Re: Rotating a surface similar to a helix
- To: mathgroup at smc.vnet.net
- Subject: [mg118883] Re: Rotating a surface similar to a helix
- From: Peter <petsie at dordos.net>
- Date: Sat, 14 May 2011 03:07:39 -0400 (EDT)
- References: <iqj12v$reh$1@smc.vnet.net>
Am 13.05.2011 12:27, schrieb Bill:
> Rotating a surface similar to a helix
>
> Hi:
>
> I have the following 2D parametric plot, showing a parabola mirrored about the x axis, forming a closed curve.
>
> ParametricPlot[{{t,t^2-2},{t,-t^2+2}},{t,-1.41421,1.41421},PlotStyle->Red,Axes->True,AxesLabel->{x,y},PlotRange->{{-2.5,2.5},{-2.5,2.5}}]
>
> I'd like to show these curves in 3D as:
>
> ParametricPlot3D[{{t,t^2-2,u},{t,-t^2+2,u}},{t,-1.41421,1.41421},{u,0,6},Mesh->None,Axes->True,AxesLabel->{x,y,z},PlotRange->All,ViewPoint->{1.14,-1.85,5}].
>
> Ok, got that.
>
> The next thing that I'd like to do is to rotate the closed 3D cylinder, say 90 degrees. That is, the base would be at the 2D position plotted, and the top would be rotated 90 degrees. I'd like a smooth transition from the base to the top of the cylinder, like one see's with a helix.
>
> Question: How can I do that in a 3D plot?
>
>
> Thanks,
>
> Bill
>
Hi Bill,
using a rotaion-matrix seems a good idea to me:
ParametricPlot3D[Evaluate @ Apply[{##1, u} & ,
(RotationMatrix[(Pi*u)/(2*(umax = 6))] .
{t, #1*(t^2 - 2)} & ) /@ {-1, 1}, {1}],
{t, -Sqrt[2], Sqrt[2]}, {u, 0, umax}, Mesh -> None,
Axes -> True, AxesLabel -> {x, y, z},
PlotRange -> All]
Peter