Soltions for Assignment 1

1.1 (3pts) We can apply the formula from page 18:

where we have replaced the length of the camera d with the focal length of the lens f. Solving
for f, we have

We can use the diagonal of the 24 mm x 36 mm
le for h. Solving, we find

(I accepted solutions 18mm and 12mm as well)

1.3 (2pts) Suppose that the line segment is between the points (x₁; y₁) and (x₂; y₂): We can use
the endpoints of the line segment to de termine the slope and y intercept of a line of which
the segment is part,i.e.

Note that we can deal with horizontal and vertical line segments as special cases. We can find
the intersections with the sides of the window by substituting y = y_max, y = y_min, x = x_max,
and x = x_min (the equations for the sides of the window) into the above equation. We can
check the locations of the points of intersection to determine if they are on the line segment
or only on the line of which it is part.

1.4 (2pts) In Exercise 1.3 we saw that we could intersect the line of which the line segment is part
independently against each of the sides of the window. We could do this process iteratively,
each time shortening the line segment if it intersects one side of the window.

1.7 (3pts) We have to process 1280 x 1024 x 72 pixels/sec. If we process each successively, there
is only about 10 nanoseconds to process each. For a 480 x 640 interlaced display operating at
60 Hz we must process only 480 x 640 x 30 pixels/sec which gives us about 109 nanoseconds
to process each pixel.