> > >>> I don't know the best way to be "smart" about fixing this such as how > >>> much of the asymptote to include, etc. > >> Yeah, I was thinking about this, because what you would really want to > >> do is have an algorithm which would automatically check if the 'bend' > >> was too great compared to the rest of the function and then NOT plot > >> the line connecting those points. But would that slow plotting down > >> too much (since you'd have to compare *all* the bends to each other, > >> not just to max_bend like in adaptive refinement, as I understand > >> it)? Not to mention trying to decide what "too great compared" means. > > > It might be easier to detect a root in 1/f(x) (or some kind of > > heuristic given a sign change between f(a) and f(b), is a root of f > > (x) or 1/f(x) more likely).
Thanks for your thoughts, Jason. > > Another thing: does the adaptive plotting code handle asymptotes > intelligently? That is, when it picks one point on either side of an > asymptote, it seems like it would try to recursively subdivide unless it > knows there is an asymptote there or can somehow guess there is an > asymptote. > Not currently, that's for sure, but combined with Robert's idea it might be a good starting point, given this snippet of the result of the xdata: sage: P=plot(tan,-5,5); list=P[0].xdata;len(list) 1201 sage: list <snip> -4.7260837325003902, -4.7260666712822843, -4.7260496100641793, -4.7260325488460744, -4.7260154876279685, -4.7259984264098627, -4.7259813651917577, <snip> -0.10341837811481863, -0.03500403414505103, -0.010279622543906589, 0.069496699401952633, 0.10646492301295057, 0.13438881092313087, 0.20201941119890751, Interesting that Mma includes the "asymptotes", but that they really look like asymptotes given that it intelligently chooses the ymin and ymax. That could be another way to go. - kcrisman --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
