CMSC 635: Advanced Computer Graphics

Advanced Illumination

Spring 1999

David S. Ebert
Computer Science and Electrical Engineering Department
University of Maryland, Baltimore County

Illumination Review

• ambient -- approximate global illumination effects.
• diffuse -- Lambert's Law -- absorbed and reradiated equally in all directions (depend on wavelength, independent of observer)
• specular -- reflects off surface => color of light in many cases is color of object.

Definitions

flux

-- rate at which energy is emitted (Watts).

solid angle

-- angle at the apex of a cone. It is measured in terms of the area on a sphere intercepted by a cone whose apex is at the sphere`s center.

steradian (sr)

-- solid angle of a cone that intercepts an area equal to square of the sphere's radius r.

• hemisphere has sr.

Radiant intensity

-- flux per unit solid angle in a given direction.

Radiance

-- radiant intensity per unit foreshortened surface area. (W/sr*m²)

Foreshortened surface area

- projected surface area -- projection of surface onto the plane perpendicular to the direction of radiation. It equals to

where is the angle between radiation and surface normal.

Irradiance

-- the incident flux per (unforeshortened) unit surface area.

Irradiance of incidence light : . where is incident radiance.

Bidirectional reflectivity :

Cook-Torrance use
* (N*L)
where

D is distribution function of microfacets orientations

G is geometrical attenuation factor -- masking and shadowing effects of the microfacet on each other.

is the Fresnel term.

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Blinn's model

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Distribution Functions

• Phong's model
  
  
• Blinn
  
  where and .
  
• T-Sparrow
  
  
• C-Torrance
  
  
  where m is root mean square slope of microfacets (Beckman distribution).

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Shadowing and masking

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Fresnel Factor

where , is angle of incidence relative to , and n is index of refraction.

In another form

where and .

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Cook-Torrance Illumination (continued)

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Formula:

where , and .

Also can do it as:



where Red(0) is color of material at normal incidence. Then,

Hall suggested a similar method.

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Return to CMSC 635 Notes Page

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Last modified: Wed Mar 10 17:07:01 EST 1999