![Page 1: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/1.jpg)
Reflection models
Digital Image SynthesisYung-Yu Chuang11/01/2005
with slides by Pat Hanrahan and Matt Pharr
![Page 2: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/2.jpg)
Rendering equation
![Page 3: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/3.jpg)
Taxonomy 1
( , , , , , ) ( , , , , , )in outx y t x y t
General function = 12D
Scattering function = 9D
Assume time doesn’t matter (no phosphorescence)
Assume wavelengths are equal (no fluorescence)
Single-wavelength Scattering function = 8D
Assume wavelength is discretized or integrated into RGB(This is a common assumption for computer graphics)
( , , , ) ( , , , )in outx y x y
![Page 4: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/4.jpg)
Taxonomy 2
Single-wavelength Scattering function = 8D( , , , ) ( , , , )in outx y x y
Bidirectional Texture Function (BTF)Spatially-varying BRDF (SVBRDF) = 6D
Ignore subsurface scattering (x,y) in = (x,y) out
Bidirectional Subsurface ScatteringDistribution Function (BSSRDF) = 6D
Ignore dependence on position
Light Fields, Surface LFs = 4D
Ignore direction of incident light
( , , , )outx y
Texture Maps = 2D
Assume Lambertian
( , )outx y
3D
Assume isotropy
BRDF = 4D
Ignore subsurface scattering
( , ) ( , )in out
Ignore dependenceon position
![Page 5: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/5.jpg)
Properties of BRDFs
![Page 6: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/6.jpg)
Properties of BRDFs
![Page 7: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/7.jpg)
Isotropic and anisotropic
![Page 8: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/8.jpg)
Reflection models
• BRDF/BTDF/BSDF• Scattering from realistic surfaces is best descri
bed as a mixture of multiple BRDFs and BSDFs.• Material = BSDF that combines multiple BRDFs
and BSDFs. (chap. 10)• Textures = reflection and transmission propert
ies that vary over the surface. (chap. 11)
![Page 9: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/9.jpg)
Surface reflection models
• Measured data• Phenomenological models: models with intui
tive parameters• Simulation• Physical optics: solve Maxwell’s equation• Geometric optics: microfacet models
![Page 10: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/10.jpg)
Reflection categories
diffuse
perfect specular retro-reflective
glossy specular
![Page 11: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/11.jpg)
Geometric setting
n
t
s
sinsin ,
sincos
1sin ,cos 2
yx
zz
![Page 12: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/12.jpg)
BxDF
• BSDF_REFLECTION, BSDF_TRANSMISSION• BSDF_DIFFUSE, BSDF_GLOSSY (retro-reflective), BSDF_SPECULAR
• Spectrum f(Vector &wo, Vector &wi);• Spectrum Sample_f(Vector &wo, Vector *wi, float u1, float u2, float *pdf);
• Spectrum rho(Vector &wo, int nSamples, float *samples);
• Spectrum rho(int nSamples, float *samples);
![Page 13: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/13.jpg)
Specular reflection and transmission• Reflection: • Transmission: (Snell’s law)
oi
ttii sinsin
n
i o
n
i
t
index of refraction dispersion
![Page 14: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/14.jpg)
Fresnel reflectance• Reflectivity and transmissiveness are view dep
endent• For dielectrics
![Page 15: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/15.jpg)
Fresnel reflectance• For conductors
![Page 16: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/16.jpg)
Perfect specular reflection
![Page 17: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/17.jpg)
Perfect specular transmission
![Page 18: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/18.jpg)
Fresnel modulation
![Page 19: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/19.jpg)
Lambertian reflection• It is not physically feasible, but provides a goo
d approximation to many real-world surfaces.
class COREDLL Lambertian : public BxDF {
public:
Lambertian(Spectrum &reflectance)
: BxDF(BxDFType(BSDF_REFLECTION | BSDF_DIFFUSE)),
R(reflectance), RoverPI(reflectance * INV_PI) {}
Spectrum f(Vector &wo, Vector &wi) {return RoverPI}
Spectrum rho(Vector &, int, float *) { return R; }
Spectrum rho(int, float *) { return R; }
private:
Spectrum R, RoverPI;
};
![Page 20: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/20.jpg)
Microfacet models• Rough surfaces can be modeled as a collection
of small microfacets.• Two components: distribution of microfacets
and how light scatters from individual microfacet → closed-form BRDF expression
n
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Important effects in microfacet models
![Page 22: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/22.jpg)
Oren-Nayar model• Many real-world materials such as concrete, sa
nd and cloth are not Lambertian.• A collection of symmetric V-shaped perfect La
mbertian grooves with a Gaussian distribution• Don’t have a closed-form solution, instead us
e the approximation
),min( ,),max(
09.0
45.0 ,
)33.0(21
)tansin))cos(,0max((),(
2
2
2
2
oioi
oioir
BA
BAf
![Page 23: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/23.jpg)
Lambertian
![Page 24: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/24.jpg)
Oren-Nayer model
![Page 25: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/25.jpg)
Torrance-Sparrow model
• One of the first microfacet models, designed to model metallic surfaces
• A collection of perfectly smooth mirrored microfacets with distribution
io
)( hD
h
![Page 26: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/26.jpg)
Torrance-Sparrow model
![Page 27: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/27.jpg)
Blinn microfacet distribution• Distribution of microfacet normals is modeled
by an exponential falloffe
hh nD )()(
ehh n
eD )(
2
2)(
![Page 28: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/28.jpg)
Torrance-Sparrow with Blinn distribution
![Page 29: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/29.jpg)
Anisotropic microfacet model
22 sincos)()1)(1()( yx ee
hyxh neeD
• Ashikmin and Shirley have developed a microfacet model for anisotropic surfaces
![Page 30: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/30.jpg)
Anisotropic microfacet model
![Page 31: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/31.jpg)
Lafortune model• An efficient BRDF model to fit measured
data to a parameterized model with a relatively small number of parameters
n
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eziizyiiyxiixo
d
ior
iooo
pf
1,,, )),,((
),,(
![Page 32: Reflection models Digital Image Synthesis Yung-Yu Chuang 11/01/2005 with slides by Pat Hanrahan and Matt Pharr](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649f505503460f94c72711/html5/thumbnails/32.jpg)
Lafortune model (for a measured clay)