Plot 3D 

Exercise 15.3.14 (Page 1042):  This shows the intersection of the cone  with the right circular cylinder .  The figure will be drawn in four stages, with a the viewing cube defined as , the viewer angle with the x-axis as 45 degrees and the view angle with the z-axis as 60 degrees.

 

Stage 1:  The cone is parameterized as

 . 

 

The "backside" of the surface is plotted for  (s-resolution is 32) and for  (t-resolution 24) and is shown to the right.

EXERCISE 14A.BMP
   

Stage 2: The cylinder is parameterized as

  

 

and is plotted for  (s-resolution is 1) and for  (t-resolution 32).  The surface is plotted without erasing the previous plot and is shown to the right. 

EXERCISE 14B.BMP
   

Stage 3:  Next, the "front side" of the cone is graphed, using the same parameterization as in Stage 1, but plotting   (s-resolution is 32) and  (t-resolution is 8). This portion of the cone is plotted without erasing the previous graph and is shown to the right.

 EXERCISE 14C.BMP
   

Stage 4:  When the "front side" of the cone was drawn in stage 3, it covered a portion of the cylinder lying below the cone.  Note that the cone and cylinder intersect when  , or in terms of the original cylinder parameterization for y, when The cylinder is reparameterized as

  

 

and is plotted for  (s-resolution is 1) and for (t-resolution 16).  The surface is plotted without erasing the previous plot and is shown to the right. 

EXERCISE 14D.BMP

 

Previous Next

Back to Examples