Microfacet models for reflection and refraction

Transcription

1 Mcrfacet mdels fr reflectn and refractn Steve Marschner Crnell Unversty CS 6630 Sprng 2012 (based n presentatn fr Walter, Marschner, L, and Trrance EGSR 07)

2 Mcrfacet scatterng mdels Rugh delectrc surface smth at wavelength scale rugh at mcrscale flat at macrscale mcrsurface macrsurface ar delectrc

3 Mcrfacet scatterng mdels Incdent rradance E llumnates macrsurface area da frm drectn. da

4 Mcrfacet scatterng mdels Incdent rradance E llumnates macrsurface area da frm drectn. dω Scattered radance L r r L t measured n drectn n sld angle dω.

5 Mcrfacet scatterng mdels Incdent rradance E llumnates macrsurface area da frm drectn. dω Scattered radance L r r L t measured n drectn n sld angle dω. f s (, ) = L r,t E Bdrectnal Scatterng Dstrbutn Functn

6 half-vectr functn nrmal dstrbutn shadwng maskng attenuatn h(, ) D(m) G(,, m) ρ(, )

7 half-vectr functn nrmal dstrbutn shadwng maskng attenuatn h(, ) D(m) G(,, m) ρ(, ) Gves the ne mcrsurface nrmal m that wll scatter lght frm t. m = h(, )

8 half-vectr functn nrmal dstrbutn shadwng maskng attenuatn h(, ) D(m) G(,, m) ρ(, ) Gves the ne mcrsurface nrmal m that wll scatter lght frm t. dω m dω The sze f the set f relevant nrmals dω m relatve t the recevng sld angle dω s determned by h. dω

9 half-vectr functn nrmal dstrbutn shadwng maskng attenuatn h(, ) D(m) G(,, m) ρ(, ) Measures densty f mcrsurface area wth respect t mcrsurface nrmal. m da

10 half-vectr functn nrmal dstrbutn shadwng maskng attenuatn h(, ) D(m) G(,, m) ρ(, ) Measures densty f mcrsurface area wth respect t mcrsurface nrmal. m da

11 half-vectr functn nrmal dstrbutn shadwng maskng attenuatn h(, ) D(m) G(,, m) ρ(, ) Measures densty f mcrsurface area wth respect t mcrsurface nrmal. dω m m The rat f relevant mcrsurface area da m t macrsurface area da s D(m)dω m. da m da da m = D(m) dω m da

12 half-vectr functn nrmal dstrbutn shadwng maskng attenuatn h(, ) D(m) G(,, m) ρ(, ) Measures the fractn f pnts wth mcrsurface nrmal m that are vsble n drectns and. da m = D(m) dω m da

13 half-vectr functn nrmal dstrbutn shadwng maskng attenuatn h(, ) D(m) G(,, m) ρ(, ) Measures the fractn f pnts wth mcrsurface nrmal m that are vsble n drectns and. da m = D(m) dω m da

14 half-vectr functn nrmal dstrbutn shadwng maskng attenuatn h(, ) D(m) G(,, m) ρ(, ) Measures the fractn f pnts wth mcrsurface nrmal m that are vsble n drectns and. da m = D(m) G(,, m) dω m da

15 half-vectr functn nrmal dstrbutn shadwng maskng attenuatn h(, ) D(m) G(,, m) ρ(, ) Measures the fractn f pnts wth mcrsurface nrmal m that are vsble n drectns and. We nw knw the sze f the scatterng area, whch determnes hw much lght reflects. da m = D(m) G(,, m) dω m da

16 half-vectr functn h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn ρ(, ) Gves the fractn f the pwer ncdent n the scatterng area da m that s scattered. Φ Φ Φ dφ m = m n ρ(, ) dam de da m = D(m) G(,, m) dω m da

17 half-vectr functn h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn ρ(, ) Gves the fractn f the pwer ncdent n the scatterng area da m that s scattered. Φ Φ Ths scattered pwer s related t the ncdent rradance by the attenuatn and the scatterng area, prjected n the ncdent drectn. Φ dφ m = m n ρ(, ) dam de da m = D(m) G(,, m) dω m da

18 half-vectr functn h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn ρ(, ) The BSDF s the rat f scattered radance t ncdent rradance: f s (, ) = dl de = dφm /(da n dω ) de dφ m = m n ρ(, ) dam de da m = D(m) G(,, m) dω m da

19 half-vectr functn h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn ρ(, ) The BSDF s the rat f scattered radance t ncdent rradance: f s (, ) = m n n ρ(, ) D(m) G(,, m) dω m dω dφ m = m n ρ(, ) dam de da m = D(m) G(,, m) dω m da

20 half-vectr functn nrmal dstrbutn shadwng maskng attenuatn h(, ) D(m) G(,, m) ρ(, ) f s (, ) = m n n ρ(, ) D(m) G(,, m) dω m dω

21 half-vectr functn nrmal dstrbutn shadwng maskng attenuatn h(, ) D(m) G(,, m) ρ(, ) Fresnel reflectn f s (, ) = m n n ρ(, ) D(m) G(,, m) dω m dω

22 half-vectr functn nrmal dstrbutn shadwng maskng attenuatn h(, ) D(m) G(,, m) ρ(, ) Fresnel reflectn surface rughness f s (, ) = m n n ρ(, ) D(m) G(,, m) dω m dω

