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1GR2-00 GR2 Advanced Computer Graphics AGR Lecture 6 Physically Based Reflection Model

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2GR2-00 Phong Reflection Objects tend to have plastic appearance

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3GR2-00 Phong Model - Limitations Whats 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

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4GR2-00 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

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5GR2-00 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

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6GR2-00 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

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7GR2-00 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

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8GR2-00 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

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9GR2-00 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 – Fresnels reflectance equations predict colour change depending on angle of incidence

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10GR2-00 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

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11GR2-00 Shadowing and Masking n Light can be fully reflected n Some reflected light may hit other facets n Some incident light may never reach a facet Cook and Torrance give formula for G, fraction of reflected light, depending on angle of incidence and angle of view

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12GR2-00 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

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13GR2-00 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

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14GR2-00 Aluminium

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15GR2-00 Bronze

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16GR2-00 Chrome

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17GR2-00 Stainless Steel

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18GR2-00 Phong Movie

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19GR2-00 Physically Based Movie

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1 Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009 Shading I.

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