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\section*{Chapter 6 Solutions}
6.1 Point sources produce a very harsh lighting. Such images are
characterized by abrupt transitions between light and dark.
The ambient light in a real scene is dependent on {\em both} the
lights on the scene and the reflectivity properties of the objects
in the scene, something that cannot be computed correctly with OpenGL.

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6.3 If we were to take into account a light source being obscured
by an object, we would have to have all polygons available so as
to test for this condition. Such a global calculation is incompatible
with the pipeline model that assumes we can shade each polygon independently
of all other polygons as it flows through the pipeline.

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6.5 Materials absorb light from sources. Thus, a surface that appears
red under white light appears so beacuse the surface absorbs all wavelengths
of light except in the red range---a subtractive process. To be compatible
with such a model, we should use  surface absorbtion constants
that define the materials for cyan, magenta and yellow, rather than
red, green and blue.

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6.7 Let $\psi$ be the angle between the normal and the halfway vector,
$\phi$ be the angle between the viewer and the reflection angle, and $\theta$
be the angle between the normal and the light source. If all the vectors 
lie in the same plane, the angle between the light source and the viewer
can be computer either as $\phi+2\theta$ or as $2(\theta+\psi)$. Setting
the two equal, we find $\phi=2\psi$. If the vectors are not coplanar then
$\phi<2\psi$.

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6.13 If the only light source is a point light source that is
located at the center of projection, there can be no shadows in the
image.

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6.15 If we orient the surface so it points in the direction of the
halfway vector, then we have equal angles between the halfway vector
and the viewer and between the halfway vector and the light source.
This configuration is exactly that of a mirror which reflects all the
light towards the viewer.

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