23 half-vectr functn nrmal dstrbutn shadwng maskng attenuatn h(, ) D(m) G(,, m) ρ(, ) Fresnel reflectn surface rughness f s (, ) = m n n ρ(, ) D(m) G(,, m) dω m dω determned by gemetry

24 Cnstructn f half-vectr reflectn refractn m + parallel t m

25 Cnstructn f half-vectr reflectn refractn h r = nrmalze( + ) m + parallel t m

26 Cnstructn f half-vectr reflectn refractn h r = nrmalze( + ) m m + parallel t m

27 Cnstructn f half-vectr reflectn refractn h r = nrmalze( + ) m m + parallel t m n + n parallel t m

28 Cnstructn f half-vectr reflectn h r = nrmalze( + ) refractn h t = nrmalze( + n) m m + parallel t m n + n parallel t m

29 Cnstructn f half-vectr sld angle reflectn h r = nrmalze( + ) refractn h t = nrmalze( + n) dω

30 Cnstructn f half-vectr sld angle reflectn h r = nrmalze( + ) refractn h t = nrmalze( + n) dω

31 Cnstructn f half-vectr sld angle reflectn h r = nrmalze( + ) refractn h t = nrmalze( + n) dω dω

32 Cnstructn f half-vectr sld angle reflectn h r = nrmalze( + ) refractn h t = nrmalze( + n) dω h r dω

33 Cnstructn f half-vectr sld angle reflectn h r = nrmalze( + ) refractn h t = nrmalze( + n) dω h r dω m dω dω m = h r + 2 dω

34 Cnstructn f half-vectr sld angle reflectn h r = nrmalze( + ) refractn h t = nrmalze( + n) dω dω m h r dω dω dω m = h r + 2 dω

35 Cnstructn f half-vectr sld angle reflectn h r = nrmalze( + ) refractn h t = nrmalze( + n) h r dω dω m dω n dω dω m = h r + 2 dω

36 Cnstructn f half-vectr sld angle reflectn h r = nrmalze( + ) refractn h t = nrmalze( + n) h r dω dω m dω n n 2 dω dω dω m = h r + 2 dω

37 Cnstructn f half-vectr sld angle reflectn h r = nrmalze( + ) refractn h t = nrmalze( + n) h r dω dω m dω n h t n 2 dω dω dω m = h r + 2 dω

38 Cnstructn f half-vectr sld angle reflectn h r = nrmalze( + ) refractn h t = nrmalze( + n) h r dω dω m dω n dω m h t n 2 dω dω dω m = h r + 2 dω dω m = h t + n 2 n2 dω

39 Result: scatterng functns reflectn f s (, ) = m n n ρ(, ) D(m) G(,, m) dω m dω transmssn f s (, ) = m n n ρ(, ) D(m) G(,, m) dω m dω

40 Result: scatterng functns reflectn f r (, ) = m n n F (, m) D(m) G(,, m) m + 2 transmssn f s (, ) = m n n ρ(, ) D(m) G(,, m) dω m dω

41 Result: scatterng functns reflectn f r (, ) = m n n F (, m) D(m) G(,, m) m + 2 transmssn f t (, ) = m n n (1 F (, m)) D(m) G(,, m) n2 m + n 2

42 Result: scatterng functns reflectn f r (, ) = m m n n F (, m) D(m) G(,, m) + 2 transmssn f t (, ) = m n n (1 F (, m)) D(m) G(,, m) n2 m + n 2

43 Result: scatterng functns reflectn f r (, ) = m m n n F (, m) D(m) G(,, m) + 2 transmssn f t (, ) = m m n n n 2 (1 F (, m)) D(m) G(,, m) + n 2

44 Result: scatterng functns reflectn f r (, ) = 1 n n F (, m) D(m) G(,, m) 4 transmssn f t (, ) = m m n n n 2 (1 F (, m)) D(m) G(,, m) + n 2

45 Result: scatterng functns reflectn f r (, ) = F (, m) D(m) G(,, m) 4 n n transmssn f t (, ) = m m n n n 2 (1 F (, m)) D(m) G(,, m) + n 2

46 Fresnel reflectance Glassner, Prncples f Dgtal Image Synthess

47 Fresnel reflectance Glassner, Prncples f Dgtal Image Synthess

48 Nrmal dstrbutns Chce f dstrbutn s determned by surface Phng, Beckman are ppular chces GGX dstrbutn s anther ptn [Smth 67] gves a way t prduce smth Gs 8 Phng D(θ m )

49 Nrmal dstrbutns Chce f dstrbutn s determned by surface Phng, Beckman are ppular chces GGX dstrbutn s anther ptn [Smth 67] gves a way t prduce smth Gs 8 Phng Beckman D(θ m )

50 Nrmal dstrbutns Chce f dstrbutn s determned by surface Phng, Beckman are ppular chces GGX dstrbutn s anther ptn [Smth 67] gves a way t prduce smth Gs 8 Phng Beckman GGX (new) D(θ m )

51 Nrmal dstrbutns Chce f dstrbutn s determned by surface Phng, Beckman are ppular chces GGX dstrbutn s anther ptn [Smth 67] gves a way t prduce smth Gs 8 Phng Beckman GGX (new) D(θ m ) G 1 (θ, )