Exercise 15.3.15 (Page 1042):
This shows the intersection of the paraboloid and
the right circular cylinder .
The figure will be drawn in three stages, with the viewing cube
defined as and
the viewer angle with the x-axis as 40 degrees.
Stage 1:
The cone is parameterized as
.
The "backside" of the surface is plotted for (s-resolution
is 1) and for
(t-resolution 12) and is shown to the right.
Stage 2:
The paraboloid is parameterized as
and is plotted for
(s-resolution is 16) and for
(t-resolution 32). The surface is plotted without
erasing the previous plot and is shown to the right.
Stage 3:
The "front side" of the cylinder is the last to be drawn.
Note that the paraboloid and cylinder intersect when ,
or in terms of the original cylinder parameterization for
x, when .
The cylinder is reparameterized as
and is plotted for
(s-resolution is 1) and for
(t-resolution 20). With this parameterization,
when
and when
.
The surface is plotted without erasing the previous plot and
is shown below.
