Re: Motion on ``discontinuous'' decoration bit
On 08/30/2010 03:36 PM, Corliss, George wrote:
> P1788,
>
> For several days, there has been a VERY active discussion going on
> among several people, and it should be exposed to everyone.
> Unfortunately, you are being brought into the middle of the
> discussion, and I'm not willing to summarize all that has gone
> before. Basically, we have been discussing Motion on
> ``discontinuous'' decoration bit. Much of the discussion has been on
> decorations for the results of intersect(), union(), and hull(),
> which are NOT interval extensions of point functions.
The idea of continuity of an interval function over a given interval
is *very* important in many interval techniques, notably graphing
equations. If you can query a function to see if it is continuous over
over specific interval(s), you can perform extremely powerful
optimizations when graphing equations.
This brings to mind a very obvious person who should be part of this
standards effort: Jeff Tupper. I haven't seen his name in the
archives, and if he's not here, we need to invite him.
One of the best ways to demonstrate the power and superiority of
interval techniques is to use it to graph horrifically complicated
equations (a quick demonstration to show how simple the code can be to
graph arbitrarily-complicated equations can be found on my website at:
http://futureboy.us/fsp/simplegraph.fsp , the entire source of which is
available at:
http://futureboy.us/fsp/highlight.fsp?fileName=simplegraph.fsp
Jeff Tupper's program GrafEq is a wonderful demonstration of the
power of interval arithmetic for graphing functions:
http://www.peda.com/grafeq/
Especially see his "Rogues' Gallery" of equations that other software
packages that don't use interval arithmetic can graph drastically
incorrectly:
http://www.peda.com/grafeq/gallery/rogue.html
Hopefully everyone here has read his master's thesis on graphing
equations with interval arithmetic (which also compares affine
arithmetic and other techniques.) If you haven't read it, please do so.
http://www.dgp.toronto.edu/~mooncake/msc.html
Would one of the administrators be interested in inviting him? His
e-mail address is found on the page above.
--
Alan Eliasen
eliasen@xxxxxxxxxxxxxx
http://futureboy.us/