On Oct 16, 2009, at 1:17 PM, kcrisman wrote: > On Oct 16, 2:29 pm, Francois Maltey <fmal...@nerim.fr> wrote: >> Hello, >> >> Functions plot is fine with singular functions as >> >> plot (sin(1/x), x, 0, 5) >> >> Plot has also a symbolic option detect_poles=True. >> But this option isn't designed for theses plots. >> There are unpleasant vertical lines. >> >> plot (floor(10*x), x, 0, 2) >> plot (x*floor(1/x), x, 0, 2) >> plot (arctan ((tan(x)^2-1)/(2*tan(x)), x, 0, 2) > > These are cool examples! I believe there is an 'exclude points' > option in the pipeline, though I can't remember the Trac number. > >> I don't think it's too hard to compute about one function call per >> pixel, >> and then the mathematic are more respected ! > > Well, that's easier said than done - how many points is a pixel? The > plotting code doesn't say anything about pixels, I don't believe, and > setting ridiculously large tolerances is kind of fun to understand how > the code works. In general this algorithm does pretty well, though > plotting tan(x) is annoying still, if you want to fix that without > using show options. > >> It's not pleasant to build a large list of points and then plot >> theses >> points (and not the polygonal line) because the speed isn't >> constant for >> any curves. > > I'm not sure what you mean. Are you suggesting we use some sort of > curved primitives?
One needs to be very careful with this, as an interpolated curve may give false maximums, etc. Safer to stay with lines--there should be enough of them that it looks smooth anyways. Also, some functions are cheap to compute, but others not so much. > A line with that many points is indistinguishable > from a curve (which Archimedes wouldn't have liked, but some other > Greeks argued), at least in a plot. > > I think the real issue is that you don't want (nearly) vertical lines > in step-type functions, and this is a legitimate point of contention. > I think that at least on this side of the pond, step functions with > vertical lines are considered a legitimate representation of the > function. However, perhaps that should be revisited? Certainly the > graphs plot produces in such situations look like not the graphs of > functions, in a technical sense. However, note that the list of > points almost assuredly does not actually violate the vertical line > test! > > Opinions from others? It's very difficult to (numerically) distinguish between sage: plot(atan(x), (x, -1e6, 1e6)) and sage: plot(floor(atan(x)), (x, -1e6, 1e6)) Also, the current behavior leads to more correct (IMHO) pictures of, say sage: plot(sin(1/x), (x, -1, 1)) - Robert --~--~---------~--~----~------------~-------~--~----~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
