1. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell Previous lecture Reflectance I BRDF, BTDF, BSDF Ideal specular model Ideal diffuse (Lambertian) model Phong

2. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell Microfacet Reflectance Models

3. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell Outline Microfacet models Diffuse Oren-Nayar Specular Torrance-Sparrow Blinn Ashikhmin-Shirley (anisotropic) Ward Schlick Lafortune’s model Two layer models

4. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell 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

5. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell 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?

6. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell 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

7. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell 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

8. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell Oren-Nayar effects LambertianOren-Nayar

9. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell 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 ii n hh oo Half vector – facet orientation to produce specular transfer

10. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell 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 F r (  o ) is the Fresnel reflection coefficient

11. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell Geometry term Masking: Shadowing: Together:

12. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell Blinn’s microfacet distribution Parameter e controls “roughness”

13. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell 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 …

14. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell 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 …

15. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell Arbitrary reflection Coordinate system is not nicely aligned, so use construction

16. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell 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 

17. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell Sampling anisotropic distribution Sampling is discussed in section 15.5.2 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 01 1st2nd3rd4th

18. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell 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

19. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell 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

20. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell 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

21. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell 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)

22. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell Schlick’s model Facet Distribution: Geometry Terms:

23. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell 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

24. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell 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

25. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell 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)

26. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell 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.

27. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell 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

28. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell Lafortune’s clay

29. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell 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

30. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell 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

31. University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell Fresnel blend model