Having listened to the rest of the conversation, I have chosen to reply
to my own message:
On Thu, 2004-04-22 at 07:59, James Amundson wrote:
> I think we should definitely print a warning when a singularity is
> encountered in the 3d plotting routines. After that, I see three
> options:
>
> 1) Replace the singular point with a large positive value. Since the
> singularity may have been -infinity, this answer could be maximally
> wrong. (The "singularity" could also be sqrt(-1). A large positive value
> isn't a very useful marker for that, either.)
>
> 2) Replace the singular point with 0.0. Roughly the same issues as (1).
>
> 3) Try to leave the point out of the plot. With gnuplot, at least, this
> makes a strange 3d plot.
>
> 4) Print an error message and stop.
>
> I'm not sure what to do here.
First of all, I notice that I can't count to four. ("I see three
options...")
I now think we should choose (4). Here is my reasoning:
1) Plotting functions with singularities is difficult.
2) Research has been done on this problem, so it doesn't make sense to
implement some half-baked impromptu solution.
3) Even if we choose a satisfactory algorithm, I don't think the plot
tools we are presently using (i.e., gnuplot) are up to the challenge of
plotting the results we want. Surfaces with missing areas, uneven grids,
etc., are not satisfactorily handled.
The third point is really the show-stopper.
--Jim