Smoothing/Relaxation battery tests

This end of the year /new year will be full of surprises and good news … I hope that. 😉

Regarding Unlimited clay I have very good news and also a new development surprise in the particles simulation field … but sorry, you will have to wait a bit more for that ;), as I have a very low bandwith and in order to upload a new video I have to do wonders to shrink and split it in dozens of parts and send it by email to my friend Lapinou  … so new videos are staking here 😦 (lapinou’s note: finally uploaded!)

It’s now the turn of the test smoothing/relaxation algorithm I have been developing last week:

Three smoothing/relaxation algorithms are currently implemented in Blender (not counting the subdivision surfaces because it changes topology but the output of that algorithm is also a smooth surface) the smooth vertex editmesh tool, the relax addon and the UV Minimize stretch tool. I want to point out that there´s not the ideal relaxation algorithm valid
for every object: every relaxation scheme has advantages and drawbacks over others and are more or less suited for the task.

The smooth vert algorithm is an all around average solution, it performs a laplacian relaxation in the field and while is a very stable method it suffers from an excessive shrinkage effects of the shapes. The relax addon tries to solve the shrinkage issue and is very good on that, but it’s somehow slower since it’s based on shrinkwrap and laplacian smoothing.

The UV minimize stretch tool performs a different relaxation: it’s based on smoothing angles, not edges, and while it’s very useful for many cases, it’s not valid for others (see my test video).

Currently I have implemented four algorithms more (eventually I will only stay with two of them only)

1) edge – spring relaxation: it acts push/pulling verts of the mesh based on elastic forces , very good on retaining original shape much with no shrinkage, is very similar to other cases but have some ill outputs.

2) revised ideal length relaxation: this is very similar to the spring relaxation and acts in a similar fashion, without many of the ill cases that affect the former.

3) revised laplacian relaxation: this one, based on the original laplacian, is also an all around good average solution but with zero shrinkage and much more faster/cheaper than the relaxation addon since it doesn´t perform shrinkwrap evaluations.

4) HC – relaxation: taken from the paper “Improved Laplacian Smoothing of Noisy Surface Meshes” this one again is based on the laplacian relaxation with a shrinkage component but very small and needed in the reconstruction cases, this algorithm is very good on smoothing and shape retaining at the same time.

All the previous algorithms have boundary/open mesh detections to avoid shape deformation but again that is an optional user feature. In general, every smoothing algorithm perform a tradeoff between smoothing and shape retention: the more the shape is maintained the less it is smoothed and vice versa, the first three are aimed to shape retention, while the fourth is aimed in the middle, to retain shape and to smooth at the same time.

I have made a new video test, this time with a wider battery tests and all the smoothing algoritms, since I haven´t implemented yet for UV I replicate a mesh with a Suzanne´s UV to get an idea of how it may work. Please be a little patient since this may take me very long to upload.

All the best
Farsthary