Computer Graphics. - Shading - Hendrik Lensch. Computer Graphics WS07/08 Light Transport

Transcription

1 Compute Gaphics - Shading - Hendik Lensch Compute Gaphics WS07/08 Light Tanspot

2 Oveview So fa Nuts and bolts of ay tacing Today Reflectance Reflection models Compute Gaphics WS07/08 Light Tanspot

3 Mateial Samples diffuse glossy mio Compute Gaphics WS07/08 Light Tanspot

4 Mateial Samples diffuse glossy mio Compute Gaphics WS07/08 Light Tanspot

5 Mateial Samples anisotopic Compute Gaphics WS07/08 Light Tanspot

6 Mateial Samples tanslucent Compute Gaphics WS07/08 Light Tanspot

7 Mateial Samples tanslucent Compute Gaphics WS07/08 Light Tanspot

8 Mateial Samples complex suface stuctue Compute Gaphics WS07/08 Light Tanspot

9 Mateial Samples fibes Compute Gaphics WS07/08 Light Tanspot

10 How to descibe mateials? mechanical, chemical, electical popeties eflection popeties suface oughness geomety/meso-stuctue elightable epesentation of appeaance Compute Gaphics WS07/08 Light Tanspot

11 Gloss Model Compute Gaphics WS07/08 Light Tanspot

12 Reflection of an Opaque Suface ω o ωo n ω i t ωo s Compute Gaphics WS07/08 Light Tanspot

13 Reflection of an Opaque Suface ω o ωo ωo ω i Compute Gaphics WS07/08 Light Tanspot

14 BRDF 4D (bidiectional eflectance distibution function) f ( ω ω ) i o ω o ω i Compute Gaphics WS07/08 Light Tanspot

15 BRDF 4D (bidiectional eflectance distibution function) f dl( ) ( ω ω o i ω o) = de( ω ) atio of eflected adiance to incident iadiance i ω o ω i Compute Gaphics WS07/08 Light Tanspot

16 Spatially Vaying BRDF 6D heteogeneous mateials f ( ω ω ) i o ω o ω i x Compute Gaphics WS07/08 Light Tanspot

17 Spatially Vaying BRDF 6D heteogeneous mateials f fx; ω ω ) ( ( i o ω o ω i x Compute Gaphics WS07/08 Light Tanspot

18 Isotopic BRDF 3D invaiant with espect to otation about the nomal ω o ω i x Compute Gaphics WS07/08 Light Tanspot

19 Isotopic BRDF 3D invaiant with espect to otation about the nomal f ( ω i ωo) ω o ωi x Compute Gaphics WS07/08 Light Tanspot

20 Isotopic BRDF 3D invaiant with espect to otation about the nomal ff ( Δ θ, ϕ; ϕθ ) ( θ ), ϕ )) ( i i i oo o ω o ω i x Δϕ Compute Gaphics WS07/08 Light Tanspot

21 Subsuface Scatteing ω o ω i x oi Compute Gaphics WS07/08 Light Tanspot

22 BSSRDF 8D (bidiectional scatteing suface eflectance distibution function) ω f ( x, ω ) ( x, ω )) o ( i i o o ω i x o x i Compute Gaphics WS07/08 Light Tanspot

23 Subsuface Scatteing Homogeneous Mateial ω o ω i x o x i Compute Gaphics WS07/08 Light Tanspot

24 Homogeneous Mateial BSSRDF 6D f ( Δx x, ; ω) ( ωx ), ω )) f ( i i i o o ω o x o Δx x i ω i Compute Gaphics WS07/08 Light Tanspot

25 Genealization 12D f ( λ ;( x, ω i i ) ( xo, ωo) ) ω o ω i x o x i Compute Gaphics WS07/08 Light Tanspot

26 Genealization 12D f ( λ ;( x, ω i i ) ( xo, ωo) ) ω o ω i x o x i Compute Gaphics WS07/08 Light Tanspot

27 Genealization 12D f ( ) ( x, ω, λ i i i ) ( xo, ωo, λo ) fluoescence ω o ω i x o x i Compute Gaphics WS07/08 Light Tanspot

28 Genealization 12D f ( ) t; ( x, ω, λ i i i ) ( xo, ωo, λo ) time-vaying scenes ω o ω i x o x i Compute Gaphics WS07/08 Light Tanspot

