[diagrams] diagrams status
Brent Yorgey
byorgey at seas.upenn.edu
Fri Aug 20 12:39:17 EDT 2010
On Fri, Aug 20, 2010 at 12:23:03PM -0400, Ryan Yates wrote:
> Oops I forgot to reply all:
>
> Hmm, interesting idea. Sort of like what we currently do to keep
> > track of inverse transformations.
> >
> >
> Right, in fact I realized recently that a lot of people run into a similar
> issue when doing non-uniform transformations on 3D objects that that have
> explicitly set normals. I searched around some and found [1] which uses the
> transpose of the inverse of the transformation. I haven't had time to work
> up any tests but we *could* get the transpose by converting to a matrix
> (transform with each basis vector to get the matrix) and then transposing
> that but it seems like it would be pretty ugly and I don't know if that
> holds for higher than 3 dimensions.
>
> [1] http://www.unknownroad.com/rtfm/graphics/rt_normals.html
Interesting, I look forward to hearing more. Yes, getting a matrix
out can be done but it is a bit ugly.
>
>
> > Here's a somewhat related idea I just had. Currently we represent
> > bounding regions by a function which given a vector, tells you how far
> > you have to go in that direction to reach an enclosing hyperplane
> > (call this function h, for Hyperplane). Consider instead a function e
> > (for Envelope) which given a vector, tells you how far you have to go
> > in that direction to reach the edge of the bounding region itself.
>
>
> e should be much easier to transform under any sort of transformation
> > at all. But h is rather nice for other reasons (placing diagrams next
> > to one another using e seems very difficult; using h it is a snap).
> > However, given e (or e plus some extra information which is also easy
> > to maintain under transformations) can we easily recover h? Perhaps
> > using some sort of automatic differentiation? Essentially to compute
> > h from e we are doing some sort of maximization I think.
> >
>
> So something like h v will be the maximum of e v and the dot product of v
> with all inflection/first derivative undefined points? I'll have to think
> about that.
Yeah, something like that.
> P.S. I think I'm going to be going to the Haskell Symposium. Anyone else
> going?
I'll be there (I'm actually presenting a paper! =) I look forward to
meeting you.
-Brent
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