflection, change o
Can get retro-reflection, more reflection at grazing, etc.
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

27. Lafortune’s model (Text ch. 9.5)
A diffuse component plus a sum of Phong lobes
Allow all parameters to vary with wavelength
Lots of parameters, 12 for each lobe, so suited for fitting to data
It’s reasonably easy to fit
Parameters for many surfaces are available
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

28. Lafortune’s clay
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

29. Sampling Lafortune First choose a lobe (or diffuse)
Could be proportional to lobe’s contribution to outgoing direction
But that might be expensive
Then sample a direction according to that lobe’s distribution
Just like sampling from Blinn’s microfacet distribution, but sampling the direction directly
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

30. Two-layer models (Text chs. 9.6 and 15.5.3))
Captures the effects of a thin glossy layer over a diffuse substrate
Common in practice – polished painted surfaces, polished wood, …
Glossy dominates at grazing angles, diffuse dominates at near-normal angles
Don’t need to trace rays through specular surface to hit diffuse
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell

31. Fresnel blend model
University of Texas at Austin CS395T - Advanced Image Synthesis Fall Don Fussell