29 Genealization 12D f ( ) ( x, ω i i, t, λ i i ) ( xo, ωo, to, λo ) diffeent path length ω o phosphoescence ω i x o x i Compute Gaphics WS07/08 Light Tanspot

30 What is necessay? Light souce position View point Suface nomal / local coodinate fame Reflectance model Compute Gaphics WS07/08 Light Tanspot

31 Light Souce Desciption Point light souce Position Intensity ω i Compute Gaphics WS07/08 Light Tanspot

32 Light Souce Desciption Point light souce Position Intensity ~ 1/^2 ω i Compute Gaphics WS07/08 Light Tanspot

33 Viewpoint Distance not so impotant fo now ω o ω i Compute Gaphics WS07/08 Light Tanspot

34 Suface Nomal Tivial fo a plane Hesse fom: ( p, n ) n Compute Gaphics WS07/08 Light Tanspot

35 Compute Gaphics WS07/08 Light Tanspot Suface Nomal - Tiangle Oientation? Use ight-hand ule. Nomals should point towads the outside of an object. n c a b ) ( ) ( ) ( ) ( b a b c b a b c n =

36 Suface Nomals Tiangle Mesh Pe-suface nomal Flat shading [wikipedia] Compute Gaphics WS07/08 Light Tanspot

37 Suface Nomals Tiangle Mesh Pe-vetex nomal Compute Gaphics WS07/08 Light Tanspot

38 Suface Nomals Tiangle Mesh Pe-vetex nomal Goaud shading L ~ f ( ω, n, ω ) L linea intepolation of the shaded colos x o x i i Lp = λ La + 2Lb + 3 λ λ 1 a c p b L c [wikipedia] Compute Gaphics WS07/08 Light Tanspot

39 Compute Gaphics WS07/08 Light Tanspot Suface Nomals Tiangle Mesh Pe-vetex nomal Phong shading linea intepolation of the suface nomal [wikipedia] c a b p c b a c b a p n n n n n n n λ λ λ λ λ λ = i i p o p L n f L ),, ( ~ ω ω

40 Compute Gaphics WS07/08 Light Tanspot Suface Nomals Tiangle Mesh Pe-vetex nomal Phong shading linea intepolation of the suface nomal spheical intepolation [wikipedia] c a b p c b a c b a p n n n n n n n λ λ λ λ λ λ = i i p o p L n f L ),, ( ~ ω ω

41 Phong Reflection Model Cosine powe lobe f ( ω, x, ω ) o i s k ( R( I V ) e = k ) L,s = L i k s cos ke θ RV Dot poduct & powe Not enegy conseving/ecipocal Plastic-like appeaance I N θ HN H R(I) θ RV I R(V) N R(I) V H V Compute Gaphics WS07/08 Light Tanspot

42 Phong Exponent k e f ( ω, x, ω ) Detemines size of highlight o i s k ( R( I V ) e = k ) Compute Gaphics WS07/08 Light Tanspot

43 Blinn-Phong Reflection Model Blinn-Phong eflection model f ( ω, x, ω ) o i = k s k ( H N ) e L,s = L i k s cos ke θ HN θ RV θ HN Light souce, viewe fa away I, R constant: H constant θ HN less expensive to compute I N θ HN H R(I) θ RV I R(V) N R(I) V H V Compute Gaphics WS07/08 Light Tanspot

44 Compute Gaphics WS07/08 Light Tanspot Phong Illumination Model Extended light souces: l point light souces Colo of specula eflection equal to light souce Heuistic model Contadicts physics Puely local illumination Only diect light fom the light souces No futhe eflection on othe sufaces Constant ambient tem Often: light souces & viewe assumed to be fa away (Blinn) ) ( ) ( L (Phong) ) ) ( ( ) ( L,, + + = + + = l k l l l s l l d a i a l k l l l s l l d a i a e e N H L k N I L k L k V I R L k N I L k L k

45 Multiple Light Souces Add thei contibutions ω o ω i Compute Gaphics WS07/08 Light Tanspot

46 Occlusions The point on the suface might be in shadow fom some object Tace ay to light souce and test fo occlusion ω o ω i Compute Gaphics WS07/08 Light Tanspot

47 Aea Light souces Typically appoximated by sampling ω o ω i Compute Gaphics WS07/08 Light Tanspot

48 Aea Light souces Typically appoximated by sampling ω o ω i Compute Gaphics WS07/08 Light Tanspot