2. 6.1 si31_2001 SI31 Advanced Computer Graphics AGR Lecture 6 Physically Based Reflection Model

3. 6.2 si31_2001 Phong Reflection Objects tend to have plastic appearance

4. 6.3 si31_2001 Phong Model - Limitations What’s Wrong with Phong n The Phong model is based more on common sense than physics n However it fails to handle two aspects of specular reflection that are observed in real life: – intensity varies with angle of incidence of light, increasing particularly when light nearly parallel to surface – colour of highlight DOES depend on material, and also varies with angle of incidence

5. 6.4 si31_2001 Physically Based Model n Cook and Torrance have proposed an alternative model which has a basis in physics and which more accurately represents specular highlights n Diffuse reflection handled as in Phong model n Start by assuming perfectly smooth surface, ie mirror type surface

6. 6.5 si31_2001 Fresnel Equation In general, light is partly reflected, partly refracted Reflectance = fraction reflected reflected refracted Refractive Index:  = sin  / sin  [Note that  varies with the wavelength of light] The Fresnel equation gives the reflectance, F, of a perfectly smooth surface in terms of refractive index  of material and angle of incidence  N  

7. 6.6 si31_2001 Fresnel Equation Reflectance, F, is a minimum for incident light normal to the surface, ie  = 0 : F 0 = (  - 1 ) 2 / (  + 1 ) 2 n So different F 0 for different materials Because the refractive index  of a material depends on the wavelength of light,, so we also have different F 0 for different wavelengths – burnished copper has roughly: F 0,blue = 0.1, F 0,green = 0.2, F 0,red = 0.5 n Thus colour of specular reflection does depend on material

8. 6.7 si31_2001 Aluminium and Bronze

9. 6.8 si31_2001 Fresnel Equation As  increases from 0... F  = F 0 + ( 1 - cos  ) 5 ( 1 - F 0 ) – so, as  increases, then F  increases until F 90 = 1 (independent of  ) n This means that when light is tangential to the surface: – full reflectance, independent of  – reflected colour independent of the material n Thus reflectance does depend on angle of incidence

10. 6.9 si31_2001 In Reality... n In reality, surfaces are not perfect mirrors n A physically based approach models the surface as microfacets n Each microfacet is a perfect reflecting surface, ie a mirror, but oriented at an angle to the average surface normal cross-section through the microfaceted surface average surface normal (N)

11. 6.10 si31_2001 Specular Reflection from Microfaceted Surface n The specular reflectance from this surface depends on three factors: – the number of facets oriented correctly to the viewer (remember facets are mirrors) – incident light may be shadowed, or reflected light may be masked – Fresnel’s reflectance equations predict colour change depending on angle of incidence

12. 6.11 si31_2001 Orientation of Facets n Only a certain proportion (D) of facets will be correctly aligned with the viewer Cook and Torrance give formula for D in terms of: - angle of viewer - average roughness H eye light

13. 6.12 si31_2001 Orientation of Facets n The distribution of facets is modelled as: D(  ) = (1/4m 2 cos 4 (  )) exp(-(tan(  )/m) 2 ) where  is angle between facet and average normal n. m gives a measure of roughness of surface D has maximum - where? N  H N microfacet Overall effect from many microfacets

14. 6.13 si31_2001 Shadowing and Masking n Light can be fully reflected n Some reflected light may hit other facets (masking) n Some incident light may never reach a facet (shadowing) Cook and Torrance give formula for G, fraction of reflected light, depending on angle of incidence and angle of view

15. 6.14 si31_2001 Shadowing and Masking Formulae n Masking: – G m = 2(N.H)(N.L) / (H.L) n Shadowing: – G s = 2(N.H)(N.V) / (H.L) Then, overall, we define G = min {1, G m, G s }

16. 6.15 si31_2001 Specular Term n This leads to: R s ( ) = F(  ) D G / (N.V) where: D = proportion of microfacets correctly aligned G = fraction of light shadowed or masked F = Fresnel factor N.V adjusts for facets visible to viewer n In practice, R s is calculated for red, green, blue n Note it depends on angle of incidence and angle of view

17. 6.16 si31_2001 Cook and Torrance Reflection Model n The specular term is calculated as described and combined with a uniform diffuse term: – Reflection (angle of incidence, viewing angle) = s R s + d R d (where s + d = 1) – Known as bi-directional reflectance n For metals: d = 0, s = 1 n For shiny plastics: d = 0.9, s = 0.1 n Further reading: Watt (3rd ed) Chap 7; Foley et al, Ch 16

18. 6.17 si31_2001 Aluminium

19. 6.18 si31_2001 Bronze

20. 6.19 si31_2001 Chrome

21. 6.20 si31_2001 Stainless Steel

22. 6.21 si31_2001 Phong Movie

23. 6.22 si31_2001 Physically Based Movie