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MathGroup Archive 1997

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Re: tubes

  • To: mathgroup at smc.vnet.net
  • Subject: [mg6235] Re: [mg6204] tubes
  • From: Xah Lee <xah at best.com>
  • Date: Fri, 28 Feb 1997 03:22:07 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

At 7:54 AM -0000 2/27/97, arbobyar wrote:
>...
>I have defined a function
>that creates a circle in the XZ plane. I would like to show how this
>function varies (either parametrically or incrementally) along Y by
>variations in position and size of the XZ plots. The result should be a
>tube (or cylinder...) parallel to the Y axis. I can plot a series of
>circles along Y to show this, but I would prefer to stretch a skin over
>those circles, i.e., to define a surface.
>...

You might look at my package RuledSurfacePlot.m, available at MathSource <http://www.mathsource.com> or my site <http://www.best.com/~xah/SpecialPlaneCurves_dir/specialPlaneCurves.html>

The package will not solve your problem directly, but may work as a module in your solution. Use RuledSurfacePlot to plot the strip connecting two consetive circles. Repeatedly apply this to build your tube.

If you wish to write you own strip function, here's the outline:

suppose

cir1={p1, p2, p3, ...p1}

cir2={q1, q2, q3,...,q1}

where cir1 and cir2 are two consecutive circles in your problem, and p...,q.... are points on the circles. You want to construct a list of Polygon graphics object that looks like

{Polygon[{p1,p2,q2,q1}],Polygon[{p2,p3,q3,q2}],..}

This you can easily do with Transpose, MapThread, Map, RotateRight, or a combo of these.

 Xah  (available for remote Mathematica consulting work)
 xah at best.com
 http://www.best.com/~xah/SpecialPlaneCurves_dir/specialPlaneCurves.html
 Mountain View, CA, USA




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