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piecewise plotting of curves
*To*: mathgroup at smc.vnet.net
*Subject*: [mg20421] piecewise plotting of curves
*From*: "Kai G. Gauer" <gauer at sk.sympatico.ca>
*Date*: Tue, 26 Oct 1999 00:33:06 -0400
*Sender*: owner-wri-mathgroup at wolfram.com
Your email almost gave me an idea, but I'm not sure if this would work
too easily or if it can easily be reproduced in more generalized terms.
Define a subfunction that looks at which intervals that you find it
unnecessary to plot at, cut it in to those three or four or five regions
of piecewise defined curves (or however many pieces of a curve that you
actually have), use a sort of list plot idea for each piecewise defined
interval (since they'll all occur in one unique bounding box, I don't
think you you'll have to worry about resizing your curves for two
distinct pieces of your curves.) The way I thought that I might try to
get around the idea of piecwising your curve would be to just colour
your unwanted pieces of your curve equal to white (or whatever it is
that assigns a curve colour to white. Then, you'll have your favorite
coloured curve and a few pieces of curves that may or may not appear
transparent when going to plot this curve. I'm not sure, though, if one
could get away without having to write some small bit of coding fcn that
plots your piecewise functions piece by piece all going to the same
bounding box
I hope that this idea may help.
Does anone know if this same idea would work for other singularities (ie
asymptotes, but, maybe for asymptotes, we'd want to plot a dashing line
in place of the error being plotted)? How easily can we supress these
errata and overwrite them with better looking graphics? By attempting to
supress these sorts of errata, could we also guarantee that the "normal"
areas of the curve will also plot nicely? ie. in some cases, it has just
given me a blank plot screen (most of the time, because I chose the
wrong sized interval. If I could expand/contract the size of the
interval after the graphics primitive has been completely rendered to
the screen, I for one would be a much happier programmer. One of the
reasons that I like to use animate or a do loop is so that I don't have
to do 50 similar renderings of the same curve and keep on retyping plot,
plot, etc and waiting minutes on end in between while Mathematica mainly
does graphics plot checking tests to find out if/when I've picked a good
interval.
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