# [diagrams] diagrams status

Ryan Yates fryguybob at gmail.com
Fri Aug 20 12:23:03 EDT 2010

```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.

> 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