Plot 3D 

Exercise 15.5.19  (Page 1063): This figure shows the intersection of the surfaces   and  .  The figure will be drawn in seven (yes, seven) stages.  First of all, the screen viewing cube is set up as  , and the viewer angle with the x-axis is 55 degrees.

Stage 1: The surface   is parameterized as

The "back side" of this surface is plotted for   ( s-resolution is 16) and  (t-resolution is 16) and is shown to the right. 

EXERCISE 19A.BMP
   

Stage 2: The surface   will be plotted in several stages.  First, its back bottom is drawn.  It is parameterized as

      

 

and is plotted for   ( s-resolution is 1) and   ( t-resolution is 2).  This portion of the surface is plotted without erasing the previous graph and is shown to the right.

 EXERCISE 19B.BMP
   

Stage 3:  Next, the top of the surface   is drawn. It is parameterized as in stage 2, but it is plotted for   ( s-resolution is 1) and  ( t-resolution is 16).  This portion of the surface is plotted without erasing the previous graph and is shown to the right.

 EXERCISE 19C.BMP
   

Stage 4:  Next, the "front side" of the surface   is drawn. It is parameterized as in stage 1 but is plotted for    ( s-resolution is 16) and  (t-resolution is 18).  This portion of the surface is plotted without erasing the previous graph and is shown to the right.

 EXERCISE 19D.BMP

The three remaining stages plot the rest of the surface   which lies in front of the surface  .

Stage 5:  In this stage the left front of  is plotted. It is parameterized as  

 

 

and is plotted for   ( s-resolution is 1) and   ( t-resolution is 16).  This portion of the surface is plotted without erasing the previous graph and is shown to the right.

 EXERCISE 19E.BMP
   

Stage 6:  In this stage the bottom front of   is plotted. It is parameterized as in stage 2, but it is plotted for    ( s-resolution is 1) and   ( t-resolution is 2).  This portion of the surface is plotted without erasing the previous graph and is shown to the right.

 EXERCISE 19F.BMP
   

Stage 7:  Finally, the last stage!  Here the back left of   is plotted.  It is parameterized as in stage 5, but it is plotted for    ( s-resolution is 1) and   ( t-resolution is 16).  This portion of the surface is plotted without erasing the previous graph and is shown to the right.

 EXERCISE 19G.BMP

 

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