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Reflection Models I. Today Types of reflection models The BRDF and reflectance The reflection equation Ideal reflection and refraction Fresnel effect Ideal diffuse Next lecture Glossy and specular reflection models Rough surfaces and microfacets Self-shadowing

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Reflection Models I

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Reflection models i l.jpg

Reflection Models I

  • Today

    • Types of reflection models

    • The BRDF and reflectance

    • The reflection equation

    • Ideal reflection and refraction

    • Fresnel effect

    • Ideal diffuse

  • Next lecture

    • Glossy and specular reflection models

    • Rough surfaces and microfacets

    • Self-shadowing

    • Anisotropic reflection models

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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Reflection Models

  • Definition: Reflection is the process by which light incident on a surface interacts with the surface such that it leaves on the incident side without change in frequency.

  • Properties

    • Spectra and Color [Moon Spectra]

    • Polarization

    • Directional distribution

  • Theories

    • Phenomenological

    • Physical

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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Types of Reflection Functions

  • Ideal Specular

    • Reflection Law

    • Mirror

  • Ideal Diffuse

    • Lambert’s Law

    • Matte

  • Specular

    • Glossy

    • Directional diffuse

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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Materials

Plastic

Metal

Matte

From Apodaca and Gritz, Advanced RenderMan

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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The Reflection Equation

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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The BRDF

  • Bidirectional Reflectance-Distribution Function

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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The BSSRDF

  • Bidirectional Surface Scattering Reflectance-Distribution Function

Translucency

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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Gonioreflectometer

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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Properties of BRDF’s

  • 1. Linearity

  • 2. Reciprocity principle

From Sillion, Arvo, Westin, Greenberg

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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Properties of BRDF’s

  • 3. Isotropic vs. anisotropic

  • 4. Energy conservation

Reciprocity and isotropy

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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Energy Conservation

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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The Reflectance

  • Definition: Reflectance is ratio of reflected to incident power

  • Conservation of energy: 0 <r< 1

  • 3 by 3 set of possibilities:

  • Units: r [dimensionless], fr [1/steradians]

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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Law of Reflection

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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Ideal Reflection (Mirror)

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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Snell’s Law

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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Total internal reflection:

Law of Refraction

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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Optical Manhole

Total internal reflection

From Livingston and Lynch

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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Fresnel Reflectance

Metal (Aluminum)

Dielectric (N=1.5)

Gold F(0)=0.82

SilverF(0)=0.95

Glass n=1.5 F(0)=0.04

Diamond n=2.4 F(0)=0.15

Schlick Approximation

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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Experiment

  • Reflections from a shiny floor

From Lafortune, Foo, Torrance, Greenberg, SIGGRAPH 97

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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Approximated Reflectance

Cook-Torrance approximation

Cook-Torrance Model for Metals

Reflectance of Copper as a

function of wavelength and

angle of incidence

Measured Reflectance

Light spectra

Copper spectra

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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Lambert’s Cosine Law

Ideal Diffuse Reflection

  • Assume light is equally likely to be reflected in any output direction (independent of input direction).

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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“Diffuse” Reflection

  • Theoretical

    • Bouguer - Special micro-facet distribution

    • Seeliger - Subsurface reflection

    • Multiple surface or subsurface reflections

  • Experimental

    • Pressed magnesium oxide powder

    • Almost never valid at high angles of incidence

  • Paint manufactures attempt to create ideal diffuse

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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Phong Model

R(E)

E

R(L)

E

N

N

L

L

Reciprocity:

Distributed light source!

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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s

Phong Model

Diffuse

Mirror

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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Properties of the Phong Model

  • Energy normalize Phong Model

University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2007 Don Fussell


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