Angel and Shreiner: Interactive Computer Graphics, Seventh
Edition
Chapter 1 Solutions
1.1 The main advantage of the pipeline is that each primitive can be
processed independently. Not only does this architecture lead to fast
performance, it reduces memory requirements because we need not keep all
1.2 If we use lines of constant longitude and lines of constant latitude, their
intersections define a set of quadrilaterals. If we draw diagonals for each
1.3 We derive this algorithm later in Chapter 6. First, we can form the
tetrahedron by finding four equally spaced points on a unit sphere centered
at the origin. One approach is to start with one point on the zaxis
1.4 Suppose that the line segment is between the points (x1, y1) and
(x2, y2) We can use the endpoints of the line segment to determine the
slope and y intercept of a line of which the segment is part, i.e.
y=mx +h=y2−y1
x2−x1
x+y1−
y2−y1
x2−x1
x1.
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1.5 In Exercise 1.4, we saw that we could intersect the line of which the
line segment is part independently against each of the sides of the window.
1.6 Here we have to intersect the line segment against the polygons that
determine the sides of the window. Each of these polygons is part of a
plane. The equation of each plane is of the form
ax +by +cz +d= 0,
where the coefficients a,b,c, and dcan be determined from the vertices of
the parallelepiped. The line segment is either parallel to a particular plane
1.7 In a one–point perspective, two faces of the cube is parallel to the
projection plane, while in a two–point perspective only the edges of the
1.8 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
1.9 Each frame for a 480 x 640 pixel video display contains only about
300k pixels whereas the 2000 x 3000 pixel movie frame has 6M pixels, or
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1.10 Good examples for this problem are architecture, mechanical parts
1.11 A 1024 x 1280 display has a 4 to 5 aspect ratio. Hence, if the diagonal
is 50 cm and we want square pixels, the screen must be approximately 31
cm x 39 mm. Each pixel is then about 0.3 mm on each side. A smooth
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