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Torrance Sparrow Model of Reflectance + Oren Nayar Model of Reflectance. Torrance-Sparrow Model – Main Points. Physically Based Model for Surface Reflection. Based on Geometric Optics. Explains off-specular lobe (wider highlights). Works for only rough surfaces.

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torrance sparrow model of reflectance oren nayar model of reflectance
Torrance Sparrow Model of Reflectance

+

Oren Nayar Model of Reflectance

slide2

Torrance-Sparrow Model – Main Points

  • Physically Based Model for Surface Reflection.
  • Based on Geometric Optics.
  • Explains off-specular lobe (wider highlights).
  • Works for only rough surfaces.
  • For very smooth surfaces, electromagnetic nature of light must be used
  • Beckmann-Spizzichinno model.
  • Beyond the scope of this course.
slide3

Modeling Rough Surfaces - Microfacets

  • Roughness simulated by Symmetric V-groves at Microscopic level.
  • Distribution on the slopes of the V-grove faces are modeled.
  • Each microfacet assumed to behave like a perfect mirror.
slide5

Torrance-Sparrow or Cook-Torrance BRDF

  • Physically based model of a reflecting surface. Assumes a surface is a collection of planar microscopic facets, microfacets. Each microfacet is a perfectly smooth reflector.
  • D describes the distribution of microfacet orientations.
  • G describes the masking and shadowing effects between the microfacets.
  • F term is a Fresnel reflection term related to material’s index of refraction.
slide6

Torrance-Sparrow or Cook-Torrance BRDF

  • Microfacet Distribution Function
  • Statistical model of the microfacet variation in the halfway-vector H direction
  • Based on a Beckman distribution function
  • Consistent with the surface variations of rough surfaces
  • β - the angle between N and H
  • m - the root-mean-square slope of the microfacets
slide8

Torrance-Sparrow or Cook-Torrance BRDF

Geometric Attenuation Factor:

The geometric attenuation factor G accounts for microfacet shadowing. The factor G is in the range from 0 (total shadowing) to 1 (no shadowing). There are many different ways that an incoming beam of light can interact with the surface locally. The entire beam can simply reflect, shown here.

slide9

Torrance-Sparrow or Cook-Torrance BRDF

Geometric Attenuation Factor:

A portion of the outgoing beam can be blocked. This is called masking.

slide10

Torrance-Sparrow or Cook-Torrance BRDF

Geometric Attenuation Factor:

A portion of the incoming beam can be blocked. This is called shadowing.

slide11

Torrance-Sparrow or Cook-Torrance BRDF

Geometric Attenuation Factor:

In each case, the geometric configurations can be analyzed to compute the percentage of light that actually escapes from the surface.

slide13

Torrance-Sparrow or Cook-Torrance BRDF

Fresnel Factor:

The Fresnel effect is wavelength dependent. It behavior is determined by the index-of-refraction of the material (taken as a complex value to allow for attenuation). This effect explains the variation in colors seen in specular regions particular on metals (conductors). It also explains why most surfaces approximate mirror reflectors when the light strikes them at a grazing angle.

slide20

Next Class – Rough Diffuse Surfaces

Same Analysis of Roughness for Diffuse Objects – Oren Nayar Model

slide23

Diffuse Reflection and Lambertian BRDF - Recap

source intensity I

incident

direction

normal

viewing

direction

surface

element

  • Surface appears equally bright from ALL directions! (independent of )

albedo

  • Lambertian BRDF is simply a constant :
  • Surface Radiance :

source intensity

  • Commonly used in Vision and Graphics!
slide24

Diffuse Reflection and Lambertian BRDF - Recap

Radiance decreases with increase in angle between surface normal and source

slide25

Rendered Sphere with Lambertian BRDF

  • Edges are dark (N.S = 0) when lit head-on
  • See shading effects clearly.
slide26

Why does the Full Moon have a flat appearance?

  • The moon appears matte (or diffuse)
  • But still, edges of the moon look bright
  • (not close to zero).
slide27

Why does the Full Moon have a flat appearance?

Lambertian Spheres and Moon Photos illuminated similarly

slide30

Surface Roughness Causes Flat Appearance

Increasing surface roughness

Lambertian model

Valid for only SMOOTH MATTE surfaces.

