Angel: Interactive Computer Graphics, Fourth Edition
Chapter 8 Solutions
8.1 Suppose that we move across a scanline left to right starting on the
outside of a polygon. Assume that 0 corresponds to the background color
and 1 is the edge and fill color. As we move across the scanline we replace
each point by the exclusive or of its value with the value of the point on
the left (which has already been processed). If we start on the outside of
any polygon, we can assume the first point is a 0. Thus as long as we
remain outside the first polygon we generate 0
⊕
0 = 0. When we
encounter the first edge, a 1, we compute 1
⊕
0 = 1 (that is we have a 0
from the last point XORed with the edge). As we proceed inside the
polygon we compute 1
⊕
0 = 1 because we have a 1 from the last XOR and
a 0 from the unfilled point. When we encounter the second edge, we
compute 1
⊕
1 = 0, thus returning to our initial situation
8.3 The major problem is that the environment map is computed without
the object in the scene. Thus, all global lighting calculations of which it
should be a part are incorrect. These errors can be most noticeable if there
are other reﬂective objects will now not show the reﬂection of the removed
object. Other errors can be caused by the removed object no longer
blocking light and by its shadows being missing. Other visual errors can be
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 Spring '10
 Alxe
 Trigonometry, Computer Graphics, Nyquist–Shannon sampling theorem, Nyquist rate, luminance

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