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SI31 Advanced Computer Graphics AGR. Lecture 6 Physically Based Reflection Model. Phong Reflection. Objects tend to have plastic appearance. Phong Model - Limitations What’s Wrong with Phong. The Phong model is based more on common sense than physics
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SI31Advanced Computer GraphicsAGR Lecture 6 Physically Based Reflection Model
Phong Reflection Objects tend to have plastic appearance
Phong Model - LimitationsWhat’s Wrong with Phong • The Phong model is based more on common sense than physics • 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
Physically Based Model • Cook and Torrance have proposed an alternative model which has a basis in physics and which more accurately represents specular highlights • Diffuse reflection handled as in Phong model • Start by assuming perfectly smooth surface, ie mirror type surface
Fresnel Equation N reflected In general, light is partly reflected, partly refracted Reflectance = fraction reflected f refracted Refractive Index: = sin / sin f [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
Fresnel Equation • Reflectance, F, is a minimum for incident light normal to the surface, ie = 0 : F0 = ( - 1 )2 / ( + 1 )2 • So different F0 for different materials • Because the refractive index of a material depends on the wavelength of light, , so we also have different F0 for different wavelengths • burnished copper has roughly: F0,blue = 0.1, F0,green = 0.2, F0,red = 0.5 • Thus colour of specular reflection does depend on material
Fresnel Equation • As increases from 0 ... F = F0 + ( 1 - cos )5 ( 1 - F0 ) • so, as increases, then F increases until F90 = 1 (independent of ) • This means that when light is tangential to the surface: • full reflectance, independent of • reflected colour independent of the material • Thus reflectance does depend on angle of incidence
In Reality... • In reality, surfaces are not perfect mirrors • A physically based approach models the surface as microfacets • 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)
Specular Reflection from Microfaceted Surface • 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
Orientation of Facets • Only a certain proportion (D) of facets will be correctly aligned with the viewer light H eye Cook and Torrance give formula for D in terms of: - angle of viewer - average roughness
The distribution of facets is modelled as: D(d) = (1/4m2cos4(d)) exp(-(tan(d)/m)2) where d is angle between facet and average normal n. m gives a measure of roughness of surface D has maximum - where? N H d microfacet N Orientation of Facets Overall effect from many microfacets
Shadowing and Masking • Light can be fully reflected • Some reflected light may hit other facets (masking) • 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
Masking: Gm = 2(N.H)(N.L) / (H.L) Shadowing: Gs = 2(N.H)(N.V) / (H.L) Shadowing and Masking Formulae Then, overall, we define G = min {1, Gm, Gs}
Specular Term • This leads to: Rs( ) = 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 • In practice, Rs is calculated for red, green, blue • Note it depends on angle of incidence and angle of view
Cook and Torrance Reflection Model • The specular term is calculated as described and combined with a uniform diffuse term: • Reflection (angle of incidence, viewing angle) = s Rs + d Rd (where s + d = 1) • Known as bi-directional reflectance • For metals: d = 0, s = 1 • For shiny plastics: d = 0.9, s = 0.1 • Further reading: Watt (3rd ed) Chap 7; Foley et al, Ch 16
