Hi,
This is a technical discussion between Robert and me involving
our work on jmol and 3d plotting in sage. I'm cc'ing to to sage-devel
in the interest of openness...
On Dec 17, 2007 11:21 AM, Robert Bradshaw <[EMAIL PROTECTED]> wrote:
>
> On Dec 17, 2007, at 11:02 AM, William Stein wrote:
>
> > On Dec 17, 2007 10:51 AM, Robert Bradshaw
> > <[EMAIL PROTECTED]> wrote:
> >> On Dec 16, 2007, at 4:31 PM, William Stein wrote:
> >>
> >>> Attached are some misc 3d plotting changes from my plane flight...
> >>>
> >>> I'm next going to work on making it so things like
> >>>
> >>> f = sin(x+y) - cos(y^2)
> >>>
> >>> have a
> >>>
> >>> f.fast_float_function()
> >>>
> >>> method that returns a fast callable float function. This will
> >>> making writing
> >>> doctests for 3d graphics much nicer (no funny math.sin or lambda or
> >>> def f(...) stuff).
> >>
> >> That's an excellent idea. If this is the bottle-neck, it might be a
> >> reason to cythonize some of the calculus expression classes (to
> >> render much smoother plots). Or we could do something like Tom
> >> Boothby's "compiled polynomial" stuff (maybe even re-using some of
> >> the same components).
> >
> > I have something vastly more straightforward and simple in mind
> > that will work in great generality, but doesn't involve Cython at all.
> > Basically just define for each object a way of returning a function
> > from float inputs to floats. For example, given sin(x) it would
> > literally
> > return math.sin, which evaluates quickly. For erf, it would return
> > the scipy float erf function.
> >
> > As a second step something like you suggest about involving Cython
> > may be very useful for optimizing the atomic functions in some cases.
> > But already what I suggest above will be a huge win, e.g.,
> >
> > plot(sin(x), 0, 1)
> >
> > will be made way faster if sin(x).fast_float_function() is called
> > first
> > and instead
> > plot(math.sin, 0, 1)
> > happens. That easily speeds things up by a factor of about 5.
> > With 3d this matters a *lot* more.
>
> I'm not sure how straightforward things will be with more than one
> variable, but with closures (e.g. creating and returning a function
> in the function body) it should still be possible to get vast
> improvements without using Cython at all. You're much more familiar
> with the calculus codebase than I am too.
That's the main thing I hope to do then.
>
> >> Any progress on rendering applets in the browser on page reload? I
> >> have an idea to try if you haven't solved that one yet.
> >
> > I haven't even tried. How about you work on that. If I'm about to
> > work
> > on something, I'll email you and let you know.
>
> Sure. I'm actually flying out tomorrow, so I'm running around doing a
> lot of miscellaneous things today, but I think I'll have time to work
> on this too.
>
I'm going shopping with relatives now, but we'll see... Maybe I'll
do more in my head than on computer today.
> > The *main* thing I plan
> > to do at this point is look carefully at how the user interface for
> > 3d plotting
> > in mathematica works, and work on coming up with some sane structure
> > for what Sage will do based on what you already wrote. This should
> > mainly
> > mean lots of examples (docstrings) and making small changes to
> > commands
> > like plot3d so that the examples are cleaner.
>
> Sounds good. I noticed you exposed plot3d.* to sage.all, so we need
> to get the interface beyond the toy stage. I'd also like to be able
> to pass pos/cen=(x,y,z) to shapes directly (but Cython doesn't have a
> __new__ function like Python does
Heck yeah! If we're going to make this happen for the AMS meeting
we need to just go for it.
> I was wondering why you added background to objects. If there are two
> objects with different backgrounds, what does it do? Should
> backgrounds be a plotting parameter (default white) instead?
Well I wanted the background to be white by default and wanted
to do this in a clean way. I think it was a mistake. Probably background
should be an option to show. Feel free to change it.
by the way, try it now and notice that the background is now white,
which looks much better.
Maybe you could think about some of these things:
(1) make the bounding box show up by default
(2) make the axes show up by default
(3) figure out how to get the sizes of things right
(4) text in figures
(5) get rid of the "jmol" logo in the lower right
(6) rewrite plot3d to be much more user friendly, i.e., work just
like Mathematica's plot3d.
(7) shading of meshes maybe looks funny? Thoughts.
(8) If I create plots using the current refresh stuff, after about
maybe 20 plots
the browser stops showing plots, and I *have* to restart the browser. Hopefully
your idea for a fix so that we don't do a refresh after displaying a plot
will fix this.
(9) Do you think there is any hope of resizing the output plot
dynamically in the browser? I added a
P.show(figsize=8)
say option to make the plot 800 pixes instead of 400. But it would
be nicer if like Mathematica one could resize the 3d java applet
after it is generated. I have no clue how to do this.
--William
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