Microfacet models for reflection and refraction
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1 Mcrfacet mdels fr reflectn and refractn Steve Marschner Crnell Unversty CS 5625 Sprng 2016 (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. d 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. d 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 h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn (, )
7 half-vectr functn h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn (, ) Gves the ne mcrsurface nrmal m that wll scatter lght frm t. m = h(, )
8 half-vectr functn h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn (, ) Gves the ne mcrsurface nrmal m that wll scatter lght frm t. d m d The sze f the set f relevant nrmals dω m relatve t the recevng sld angle dω s determned by h. d
9 half-vectr functn h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn (, ) Measures densty f mcrsurface area wth respect t mcrsurface nrmal. m da
10 half-vectr functn h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn (, ) Measures densty f mcrsurface area wth respect t mcrsurface nrmal. m da
11 half-vectr functn h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn (, ) Measures densty f mcrsurface area wth respect t mcrsurface nrmal. d 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) d m da
12 half-vectr functn h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn (, ) Measures the fractn f pnts wth mcrsurface nrmal m that are vsble n drectns and. da m = D(m) d m da
13 half-vectr functn h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn (, ) Measures the fractn f pnts wth mcrsurface nrmal m that are vsble n drectns and. da m = D(m) d m da
14 half-vectr functn h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn (, ) Measures the fractn f pnts wth mcrsurface nrmal m that are vsble n drectns and. da m = D(m) G(,, m) d m da
15 half-vectr functn h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn (, ) 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) d m da
16 half-vectr functn h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn (, ) Gves the fractn f the pwer ncdent n the scatterng area da m that s scattered. d m = m n (, ) da m de da m = D(m) G(,, m) d m da
17 half-vectr functn h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn (, ) Gves the fractn f the pwer ncdent n the scatterng area da m that s scattered. Ths scattered pwer s related t the ncdent rradance by the attenuatn and the scatterng area, prjected n the ncdent drectn. d m = m n (, ) da m de da m = D(m) G(,, m) d m da
18 half-vectr functn h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn (, ) The BSDF s the rat f scattered radance t ncdent rradance: f s (, ) = dl de = d m /(da n d ) de d m = m n (, ) da m de da m = D(m) G(,, m) d m da
19 half-vectr functn h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn (, ) The BSDF s the rat f scattered radance t ncdent rradance: f s (, ) = m n n (, ) D(m) G(,, m) d m d d m = m n (, ) da m de da m = D(m) G(,, m) d m da
20 half-vectr functn h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn (, ) f s (, ) = m n n (, ) D(m) G(,, m) d m d
21 half-vectr functn h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn (, ) Fresnel reflectn f s (, ) = m n n (, ) D(m) G(,, m) d m d
22 half-vectr functn h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn (, ) Fresnel reflectn surface rughness f s (, ) = m n n (, ) D(m) G(,, m) d m d
23 half-vectr functn h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn (, ) Fresnel reflectn surface rughness f s (, ) = m n n (, ) D(m) G(,, m) d m d 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 refractn h r = nrmalze( + ) h t = nrmalze( + n) m m + parallel t m n + n parallel t m
29 Cnstructn f half-vectr sld angle reflectn refractn h r = nrmalze( + ) h t = nrmalze( + n) d
30 Cnstructn f half-vectr sld angle reflectn refractn h r = nrmalze( + ) h t = nrmalze( + n) d
31 Cnstructn f half-vectr sld angle reflectn refractn h r = nrmalze( + ) h t = nrmalze( + n) d d
32 Cnstructn f half-vectr sld angle reflectn refractn h r = nrmalze( + ) h t = nrmalze( + n) d h r d
33 Cnstructn f half-vectr sld angle reflectn refractn h r = nrmalze( + ) h t = nrmalze( + n) d h r d m d d m = h r + 2 d
34 Cnstructn f half-vectr sld angle reflectn refractn h r = nrmalze( + ) h t = nrmalze( + n) d d m h r d d d m = h r + 2 d
35 Cnstructn f half-vectr sld angle reflectn refractn h r = nrmalze( + ) h t = nrmalze( + n) d d m h r d n d d m = h r + 2 d
36 Cnstructn f half-vectr sld angle reflectn refractn h r = nrmalze( + ) h t = nrmalze( + n) d d m h r d n n 2 d d d m = h r + 2 d
37 Cnstructn f half-vectr sld angle reflectn refractn h r = nrmalze( + ) h t = nrmalze( + n) d d m h r d n h t n 2 d d d m = h r + 2 d
38 Cnstructn f half-vectr sld angle reflectn refractn h r = nrmalze( + ) h t = nrmalze( + n) d d m h r d n d m h t n 2 d d d m = h r + 2 d d m = h t + n 2 n2 d
39 Result: scatterng functns reflectn f s (, ) = m n n (, ) D(m) G(,, m) d m d transmssn f s (, ) = m n n (, ) D(m) G(,, m) d m d
40 Result: scatterng functns reflectn f r (, ) = m n n F (, m) D(m) G(,, m) m + 2 transmssn f s (, ) = m n n (, ) D(m) G(,, m) d m d
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( 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( 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( 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( m ) G 1 (, )
Microfacet models for reflection and refraction
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) Mcrfacet scatterng mdels Rugh delectrc surface
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