On Tue, Aug 23, 2011 at 12:36 AM, Mike Solomon <mike...@ufl.edu> wrote: > On Aug 23, 2011, at 6:55 AM, joenee...@gmail.com wrote: > >> >> http://codereview.appspot.com/4860042/diff/1/lily/bezier.cc >> File lily/bezier.cc (right): >> >> http://codereview.appspot.com/4860042/diff/1/lily/bezier.cc#newcode239 >> lily/bezier.cc:239: return p.minmax (sol[LEFT][0], sol[RIGHT][0], d != >> LEFT); >> On 2011/08/19 07:03:50, MikeSol wrote: >>> On 2011/08/18 21:36:45, joeneeman wrote: >>> > If there are multiple intersections with (say) r, then >> Polynomial::solve >>> doesn't >>> > seem to return them in any useful order. So sol[RIGHT][0] is really >> just an >>> > arbitrary solution, isn't it? >> >>> True, but this seems no worse than line 81 where ts[0] is returned. >> Not that >>> this is a good excuse... >> >> Right, but what really bothers me is that you're then using >> sol[RIGHT][0] as though it means something. So what this function seems >> to do (suppose ax=X_AXIS) is to take an arbitrary point where the curve >> intersects x=r and an arbitrary point where the curve intersects x=l and >> then finds the maximum y value of the curve between those two points. > > True. > A well-formed slur should never retrograde along the X-axis, and thus, the > size of sol[LEFT] and sol[RIGHT] should be 1 after filtering out all values > less than 0 and greater than 1. > I think that the programming errors in the current patch should do the trick.
Is it so difficult to just make the solution general? Assuming axis is Y_AXIS and d is UP, the maximum must appear either at a critical point of the y-axis polynomial or when the x-axis polynomial is equal to either l or r. You can filter the critical points to make sure the x coordinate is within the correct interval, and then filter everything to make sure that the parameter is between 0 and 1. You'll have no more than 8 points left and you take the one with the largest Y coordinate. I realize that it's unlikely to trigger, at least in the way that Lilypond currently uses this code, but I do feel that code in a file called bezier.cc should work for bezier curves in general. Cheers, Joe _______________________________________________ lilypond-devel mailing list lilypond-devel@gnu.org https://lists.gnu.org/mailman/listinfo/lilypond-devel
