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Parametric Plot and Extracting Plot Points.
 To: mathgroup at smc.vnet.net
 Subject: [mg7768] [mg7768] Parametric Plot and Extracting Plot Points.
 From: Alistair.Windsor at vuw.ac.nz (Alistair.Windsor at vuw.ac.nz)
 Date: Tue, 8 Jul 1997 14:36:53 0400
 Cachepostpath: totara.its.vuw.ac.nz!unknown@windsora.slip.vuw.ac.nz
 Organization: Victoria University of Wellington, New Zealand
 Sender: ownerwrimathgroup at wolfram.com
Recent discussion of how to extract plotting points has just proved to be
of more than passing interest to me. The problem was to convert the
numerical solution of system of three ODEs into a set of points which
were then outputted to a file. The file was to be used to render the
solution using POVray. Evenly spacing the points seemed a relatively
lowtech way of outputting the data so I got ParametricPlot3D to do a plot
so that I could extract the points. I figured that the ParametricPlot3D
routine would choose the points more intelligently than simply evenly
spacing them.
The interesting part arose when I went to extract the points. Rather than
a single Line[ ] as I had expected (the ODE solution is a continuous curve
called the Rossler Band) there were multiple Line[] primitives in the
graphics directives. A Line directive would finish and then another start
with the same point as at the end of the the last. This would have been
simply an interesting observation except that one of the programs involved
in my rendering objected to primitives like a zero length cylinder. Thus I
had to eliminate the extra points. This is not a problem though it brings
up an interesting question in the process.
Now my question is why did ParametricPlot3D have these multiple Line[]
directives? Is there a limit on the number of points in a line?
It is interesting you cannont assume that the ouput of a ParametricPlot of
curve consists of a single Line[] directive even when you that the curve
is continuous.

Alistair Windsor
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