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Re: 3D Plot

• To: mathgroup at smc.vnet.net
• Subject: [mg2364] Re: [mg2302] 3D Plot
• From: Richard Mercer <richard at seuss.math.wright.edu>
• Date: Fri, 27 Oct 1995 01:51:06 -0400

>  

>  There is a vector
>  (x1(t1,t2,t3), x2(t1,t2,t3), x3(t1,t2,t3)) 

>  now I want
>  to plot the 3D figure for 

>  0<t1<t1max, 0<t2<t2max, 0<t3<t3max.
>  

>  How can this be done?
>  

>  Hans Friedrich Steffani

There is no command or graphics primitives for plotting "solid" 3-D  
objects, only for plotting surfaces. So what you need to do is plot the 

boundary surfaces of your object. As I understand it, they would be
the following six surfaces:

(x1(0,t2,t3), x2(0,t2,t3), x3(0,t2,t3)); 

   0<t2<t2max, 0<t3<t3max
(x1(t1max,t2,t3), x2(t1max,t2,t3), x3(t1max,t2,t3)); 

   0<t2<t2max, 0<t3<t3max
(x1(t1,0,t3), x2(t1,0,t3), x3(t1,0,t3));
   0<t1<t1max, 0<t3<t3max
(x1(t1,t2max,t3), x2(t1,t2max,t3), x3(t1,t2max,t3));
   0<t1<t1max, 0<t3<t3max
(x1(t1,t2,0), x2(t1,t2,0), x3(t1,t2,0));
   0<t1<t1max, 0<t2<t2max
(x1(t1,t2, t3max), x2(t1,t2, t3max), x3(t1,t2, t3max));
   0<t1<t1max, 0<t2<t2max

Each of these surfaces can be plotted using 

ParametricPlot3D. Actually, you can plot them all in a single 

ParametricPlot3D command, but I suggest you try them one at a time  
first to make sure things are working out.

Richard Mercer