CS348B Lecture 10 Pat Hanrahan, Spring 2004

Transcription

1 Page 1 Reflecton Models I Today Types of eflecton models The BRDF and eflectance The eflecton equaton Ideal eflecton and efacton Fesnel effect Ideal dffuse Next lectue Glossy and specula eflecton models Rough sufaces and mcofacets Self-shadowng Ansotopc eflecton models Reflecton Models Defnton: Reflecton s the pocess by whch lght ncdent on a suface nteacts wth the suface such that t leaves on the ncdent sde wthout change n fequency. Popetes Specta and Colo [Moon Specta] Polazaton Dectonal dstbuton Theoes Phenomenologcal Physcal

2 Page Types of Reflecton Functons Ideal Specula Reflecton Law Mo Ideal Dffuse Lambet s Law Matte Specula Glossy Dectonal dffuse Mateals Plastc Metal Matte Fom Apodaca and Gtz, Advanced RendeMan

3 Page 3 The Reflecton Equaton L(, xω L(, xω ˆN θ θ dω φ φ L ( x, ω = f ( x, ω ω L( x, ω cosθ dω H The BRDF Bdectonal Reflectance-Dstbuton Functon dl (, x ω ˆN θ L(, xω θ dω φ φ dl( ω ω 1 f( ω ω de s

4 Page 4 The BSSRDF Bdectonal Suface Scatteng Reflectance- Dstbuton Functon L(, xω ˆN dl(, x ω θ θ dω x x φ φ Tanslucency dl( x, ω x, ω Sx (, ω x, ω dφ Gonoeflectomete

5 Page 5 Popetes of BRDF s 1. Lneaty Fom Sllon, Avo, Westn, Geenbeg. Recpocty pncple f ( ω ω = f ( ω ω Popetes of BRDF s 3. Isotopc vs. ansotopc f ( θ, ϕ ; θ, ϕ = f ( θ, θ, ϕ ϕ Recpocty and sotopy f ( θ, θ, ϕ ϕ = f ( θ, θ, ϕ ϕ = f ( θ, θ, ϕ ϕ 4. Enegy consevaton

6 Page 6 Enegy Consevaton L( ωcosθ dω dφ Ω = dφ L( ω cosθ dω = Ω Ω Ω 1 f ( ω ω L( ω cosθ dω cosθ dω Ω L( ω cosθ dω Ω Ω The Reflectance Defnton: Reflectance s ato of eflected to ncdent powe Ω Ω ρ( Ω Ω Ω Ω Ω Ω Consevaton of enegy: 0 < ρ < 1 3 by 3 set of possbltes: Unts: ρ [dmensonless], f [1/steadans] f ( ω ω cosθ dω cosθ dω cosθ dω f ( ω ω L( ω cosθ dω cosθ dω L( ω cosθ dω Ω Ω { dω, Ω, H } { dω, Ω, H}

7 Page 7 Law of Reflecton Î θ Nˆ θ Rˆ ϕ ϕ θ = θ ϕ = ( ϕ + πmod π Rˆ + ( Iˆ = cosθ Nˆ = ( Iˆ NN ˆ ˆ Rˆ = Iˆ ( Iˆ NN ˆ ˆ Ideal Reflecton (Mo L( θ, ϕ L( θ, ϕ θ θ Lm, ( θ, ϕ = L( θ, ϕ± π f δ (cosθ cos θ ( θ, ϕ ; θ, ϕ = δ( ϕ ϕ ± π m, cosθ L ( θ, ϕ = f ( θ, ϕ ; θ, ϕ L( θ, ϕ cosθ dcosθ dϕ, m, m δ(cosθ cos θ = δ ( ϕ ϕ ± π L( θ, ϕ cos θ dcos θ d ϕ cosθ = L ( θ, ϕ ± π

8 Page 8 Snell s Law Î ˆN θ ϕ ϕt θ t ˆT ϕ = ϕ ± π t n snθ = n snθ t t n Nˆ Iˆ = n Nˆ Tˆ t Law of Refacton ˆN Î µ = n / n θ t θ t ˆT Total ntenal eflecton: ( I N 1 µ (1 ˆ ˆ < 0 Nˆ Tˆ = µ Nˆ Iˆ Nˆ ( Tˆ µ Iˆ = 0 Tˆ = µ Iˆ+ γ Nˆ ˆ ˆ ˆ T = 1= µ + γ + µγ I N { 1 ( 1 ( } 1 { } γ = µ Iˆ Nˆ ± µ Iˆ Nˆ = µ cosθ ± 1 µ sn θ = µ cosθ ± cosθ = µ cosθ cosθ t t γ = µ 1 1

9 Page 9 Optcal Manhole Total ntenal eflecton 4 n w = 3 Fom Lvngston and Lynch Fesnel Reflectance Metal (Alumnum Delectc (N=1.5 Gold Slve F(0=0.8 F(0=0.95 Glass n=1.5 F(0=0.04 Damond n=.4 F(0= Schlck Appoxmaton F( θ = F(0 + (1 F(0(1 cos θ

10 Page 10 Expement Reflectons fom a shny floo Fom Lafotune, Foo, Toance, Geenbeg, SIGGRAPH 97 Cook-Toance Model fo Metals Reflectance of Coppe as a functon of wavelength and angle of ncdence Lght specta Measued Reflectance ρ Appoxmated Reflectance π θ Coppe specta Cook-Toance appoxmaton F( θ F(0 R = R(0 + R( π / λ F( π / F(0

11 Page 11 Ideal Dffuse Reflecton Assume lght s equally lkely to be eflected n any output decton (ndependent of nput decton. L ( ω = f L( ω cosθ dω fd, = c d, d, = f L( ω cosθ dω = d, f d, M = L ( ω cosθ dω = L cosθ dω = πl M π L π f d, E ρd ρd = = = = π f, d f, d = E E E π E Lambet s Cosne Law M = ρ E = ρ E cosθ d d s s Dffuse Reflecton Theoetcal Bougue - Specal mco-facet dstbuton Seelge - Subsuface eflecton Multple suface o subsuface eflectons Expemental Pessed magnesum oxde powde Almost neve vald at hgh angles of ncdence Pant manufactues attempt to ceate deal dffuse

12 Page 1 Phong Model R(L E N E N R(E L L ( Eˆ R Lˆ Recpocty: ( s ( Lˆ R Eˆ ( ˆ ( ˆ s E R L = ( Lˆ R ( Eˆ s ( s Dstbuted lght souce! Phong Model Mo Dffuse s

13 Page 13 Popetes of the Phong Model Enegy nomalze Phong Model H ( Rˆ H ( Lˆ R Eˆ s ( H = ( cos d H ( Nˆ ρ ω θ ω ( Lˆ R ( Eˆ s π cos θ dω = s + 1 s dω