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Exercise 15.3.16 (Page 1042):
This shows the intersection of the two right circular cylinders
 and
 with
the surface  .
The figure will be drawn in three stages, with the viewing cube
defined as  ,
the viewer angle with the x-axis as 40 degrees, and the view
angle with the z-axis is 80 degrees.
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Stage 1:
The "back sides" of the two cylinders are graphed in this
stage. The smaller cylinder
is
parameterized as
and is plotted for
 (s-resolution
is 4) and for
 (t-resolution
16). The larger cylinder
is
parameterized as
and is plotted for
 (s-resolution
is 4) and for
(t-resolution
16). The resulting graph is shown to the right. |
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Stage 2:
The surface
is parameterized as
and is plotted for
 (s-resolution
is 12) and for
 (t-resolution
32). The surface is plotted without erasing the previous
plot and is shown to the right. |
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Stage 3:
The "front sides" of the cylinders are plotted with the same
parameterizations and s-intervals as in stage 1, but both
t-intervals are
 .
The surfaces are plotted without erasing the previous plot
and the resulting graph is shown below. |
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