Bad for ROUGH MATTE surfaces.

slide32

Oren-Nayar Model – Main Points

  • Physically Based Model for Diffuse Reflection.
  • Based on Geometric Optics.
  • Explains view dependent appearance in Matte Surfaces
  • Take into account partial interreflections.
  • Roughness represented like in Torrance-Sparrow Model
  • Lambertian model is simply an extreme case with
  • roughness equal to zero.
slide33

Modeling Rough Surfaces - Microfacets

  • Roughness simulated by Symmetric V-groves at Microscopic level.
  • Distribution on the slopes of the V-grove faces are modeled.
  • Each microfacet assumed to behave like a perfect Lambertian surface.
slide34

View Dependence of Matte Surfaces - Key Observation

  • Overall brightness increases as the angle between the source and viewing direction decreases. WHY?
  • Pixels have finite areas. As the viewing direction changes, different mixes between dark and bright are added up to give pixel brightness.
torrance sparrow brdf different factors recap
Torrance-Sparrow BRDF – Different Factors (RECAP)

Geometric Attenuation:

reduces the output based on the amount of shadowing or masking that occurs.

Fresnel term:

allows for wavelength dependency

Distribution:

distribution function determines what percentage of microfacets are oriented to reflect in the viewer direction.

How much of the macroscopic surface is visible to the light source

How much of the macroscopic surface is visible to the viewer

slide36

Slope Distribution Model

  • Model the distribution of slopes as Gaussian.
  • Mean is Zero, Variance represents ROUGHNESS.
slide37

Geometric Attenuation Factor

  • No interreflections taken into account in above function.
  • Derivation found in 1967 JOSA paper (read if interested).
torrance sparrow brdf different factors recap1
Torrance-Sparrow BRDF – Different Factors (RECAP)

Geometric Attenuation:

reduces the output based on the amount of shadowing or masking that occurs.

Fresnel term:

allows for wavelength dependency

Distribution:

distribution function determines what percentage of microfacets are oriented to reflect in the viewer direction.

How much of the macroscopic surface is visible to the light source

How much of the macroscopic surface is visible to the viewer

oren nayar model different factors
Oren-Nayar Model – Different Factors

Geometric Attenuation:

reduces the output based on the amount of shadowing or masking that occurs.

Fresnel term:

allows for wavelength dependency

Distribution:

distribution function determines what percentage of microfacets are oriented to reflect in the viewer direction.

How much of the macroscopic surface is visible to the light source

How much of the macroscopic surface is visible to the viewer

oren nayar model different factors1
Oren-Nayar Model – Different Factors

Geometric Attenuation:

reduces the output based on the amount of shadowing or masking that occurs.

Fresnel term:

allows for wavelength dependency

Distribution:

distribution function determines what fraction of the surface area do the facets of the same orientation cover?

How much of the macroscopic surface is visible to the light source

How much of the macroscopic surface is visible to the viewer

oren nayar model different factors contd
Oren-Nayar Model – Different Factors (contd.)
  • Take into account two light bounces (reflections).
  • Hard to solve analytically, so they find a functional approximation.
oren nayar model final expression
Oren-Nayar Model – Final Expression

Lambertian model is simply an extreme case with roughness equal to zero.

slide44

Comparison to Ground Truth

Renderings

Real Objects

slide45

Summary of Surfaces and BRDFs

Rough

Smooth

Torrance-Sparrow BRDF

Mirror BRDF

Specular

Delta Function

Speck of reflection

Broader Highlights

Off-specular lobe

Oren-Nayar BRDF

Lambertian BRDF

Diffuse

Models view dependence

No view dependence

Many surfaces may be rough and show both diffuse and surface reflection.

slide46

Summary of Surfaces and BRDFs

Rough

Smooth

Torrance-Sparrow BRDF

Mirror BRDF

Specular

Delta Function

Speck of reflection

Broader Highlights

Off-specular lobe

Oren-Nayar BRDF

Lambertian BRDF

Diffuse

Models view dependence

No view dependence

Many surfaces may be rough and show both diffuse and surface reflection.