1. Reflection and Transmission
Ed Angel
Professor of Computer Science, Electrical and Computer Engineering, and Media Arts
Director, Arts Technology Center
University of New Mexico
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2. Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
Introduction
Interactions between light and materials
Blinn-Phong model
Absorption
Diffuse and specular reflections
Purely local
Reflection:
Translucent surfaces
Refraction
Frensel effect
Chromatic dispersion
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009

3. Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
Global vs Local
Most of these effects can only be computed in a global renderer such as a ray tracer
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009

4. Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
Ray Tracing
Ray tracers can make use of all these effects in a global calculation by tracing rays N R L T -N
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009

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Environmental Map
Can use all these effects
Implement in Cg with vertex and fragment programs
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009

6. Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
Refraction
With pure refraction, all the light is transmitted but the angle of refraction is determined by Snell’s law
ήl sin θl = ήt sin θt
where ήl and ήt are the speed of light relative to the speed of light in a vacuum
Let ή = ήl / ήt
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009

7. Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
Computing T
ή2 sin2θl = ή2 (1- cos2θl )= sin2θt = 1-cos2θt
Solving for cos θt
Assuming normalized vectors
cos θt = T·N = (1- ή2 (1-cos2θl ))1/2
where cos θl = T·N
T, N, and L must be coplanar
T = a L + b N and T·T = 1
Solving
T = -1/ ή L – (cos θt - 1/ ή cos θl ) N
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009

8. Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
Notes
Critical angle: total internal reflection
1= ή2 (1-cos2θl )
Snell’s law is a statement that light takes the shortest path (in time)
Can apply to reflection maps (see Cg Tutorial) via vertex program
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009

9. Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
Fresnel Effect
Some light is reflected and some transmitted at surface between two materials
Amount of light reflected is greatest at shallow angle
Approximation: use affine combination of refracted and reflected colors where
a = max (0, min(1, bias + scale 
(1 + L·N)power))
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Chromatic Dispersion
The refraction coefficient is actually a function of wavelength
h = h(l) N L -N Tr Tg Tb
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009

11. Chromatic Dispersion with Shaders
Easy to do with reflection maps
Use three values of h
Make use of vector operations
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009