CS781 - Colour for Computer Graphics - Winter 2009
Lecture 4
Transport
Scattering
No Wavelength Dependence
Fog
Wavelength Dependence Mediated by Chromatic Aberration
Rainbow
Wavelength Dependence Mediated by Selective Absorption
Beer
- Beer's Law: I' = I exp( -\alpha (lambda) t )
- \alpha(\lambda) is the absorption coefficient
- \alpha(\lambda) t is the optical density
- zero density is transparent
- infinite density is opaque
- logarithms add
Surface Reflectances
According to Jim Kajiya, Bidirectional Reflectance Distribution Function
should tell the whole story. But where does it come from?
- R( incoming angle (2 dof), outgoing angle (2 dof), wavelength (1 dof) )
- incoming and outgoing angles: 0 < \theta < \pi/2, 0 < \phi
< 2\pi
- wavelength 400 nm < \lambda < 700nm
- we won't even talk about sampling density (3.14 million values at
10 degree, 10 nm sampling)
- potentially also a function of distance along the surface (2 dof) and
difference in surface normal (1 dof )
- if the surface varies, then also parameters that control variation
Maybe it could come from measurement
- even if you could measure it how would you encode the result
Maybe you could simulate the system
- just how complex is the system
Maybe you could find a simple model
- capturing only the important aspects of the system
Smooth Surfaces
Surface reflectance
Body reflectance
- just like selective absorption
- doesn't come out at the same place: Why doesn't it matter?
- edges of a surface
Lambertian reflectance
Lambert 1728-1777
The Moon
- What would the full moon look like if its surface were Lambertian?
- What does the full moon actually look like?
Rough Surfaces
Surface Reflectance
Surface Gloss
Colour Mixing
Paint is the usual example, but there are other examples
- Fruit ripening
- Leaves turning colour in the fall
- Colour of human skin
Kubelka-Munk colour mixing model
- Infinitesimally thin layers, thickness proportional to the density of
the pigment
- Use reflection/refraction plus Beer's law
- Solve in equilibrium at the boundaries between layers
- Infinite depth
- White underlayer
- Black underlayer
Engineering model
- We don't use densities, reflection/refraction coefficients, etc
calculated from physics.
- We get humans to say whether colours look the same or not, and by how
much they differ, and find the best coefficients.
- Recall difference between
- blind surgery -- calculate like paint -- and
- computer-animated movies -- let the artist play with
coefficients
Subjective Effects of Coloured Surfaces
Area effects
Precision of Colour Mixing
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