Microfacet models for refraction through rough surfaces

Transcription

1 Micrfacet mdels fr refractin thrugh rugh surfaces Bruce Walter Steve Marschner Hngsng Li Ken Trrance Crnell University Prgram f Cmputer Graphics

2 Diffuse transmissin

3 measured transmissin grund glass interface n =

4 measured transmissin grund glass interface n =

5 measured transmissin grund glass interface n =

6 measured transmissin grund glass interface n =

7 measured transmissin grund glass interface n =

8 measured transmissin grund glass interface n = critical angle 10

9 Prir wrk Micrfacet mdels in graphics Blinn 1977 intrduced Trrance-Sparrw mdel Ck & Trrance 1982 Trrance-Sparrw specular Ashikhmin et al micrfacet BRDF generatr Stam 2001 skin subsurface scattering mdel Wrk utside graphics we build n Smith 1967 shadwing masking framewrk Nee & Nee 2004 single-interface measurement idea

10 Cntributins Micrfacet transmissin mdel new gemetric frmulatin clean, simple generalizatin f reflectin Micrfacet distributin functins evaluate three chices against data new GGX distributin fits sme surfaces better Imprtance sampling Measurement and validatin single interface transmissin

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12 Micrfacet scattering mdels Assumptins rugh dielectric surface single scattering n m micrsurface macrsurface air dielectric

13 Micrfacet reflectin mdels Incident irradiance E i illuminates macrsurface area da frm directin i. i E i da

14 Micrfacet reflectin mdels Incident irradiance E i illuminates macrsurface area da frm directin i. i E i dω L r Reflected radiance L r measured at directin in slid angle dω. Bidirectinal Reflectance Distributin Functin: f r (i, ) = L r E i

15 Micrfacet reflectin mdels Incident irradiance E i illuminates macrsurface area da frm directin i. i E i Reflected radiance L r measured at directin in slid angle dω. dω L t Bidirectinal Reflectance Distributin Functin: f r (i, ) = L r Bidirectinal Transmittance Distributin Functin: f t (i, ) = L t E i E i

16 Reflectin t transmissin Traditinal micrfacet reflectin mdel: f r (i, ) = F (i, m) D(m) G(i,, m) 4 i n n

17 Reflectin t transmissin Traditinal micrfacet reflectin mdel: ptical gemetric f r (i, ) = F (i, m) D(m) G(i,, m) 4 i n n We generalize the gemetric analysis dealing with the surface area where scattering ccurs.

18 half-vectr functin h(i, ) nrmal distributin D(m) shadwing masking G(i,, m) i

19 half-vectr functin h(i, ) nrmal distributin D(m) shadwing masking G(i,, m) h gives the ne micrsurface nrmal m that will scatter light frm i t. i

20 half-vectr functin h(i, ) nrmal distributin D(m) shadwing masking G(i,, m) h gives the ne micrsurface nrmal m that will scatter light frm i t. selects m i m=h(i,)

21 half-vectr functin h(i, ) nrmal distributin D(m) shadwing masking G(i,, m) h gives the ne micrsurface nrmal m that will scatter light frm i t. selects m determines size f dω m i dω m m=h(i,) dω

22 half-vectr functin h(i, ) nrmal distributin D(m) shadwing masking G(i,, m) h gives the ne micrsurface nrmal m that will scatter light frm i t. i dω m m

23 half-vectr functin h(i, ) nrmal distributin D(m) shadwing masking G(i,, m) h gives the ne micrsurface nrmal m that will scatter light frm i t. D measures density f micrsurface area with respect t micrsurface nrmal m. i dω m m

24 half-vectr functin h(i, ) nrmal distributin D(m) shadwing masking G(i,, m) h gives the ne micrsurface nrmal m that will scatter light frm i t. D measures density f micrsurface area with respect t micrsurface nrmal m. i dω m m da m da da m = D(m) dω m da

25 half-vectr functin h(i, ) nrmal distributin D(m) shadwing masking G(i,, m) h gives the ne micrsurface nrmal m that will scatter light frm i t. D measures density f micrsurface area with respect t micrsurface nrmal m. G measures the fractin f pints with micrsurface nrmal m that are visible. i dω m m da m da da m = D(m) dω m da

26 half-vectr functin h(i, ) nrmal distributin D(m) shadwing masking G(i,, m) h gives the ne micrsurface nrmal m that will scatter light frm i t. D measures density f micrsurface area with respect t micrsurface nrmal m. G measures the fractin f pints with micrsurface nrmal m that are visible. i dω m m da m da da m = G(i,, m) D(m) dω m da

