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Advancements in Physically Based Reflection Models: From Phong to Cook-Torrance

This lecture explores the limitations of the Phong reflection model, highlighting its reliance on common sense rather than physics, particularly in regard to specular reflection. It introduces the Cook-Torrance model, a physically based approach that offers a more accurate representation of specular highlights by considering the Fresnel equation, microfacet surfaces, and factors like shadowing and masking. The lecture addresses how various materials and angles of incidence influence the reflectance and color of specular highlights, providing insights into more realistic rendering techniques in computer graphics.

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Advancements in Physically Based Reflection Models: From Phong to Cook-Torrance

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Presentation Transcript

  1. SI31Advanced Computer GraphicsAGR Lecture 6 Physically Based Reflection Model

  2. Phong Reflection Objects tend to have plastic appearance

  3. 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

  4. 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

  5. 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 

  6. 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

  7. Aluminium and Bronze

  8. 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

  9. 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)

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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}

  15. 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

  16. 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

  17. Aluminium

  18. Bronze

  19. Chrome

  20. Stainless Steel

  21. Phong Movie

  22. Physically Based Movie

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