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)
Mcrfacet scatterng mdels Rugh delectrc surface smth at wavelength scale rugh at mcrscale flat at macrscale mcrsurface macrsurface ar delectrc
Mcrfacet scatterng mdels Incdent rradance E llumnates macrsurface area da frm drectn. da
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.
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
half-vectr functn h(, ) nrmal dstrbutn D(m) shadwng maskng G(,, m) attenuatn (, )
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(, )
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Cnstructn f half-vectr reflectn refractn m + parallel t m
Cnstructn f half-vectr reflectn refractn h r = nrmalze( + ) m + parallel t m
Cnstructn f half-vectr reflectn refractn h r = nrmalze( + ) m m + parallel t m
Cnstructn f half-vectr reflectn refractn h r = nrmalze( + ) m m + parallel t m n + n parallel t m
Cnstructn f half-vectr reflectn refractn h r = nrmalze( + ) h t = nrmalze( + n) m m + parallel t m n + n parallel t m
Cnstructn f half-vectr sld angle reflectn refractn h r = nrmalze( + ) h t = nrmalze( + n) d
Cnstructn f half-vectr sld angle reflectn refractn h r = nrmalze( + ) h t = nrmalze( + n) d
Cnstructn f half-vectr sld angle reflectn refractn h r = nrmalze( + ) h t = nrmalze( + n) d d
Cnstructn f half-vectr sld angle reflectn refractn h r = nrmalze( + ) h t = nrmalze( + n) d h r d
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
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
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
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
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
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
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
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
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
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
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
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
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
Fresnel reflectance Glassner, Prncples f Dgtal Image Synthess
Fresnel reflectance Glassner, Prncples f Dgtal Image Synthess
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 40 20 20 40 D( m )
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 40 20 20 40 D( m )
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) 40 20 20 40 D( m )
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) 1 40 20 20 40 90 90 D( m ) G 1 (, )