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\section*{Chapter 3 Solutions}

3.1 The general problem is how to describe a set of characters
that might have thickness, curvatures and holes (such as in the
letters a and q). Suppose we consider a simple example where each
character can be approximated by a sequence of line segments.
One possibility is to use a move/line system where 0 is a move and
1 a line. Then a character can be described by a sequence of the
form $(x_0,y_0,b_0), (x_1,y_1,b_1), (x_2,y_2,b_2), .....$ where
$b_i$ is a 0 or 1. Thism approach is used in the example in the
OpenGL Programming Guide. A more elaborate font can be developed
by using polygons instead of line segments.

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3.11 There are a couple of potential problems. One is that the
application program can map different points in user coordinates
to the same point in screen coordinates. Second, a given position
on the screen when transformed back into user coordinates may lie
outside the users window.

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3.15 The problem is with the elements that are entered interactively.
When we use double buffering there elements will be rendered into whichever 
buffer is the back buffer at the time but because they are not part of the
display function they will not be the same from frame to frame. What
we would like to have but don't is a way to render these elements into
both buffers. One possibility is to save all the elements as they 
are being drawn in some data structure or a display list so they can
be rerendered as desired.

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3.19 Each scan is allocated 1/60 second. For a given scan we have to take 
10% of the time for the vertical retrace whcih means that we start to draw
scan line n at .9n/(60*1024) seconds from the beginning of the refresh.
But allocating 10% of this time for the horizontal retrace we are at pixel
m on this line at time .81nm/(60*1024). 

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3.25 When the display is changing, primitives that move or are
removed from the display will leave a trace or motion blur on the
display as the phosphors persist. Long persistence phosphors have
been used in text only displays where motion blur is less of a problem
because the long persistence gives a very stable flicker-free image.
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