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piecewise plotting of curves
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.