Re: v.6 RevolutionPlot3D

*To*: mathgroup at smc.vnet.net*Subject*: [mg75983] Re: v.6 RevolutionPlot3D*From*: Helen Read <hpr at together.net>*Date*: Mon, 14 May 2007 03:47:04 -0400 (EDT)*References*: <200705120700.DAA23589@smc.vnet.net> <f26p3f$57r$1@smc.vnet.net>*Reply-to*: HPR <read at math.uvm.edu>

Andrzej Kozlowski wrote: > On 12 May 2007, at 16:00, Helen Read wrote: > >> I see that SurfaceOfRevolution (which was in an add on package) has >> been replaced by RevolutionPlot3D. Sounds great, except that >> RevolutionPlot3D only revolves around the vertical axis. We (my >> calculus students) used the old SurfaceOfRevolution all the time >> for visualizing surfaces of revolution for computing volume and >> surface area, and we need to be able to revolve around both the >> vertical axis and the horizontal axis. > > First of all, you can still use SurfaceOfRevolution in Mathematica 6: > > << Graphics`SurfaceOfRevolution` > > (ignore the compatibility message) Well, it would be a shame to have to load a legacy package to do something that 6.0 *should* do. Frankly, I'm a bit baffled as to why RevolutionPlot3D does not have an option to set the revolution axis. Clearly it is intended as a replacement for the old SurfaceOfRevolution, which did have an option for setting the revolution axis. Why would they take that out? > Another possibility is simply to forget about RevolutionPlot3D and > use ParametricPlot3D: > > ParametricPlot3D[Evaluate[{X, Y, Z} /. Solve[RotationMatrix[{{1, 1, > 1}, {0, 0, 1}}].{X, Y, Z} == {t Cos[=CE=B8], t Sin[=CE=B8], t^2 }, = > {X, Y, > Z}]], {t, 0, 1}, {=CE=B8, 0, 2 =CF=80}] That would be a bit much for Calculus I or II students. I think what I'm going to have my students do is the following. To revolve around the vertical axis just use RevolutionPlot3D: RevolutionPlot3D[f[x], {x, 0, 2}] (or RevolutionPlot3D[{x[t],y[t]},{t,0,2}] in the case of a parametric curve). To revolve around the horizontal axis, interchange x and y, and set ViewVertical like this. RevolutionPlot3D[{f[x],x}, {x, 0, 2},ViewVertical->{-1,0,0}] or RevolutionPlot3D[{y[t],x[t]},{t,0,2},ViewVertical->{-1,0,0}] -- Helen Read University of Vermont

**References**:**v.6 RevolutionPlot3D***From:*Helen Read <read@math.uvm.edu>