27 half-vectr functin h(i, ) nrmal distributin D(m) shadwing masking G(i,, m) Fr reflectin r transmissin: f s (i, ) = i m i n n ρ(i, ) da m da dω da m = G(i,, m) D(m) dω m da

28 half-vectr functin h(i, ) nrmal distributin D(m) shadwing masking G(i,, m) Fr reflectin r transmissin: f s (i, ) = i m i n n ρ(i, ) D(m) G(i,, m) dω m dω da m = G(i,, m) D(m) dω m da

29 half-vectr functin h(i, ) nrmal distributin D(m) shadwing masking G(i,, m) Fr reflectin r transmissin: easy t generalize f s (i, ) = i m i n n ρ(i, ) D(m) G(i,, m) dω m dω da m = G(i,, m) D(m) dω m da

30 half-vectr functin h(i, ) nrmal distributin D(m) shadwing masking G(i,, m) Fr reflectin r transmissin: easy t generalize f s (i, ) = i m i n n ρ(i, ) D(m) G(i,, m) dω m dω key cntributin da m = G(i,, m) D(m) dω m da

31 Cnstructin f half-vectr reflectin refractin m i i + parallel t m

32 Cnstructin f half-vectr reflectin refractin h r = nrmalize(i + ) m i i + parallel t m

33 Cnstructin f half-vectr reflectin refractin h r = nrmalize(i + ) m m i i i + parallel t m

34 Cnstructin f half-vectr reflectin refractin h r = nrmalize(i + ) m m i i i + parallel t m n i + n parallel t m

35 Cnstructin f half-vectr reflectin h r = nrmalize(i + ) refractin h t = nrmalize(i + n) m m i i i + parallel t m n i + n parallel t m

36 Cnstructin f half-vectr slid angle reflectin h r = nrmalize(i + ) refractin h t = nrmalize(i + n) dω i

37 Cnstructin f half-vectr slid angle reflectin h r = nrmalize(i + ) refractin h t = nrmalize(i + n) dω i

38 Cnstructin f half-vectr slid angle reflectin h r = nrmalize(i + ) refractin h t = nrmalize(i + n) dω dω i

39 Cnstructin f half-vectr slid angle reflectin h r = nrmalize(i + ) refractin h t = nrmalize(i + n) dω i h r dω

40 Cnstructin f half-vectr slid angle reflectin h r = nrmalize(i + ) refractin h t = nrmalize(i + n) dω i h r dω m dω dω m = h r i + 2 dω

41 Cnstructin f half-vectr slid angle reflectin h r = nrmalize(i + ) refractin h t = nrmalize(i + n) dω dω m i i h r dω dω dω m = h r i + 2 dω

42 Cnstructin f half-vectr slid angle reflectin h r = nrmalize(i + ) refractin h t = nrmalize(i + n) i h r dω dω m dω n i dω dω m = h r i + 2 dω

43 Cnstructin f half-vectr slid angle reflectin h r = nrmalize(i + ) refractin h t = nrmalize(i + n) i h r dω dω m dω n i n 2 dω dω dω m = h r i + 2 dω

44 Cnstructin f half-vectr slid angle reflectin h r = nrmalize(i + ) refractin h t = nrmalize(i + n) i h r dω dω m dω n i h t n 2 dω dω dω m = h r i + 2 dω

45 Cnstructin f half-vectr slid angle reflectin h r = nrmalize(i + ) refractin h t = nrmalize(i + n) i h r dω dω m dω n i dω m h t n 2 dω dω dω m = h r i + 2 dω dω m = h t i + n 2 n2 dω

46 Result: scattering functins reflectin f s (i, ) = i m i n n ρ(i, ) D(m) G(i,, m) dω m dω transmissin f s (i, ) = i m i n n ρ(i, ) D(m) G(i,, m) dω m dω

47 Result: scattering functins reflectin f r (i, ) = i h r i n n F (i, h r) D(h r ) G(i,, h r ) h r i + 2 transmissin f s (i, ) = i m i n n ρ(i, ) D(m) G(i,, m) dω m dω

48 Result: scattering functins reflectin f r (i, ) = i h r i n n F (i, h r) D(h r ) G(i,, h r ) h r i + 2 transmissin f t (i, ) = i h t i n n (1 F (i, h t)) D(h t ) G(i,, h t ) n2 h t i + n 2

