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Parametric Plot and Extracting Plot Points.
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