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Subject: Mesh Correction Algorithm - Academic Question



Hi all,

I wondered if anybody had any suggestions, links to academic papers etc
about the following problem that I face as part of my research.

I am running an algorithm (which I can't really talk too much about)
which achieves the following. Given a set of lets say point cloud data
(points which are known to lie on a surface), my algorithm takes a
random triangular mesh and fits it to this data, such that on conclusion
of the algorithm the mesh represents the surface from which the range
data was taken. Now my algorithm achieves what I will describe as a good
representation of the surface.

However, two problems seem to arise,

1) In small areas, some faces of the mesh are such that the following
sort of thing has occurred. The vertices of these faces appear to
reasonable (i.e. sensibly position for the surface), however the faces
have what can best be described as collapsed ontop of each
other(Difficult to describe in text). So two faces lie across each
other. Now I could simply take the final vertex positions of all faces
and show how retriangulate the surface, but the vast majority of faces
are fine.

2) The concentration of vertices can be highly bunched in certain
localised areas, i.e. non even concentration across the face. I am not
looking for an even distribution, but in some areas that are fairly
planar they are really way too many vertices (and hence faces) which I
think is redundant information. Obviously areas of great variation in
surface need to be adequately represented.

Could anybody suggest a solution, for 1) some sort of retriangulate
certain problematic areas and 2) some sort of smoothing, to attempt give
a better overall surface likeness.

Visually the problem been at the moment, when I texture my final mesh it
can sometimes appear a little bumpy.

For 2) I have tried the Jacobi Laplace Smoother available through
OpenMesh (I know nothing really about mesh smoothing), but found that
this technique redistributed my vertices but also moved them such they
no longer represented the surface particularly well.

Now I understand this is hard to imagine in text alone and anybody
wanting to help I could send a mesh or picture if that made things clearer.

Any help would be much appreciated. I doubt anybody has the magic bullet
to this problem but a discussion / starting suggestions is what I really
need at this moment.

Adam

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