49 Result: scattering functins reflectin f r (i, ) = i h r h r i n n F (i, h r ) D(h r ) G(i,, h r ) i + 2 transmissin f t (i, ) = i h t i n n (1 F (i, h t)) D(h t ) G(i,, h t ) n2 h t i + n 2

50 Result: scattering functins reflectin f r (i, ) = i h r h r i n n F (i, h r ) D(h r ) G(i,, h r ) i + 2 transmissin f t (i, ) = i h t h t i n n n 2 (1 F (i, h t )) D(h t ) G(i,, h t ) i + n 2

51 Result: scattering functins reflectin f r (i, ) = F (i, h r) D(h r ) G(i,, h r ) 4 i n n transmissin f t (i, ) = i h t h t i n n n 2 (1 F (i, h t )) D(h t ) G(i,, h t ) i + n 2

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53 Nrmal distributins Chice f distributin is determined by surface Phng describes same surfaces as Beckman new GGX distributin fits sme surfaces better analytical Smith shadwing masking 8 Phng D(θ m )

54 Nrmal distributins Chice f distributin is determined by surface Phng describes same surfaces as Beckman new GGX distributin fits sme surfaces better analytical Smith shadwing masking 8 Phng Beckman D(θ m )

55 Nrmal distributins Chice f distributin is determined by surface Phng describes same surfaces as Beckman new GGX distributin fits sme surfaces better analytical Smith shadwing masking 8 Phng Beckman GGX (new) D(θ m )

56 Nrmal distributins Chice f distributin is determined by surface Phng describes same surfaces as Beckman new GGX distributin fits sme surfaces better analytical Smith shadwing masking 8 Phng Beckman GGX (new) D(θ m ) G 1 (θ i, )

57 Imprtance sampling Sampling prcedure chse nrmal accrding t D(m) m n explicit frmulas in paper cmpute by reflectin r refractin cmpute pdf f using dω m /dω leaves G and sme csines fr the weight can adjust sampling rughness t cntrl weight

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59 Measuring transmissin

60 Measuring transmissin

61 Measuring transmissin

62 Measuring transmissin

63 Measuring transmissin

64 Measuring transmissin

65 Measuring transmissin

66 Measuring transmissin

67 Measurement setup

68 Validatin: grund glass 5 Measured data vs. mdel fr Θ i 0, 30, 60, 80 0 GGX fit 5 Measured data vs. mdel fr Θ i 0, 30, 60, 80 0 Beckman fit 4 4 BSDF θt θt Fit is t nrmal incidence data nly

69 Validatin: grund glass 5 Measured data vs. mdel fr Θ i 0, 30, 60, 80 0 GGX fit 5 Measured data vs. mdel fr Θ i 0, 30, 60, 80 0 Beckman fit 4 4 BSDF θt θt Fit is t nrmal incidence data nly

70 Validatin: grund glass 5 4 Measured data vs. mdel fr Θ i 0, 30, 60, 80 0 GGX fit Measured data vs. mdel fr Θ i 0, 30, 60, 80 0 Beckman fit 30 BSDF θt θt Fit is t nrmal incidence data nly

71 Validatin: frsted glass 5 Measured data vs. mdel fr Θ i 0, 30, 60, 80 GGX fit 5 Measured data vs. mdel fr Θ i 0, 30, 60, 80 Beckman fit 4 4 BSDF θt θt Fit is t nrmal incidence data nly

72 Validatin: acid-etched glass Measured data vs. mdel fr Θ i 0, 30, 60, 80 Measured data vs. mdel fr Θ i 0, 30, 60, GGX fit 3.5 Beckman fit BSDF θt θt Fit is t nrmal incidence data nly

73 Validatin: antiglare glass Measured data vs. mdel fr Θ i 0, 30, 60, 80 Measured data vs. mdel fr Θ i 0, 30, 60, GGX fit 1200 Beckman fit BSDF θt θt Fit is t nrmal incidence data nly

74 Transmissin thrugh rugh glass anti-glare glass Beckman, α b = grund glass GGX, α g = acid-etched glass GGX, α g = 0.553

75 Etched glbe

76 Cntributins Micrfacet transmissin mdel new gemetric frmulatin clean, simple generalizatin f reflectin Micrfacet distributin functins evaluate three chices against data new GGX distributin fits sme surfaces better Imprtance sampling Measurement and validatin single interface transmissin

77 Acknwledgments Steve Westin initial measurement idea NSF grants ACI , CNS NSF CAREER CCF Alfred P. Slan Research Fellwship Intel Crpratin equipment dnatin