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binsansballs

gaussian curvature on a 3D mesh

4 posts in this topic

Hi all,

I need obtaining the gaussian curvature for a 3D mesh (stored in a .obj file).
I looked for some code online, but without finding anything useful.

Any hint -- an already existing implementation or some suggestions for starting writing a code by myself?
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MeshLab appears to have support for [i]mean[/i] curvature: http://meshlabstuff.blogspot.nl/2010/03/mean-curvature-cavity-map-zbrush-and.html

Not sure how similar that is but it's open source and may be a starting point...
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Actually, MeshLab seems to support also gaussian curvature...
And Gaussian curvature calculated on my 3D model, rendered in MeshLab, looks fine.

I'm totally new to MeshLab so, I was wondering if it would be possible to export by an obj file the model just rendered in MeshLab.
In other words, I'd like to export an obj file where the texture corresponds to the gaussian curvature values just calculated -- not to the original
texture map of the scan.
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http://en.wikipedia.org/wiki/Defect_(geometry)

http://en.wikipedia.org/wiki/Gauss-Bonnet_theorem

If you feel like getting to the heart of it on your own. In order to figure out the curvature at a vertex you'll need to have the adjacency data for your mesh, which I'm pretty sure is not something that an OBJ file contains, so you'd have to do that yourself. Once you do that, and know how to calculate the curvature, you'll be pretty knowledgable and you'll be able to figure out all kinds of other cool things. It's tough the first time around, but there are lots of people here who can help if you get stuck.

P.s. that 1st link is mangled, sorry. Just search for "defect geometry" on Wikipedia, I guess. Basically you need to get all triangles associated with a vertex, then loop through them and add up the total angle at that vertex. If the angle is 2pi, then there is no "curvature" at that vertex (the triangles are all coplanar)... If not, then it's "curved" at that vertex. Repeat for all vertices.
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