[diagrams] diagrams status

[Brent Yorgey]

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