RevolutionPlot3D

[Adam_Caudell]

I am trying to create a Manipulate[ ] line of code to demonstrate to my students surfaces of revolution. I have seen a few Demonstrations on the Demonstrations site, but they are very specific and more detailed that I wanted. I want to be able to change the functions and the axes of revolution.

Ideally, I want to show the 2-D shaded region and then have a slider that rotates the shaded region about any given axis.

For example, I would want to revolve the region bounded by y=(1/2)x^2+1 and y=(1/2)x+7 between x=[0,4] about the line y=-1. I would want to start by showing the shaded region bounded by the curves, then have a slider that would revolve the shaded region about the given axis.

My students have access to Mathematica and I was hoping I could create a generalized template that they could use to enter their own boundary functions as well as any axis of revolution so as to better visualize this concept.

Any help is greatly appreciated.

[Michael_Rogers]

Try modifying one of the Demonstrations. For instance, in
http://demonstrations.wolfram.com/SolidsOfRevolution/
replace the Switch at the beginning with

f[xx_] := ff /. x -> xx;
g[xx_] := gg /. x -> xx;

and replace the variable fcns (the first Manipulate variable) with

{{ff, 2 Sin[x] + 4, "f"}, InputField},
{{gg, x/4, "g"}, InputField},

The code is set up, so that if you declare yrotate a Manipulate variable and remove the initialization (yrotate=-1), you can change the axis of revolution. If you want a vertical axis, you'll have to adapt the code. Fully doing what you want to do will take a fair amount of coding anyway. RevolutionPlot3D is probably not the way to go. It seems to only do axes that pass through the origin. I'd use ParametricPlot3D, just as in the above demonstration.