[Soc-2012-dev] GSOC 2012 Texture/UV tools development week 9 report

[Antony Riakiotakis]

What I did this week
==================
* Finished coding of mirrored unwrap. Leftover of week was spent studying
isomap papers, linear algebra and libraries.
Initially, this paper was considered, due to its claimed superiority over
isomap:

http://mypage.iu.edu/~mtrosset/Courses/675/lle.pdf

However, it looks like this won't work well with non-uniform density of
input points (==vertices in 3d graphics).

http://en.wikipedia.org/wiki/Nonlinear_dimensionality_reduction

Non uniform density of input points is quite common in 3D graphics,
actually it's the norm..

Looks like the original isomap

http://web.mit.edu/cocosci/Papers/sci_reprint.pdf

can overcome some of these problems due to its global computation nature
(actually it performs based on edge lengths instead of simply on
barycentric weights).

So, after reading up on this paper, it seems I need to use an eigenvalue
solver. opennl, that is currently used in blender does not support
eigenvalue decomposition, however, eigen, that is also used does. It looks
like I will be able to produce code that works with eigen with a small
caveat: I don't know how pinned uv support can happen in eigen. We use some
kind of opennl functionality that locks variables for ABF that is missing
in eigen. Any ideas or support there is extremely welcome.

Next week
==========
I will make a first prototype of the unwrapper that doesn't support
pinning. I hope to refactor the equations to somehow do this. One idea is
to map the eigenvalue problem to a linear problem however my linear algebra
skill is somewhat lacking.


Problems so far
=============
The theoretical problems outlined above.
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