**comp.graphics.algorithms**

## 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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