What I did this week<br>==================<br>* Finished coding of mirrored unwrap. Leftover of week was spent studying isomap papers, linear algebra and libraries.<br>Initially, this paper was considered, due to its claimed superiority over isomap: <br>
<br><a href="http://mypage.iu.edu/%7Emtrosset/Courses/675/lle.pdf" target="_blank">http://mypage.iu.edu/~mtrosset/Courses/675/lle.pdf</a><br>
<br>However, it looks like this won't work well with non-uniform density of input points (==vertices in 3d graphics).<br>
<br><a href="http://en.wikipedia.org/wiki/Nonlinear_dimensionality_reduction" target="_blank">http://en.wikipedia.org/wiki/Nonlinear_dimensionality_reduction</a><br><br>Non uniform density of input points is quite common in 3D graphics, actually it's the norm..<br>
<br>Looks like the original isomap <br><br><a href="http://web.mit.edu/cocosci/Papers/sci_reprint.pdf" target="_blank">http://web.mit.edu/cocosci/Papers/sci_reprint.pdf</a><br><br>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). <br>
<br>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.<br>
<br>Next week<br>==========<br>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.<br>
<br><br>Problems so far<br>=============<br>The theoretical problems outlined above.<br>