       Re: Surface of Revolution

• To: mathgroup at smc.vnet.net
• Subject: [mg20247] Re: [mg20209] Surface of Revolution
• From: "David Park" <djmp at earthlink.net>
• Date: Fri, 8 Oct 1999 18:30:20 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Chee Lim Cheung asked:

>Hi Mathematica users & experts,
>
>There is a package in Mathematica which allows us to generate surfaces of
>revolution. It is in the context Graphics`SurfaceOfRevolution`. It is
>stated that a surface of revolution can be generated about any axis by
>setting the option RevolutionAxis. However, it is not exactly to me how to
>do this. For example, I would like to generate a surface of revolution of
>the curve y = x^2 from x = 2 to x = 3 about the axis x = 1. Anybody out
>there who can give me some pointers on how to go about it?
>
>Thanks
>Chee
>

Chee,

Sometimes it is easier to use a parametric plot than surface of revolution. We want
to revolve about a vertical axis going through {1,0,0}. The radial distance from the
center is r = x-1 or x = r +1 and the height of the surface is z = x^2 = (r+1)^2. We
can then parametrize the surface by revolving around the origin and then shifting to
the desired center.

surface = {r Cos[t], r Sin[t], (r + 1)^2} + {1, 0, 0}
{1 + r*Cos[t], r*Sin[t], (1 + r)^2}

ParametricPlot3D[Evaluate[surface], {r, 1, 2}, {t, 0, 2*Pi},
PlotPoints -> {15, 31}, AxesLabel -> {x, y, z}, ImageSize -> 500];

I don't know of an easy way to make this plot using SurfaceOfRevolution.

David Park