Reflection models. Rendering equation. Taxonomy 2. Taxonomy 1. Digital Image Synthesis Yung-Yu Chuang 11/01/2005

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1 Rederg equato Reflecto models Dgtal Image Sythess Yug-Yu Chuag 11/01/005 wth sldes by Pat Haraha ad Matt Pharr Taxoomy 1 ( xyt,,, θ, φλ, ) ( xyt,,, θφλ,, ) Geeral fucto = 1D Scatterg fucto = 9D out Assume tme does t matter (o phosphorescece) Assume wavelegths are equal (o fluorescece) Assume wavelegth s dscretzed or tegrated to RGB (Ths s a commo assumpto for computer graphcs) Sgle-wavelegth Scatterg fucto = 8D ( xy,, θ, φ) ( xy,, θ, φ) out Taxoomy ( xy,, θ, φ) ( xy,, θ, φ) out Sgle-wavelegth Scatterg fucto = 8D Igore subsurface scatterg (x,y) = (x,y) out Bdrectoal Texture Fucto (BTF) Spatally-varyg BRDF (SVBRDF) = 6D Igore drecto of cdet lght Lght Felds, Surface LFs = 4D ( xyθ,,, φ) out Assume Lamberta Texture Maps = D ( xy, ) out Igore depedece o posto Igore depedece o posto Bdrectoal Subsurface Scatterg Dstrbuto Fucto (BSSRDF) = 6D Igore subsurface scatterg BRDF = 4D ( θ, φ) ( θ, φ) 3D out Assume sotropy

2 Propertes of BRDFs Propertes of BRDFs Isotropc ad asotropc Reflecto models BRDF/BTDF/BSDF Scatterg from realstc surfaces s best descrbed as a mxture of multple BRDFs ad BSDFs. Materal = BSDF that combes multple BRDFs ad BSDFs. (chap. 10) Textures = reflecto ad trasmsso propertes that vary over the surface. (chap. 11)

3 Surface reflecto models Reflecto categores Measured data Pheomeologcal models: models wth tutve parameters Smulato Physcal optcs: solve Maxwell s equato Geometrc optcs: mcrofacet models dffuse perfect specular glossy specular retro-reflectve Geometrc settg BxDF BSDF_REFLECTION, BSDF_TRANSMISSION BSDF_DIFFUSE, BSDF_GLOSSY (retro-reflectve), BSDF_SPECULAR s Spectrum f(vector &wo, Vector &w); Spectrum Sample_f(Vector &wo, Vector *w, float u1, float u, float *pdf); t cosθ = ω, ωx cosφ =, sθ z sθ = 1 ω ω y sφ = sθ z Spectrum rho(vector &wo, t Samples, float *samples); Spectrum rho(t Samples, float *samples);

4 Specular reflecto ad trasmsso Reflecto: θ = θ o Trasmsso: η s θ = ηt sθt (Sell s law) dex of refracto dsperso Fresel reflectace Reflectvty ad trasmssveess are vew depedet For delectrcs θ θo θ θ t Fresel reflectace Perfect specular reflecto For coductors

5 Perfect specular trasmsso Fresel modulato Lamberta reflecto It s ot physcally feasble, but provdes a good approxmato to may real-world surfaces. class COREDLL Lamberta : publc BxDF { publc: Lamberta(Spectrum &reflectace) : BxDF(BxDFType(BSDF_REFLECTION BSDF_DIFFUSE)), R(reflectace), RoverPI(reflectace * INV_PI) {} Spectrum f(vector &wo, Vector &w) {retur RoverPI} Spectrum rho(vector &, t, float *) { retur R; } Spectrum rho(t, float *) { retur R; } prvate: Spectrum R, RoverPI; }; Mcrofacet models Rough surfaces ca be modeled as a collecto of small mcrofacets. Two compoets: dstrbuto of mcrofacets ad how lght scatters from dvdual mcrofacet closed-form BRDF expresso

6 Importat effects mcrofacet models Ore-Nayar model May real-world materals such as cocrete, sad ad cloth are ot Lamberta. A collecto of symmetrc V-shaped perfect Lamberta grooves wth a Gaussa dstrbuto Do t have a closed-form soluto, stead use the approxmato ρ fr ( ω, ωo) = ( A + B max(0, cos( φ φo))sα ta β ) π σ 0.45σ A = 1, B = ( σ ) σ α = max( θ, θ ), β = m( θ, θ ) o o Lamberta Ore-Nayer model

7 Torrace-Sparrow model Torrace-Sparrow model Oe of the frst mcrofacet models, desged to model metallc surfaces A collecto of perfectly smooth mrrored mcrofacets wth dstrbuto D( ωh) ω ω h θ θ ωo Bl mcrofacet dstrbuto Torrace-Sparrow wth Bl dstrbuto Dstrbuto of mcrofacet ormals s modeled by a expoetal falloff D ( ω ) ( ω ) h e + D ( ωh) = ( ωh ) π h e e

8 Asotropc mcrofacet model Asotropc mcrofacet model Ashkm ad Shrley have developed a mcrofacet model for asotropc surfaces D( ω ) = h ( e x + 1)( e y + 1)( ω ) h e cos φ s x + e y φ Lafortue model Lafortue model (for a measured clay) A effcet BRDF model to ft measured data to a parameterzed model wth a relatvely small umber of parameters f ( p, ω, ω ) r ρd = + π o = 1 ( ω ( ω o,, ω o,, ω o, )) o x x y y z z e