Phong Model. Reflection Models

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Leo Potter
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1 Page 1 Reflecton Models Last lectue Reflecton models The eflecton equaton and the BRDF Ideal eflecton, efacton and dffuse Today Phong and mcofacet models Gaussan heght suface Self-shadowng Toance-Spaow model Ansotopc eflecton models Phong Model

2 Page Reflecton Geomety ˆL Ĥ ˆN ˆ ˆ ˆ L+ E H L ˆ + E ˆ Ê Rˆ ( ˆ ) N ˆ L ˆL Rˆ ( ˆ ) N ˆ E ˆN Rˆ ( ˆ ) N ˆ L Ĥ Ê cosθ ˆ ˆ L N cosθ ˆ ˆ E N cos θ Eˆ R ( Lˆ ) R ( Eˆ ) Lˆ s Nˆ cosθ ˆ ˆ g E L cosθ ˆ ˆ s H N Nˆ 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!

3 Page 3 Phong Model Mo Dffuse s Enegy nomalzaton Enegy nomalze Phong Model ( Lˆ R ˆ Nˆ E ) s ( H ) ( ) cos d H ( Nˆ ) ρ ω θ ω H ( Rˆ ) ( Lˆ R ( ˆ ) Nˆ E ) π 1 s cos θ dω s + H s dω

4 Page 4 Mcofacet Model Bougue s lttle faces P. Bougue, Teatse on Optcs, 1760

5 Page 5 Reflecton of the Sun fom the Sea Souce: Mnnaet, Lght and Colo n Outdoos, p. 8 α α Reflecton Angles L E γ δ δ Sde vew α β Assume L and E ae at the same heght h H P H α + β γ + δ β α δ h cosθ γ α θ β α

6 Page 6 Reflecton Angles L Font vew α b H P H b tanα h h cosθ b tanψ h tanα tanα cosθ Analyss on the Sphee ˆN R ( ˆ ) N ˆ L γ α ˆL γ α

7 Page 7 Sold Angle Dstbutons θ θ θ θ θ θ ϕ ϕ ω h θ θ dω snθ dθ dϕ ( sn ) d d ( ) θ θ ϕ snθ cosθ dθ dϕ 4cosθ dω dωh 1 dω 4cosθ h ω Mcofacet Dstbutons ˆL θ ˆN Ĥ θ Ê H Nomalzaton cos θ da( ω ) da h h Mcofacet H D( ω )cosθ dω 1 h h h da( ω ) dω D( ω ) dω da h h h h

8 Page 8 Mcofacet Dstbuton Functons Isotopc dstbutons Chaacteze by half-angle β Examples: Blnn ( ) 1 cosc 1 D α α D( ωh) D( α) 1 D( β ) c1 ln ln cos β Toance-Spaow ( ) c D α ( α ) e c β Towbdge-Retz c cos β 1 cos β 3 1 D c (1 ) cos α 1 3 3( α) c3 Toance-Spaow Model

9 Page 9 Toance-Spaow Model ˆL θ ˆN Ĥ dφ L( ω )cos θ dω da( ω ) h h L ( ω )cos θ dω D( ω ) dω da h h da( ω ) dω D( ω ) dω da h h h h cosθ cosθ Lˆ Nˆ Lˆ Hˆ dφ dl ( ω ω )cosθ dω da dφ dφ dl( ω ω)cosθ dω da L ( ω )cos θ dω D( ω ) dω da h h h Toance-Spaow Model dl ( ω ω )cosθ dω da L ( ω )cos θ dω D( ω ) dω da h h ˆL ˆN Ĥ dω dω dl( ω ω) f( ω ω) de ( ω ) Ê L( ω)cos θ dω D( ω ) dω da ( cos θ dωda)( L( ω)cos θ dω ) D( ωh) dωh cosθ cosθ cosθ dω D( ωh) 4cosθ cosθ h h

10 Page 10 Self-Shadowng Shadows on Rough Sufaces Wthout self-shadowng Wth self-shadowng

11 Page 11 Gaussan Rough Suface Gaussan dstbuton of heghts pz () Gaussan dstbuton of slopes D( α) Beckmann 1 πσ πm z e σ 1 cos e α z tan α m θ τ m σ σ τ x Self-Shadowng Functon z θ σ Pobablty of shadowng ( µ m) 1 1 efc / S( θ ) 1 +Λ( µ ) ( m ) m /m ( ) e µ Λ µ efc µ / π µ τ x

12 Page 1 Self-Shadowng Functon Wm Fom Smth, 1967 Self-Consstency Condton S( θ ) D( α)cosθ dω α cosθ The sum of the aeas of the llumnated suface pojected onto the plane nomal to the decton of ncdence s ndependent of the oughness of the suface, and equal to the pojected aea of the undelyng mean plane.

13 Page 13 Toance-Spaow Expements f ( ω ω ) F( θ ) S( θ) S( θ) D( α) 4cosθ cosθ Ansotopc Reflecton Model

14 Page 14 Ansotopc Reflecton Quatehose

15 Page 15 Reflecton fom a Cylnde ˆT ˆΝ Reflecton fom a Cylnde ˆT ˆΝ

16 Page 16 Reflecton fom a Cylnde ˆT ˆL ˆN R ( ˆ ) N ˆ L Reflecton fom a Cylnde ˆT ˆL ˆN R ( ˆ ) N ˆ L

17 Page 17 Reflecton fom a Cylnde ˆT ˆL R ( ˆ ) N ˆ L Ansotopc Reflecton

18 Page 18 Shape of Ansotopc Hghlghts Fbes tangent to the plane defned by the halfway vecto eflect lght Fom Lu, Koendenk, Kappes Shape of Ansotopc Hghlghts Fom Lu, Koendenk, Kappes

19 Page 19 Kay-Kajya Model ˆT Dffuse ˆL sn 1 L Specula ( Tˆ Lˆ) θ R ( ˆ ) N ˆ L ( θ θ ) ( θ θ + θ θ ) s cos cos cos sn sn Ê E L E L E L s Hebet

20 Page 0 Ha Model Black Ha Bown Ha Self-Shadowng V-Goove Model

21 Page 1 Self-Shadowng: V-Goove Model Assumptons (Toance-Spaow) 1. Symmetc, longtudnal, sotopcallydstbuted G mn( Ga, Gb, Gc). Uppe edges le n plane G 1 a G b G c ( Nˆ Hˆ )( Nˆ Eˆ) ( Hˆ Eˆ) ( Nˆ Hˆ )( Nˆ Lˆ) ( Hˆ Lˆ) Self-Shadowng: V-Goove Model α θ m ψ ψ sn m sn l+ ψ sn lcos ψ + cos lsn ψ cosθ cos ψ + snθ sn ψ cos θ (1 sn ψ) + snθ cosψ snψ cos θ (1 cos α) + snθ cosαsnα cosθ cosα cosαcosθ snαsnθ cosθ cosαcos α + θ cosθ cosαcosθ ˆ E ˆ N ˆ H ˆ N ˆ E ˆ H ( )( ) ( ) ( ) l sn l cosθ m sn m cosl snθ l sn l snψ cosα cosψ snα m G 1 l sn m 1 sn l Hˆ Eˆ Hˆ Eˆ + ( Nˆ Hˆ )( Nˆ Eˆ) Hˆ Eˆ ( Nˆ Hˆ )( Nˆ Eˆ) Hˆ Eˆ

CS348B Lecture 10 Pat Hanrahan, Spring 2004

CS348B Lecture 10 Pat Hanrahan, Spring 2004 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