# Which mathematical criteria can I use to check either a surface is homeomorphic to a disk?

I'm currently working on 3D mesh segmentation.

And I want the segmented parts obtained to be homeomorphic to a disk (I mean easily unfoldable, so that we can map it as a 2D part without any points overlaping).

I have read a lot of papers on the subject, most of them talk about this homeomorphism to 2D disk, but none of them show how to prove it, or how to do it.

SO I really don't know what can I use on this surface to check if it is conformal to what I want.

Is there any formula using the points, the erea or the normals, or any criteria that shows that a given surface is topologycaly equivalent to disk?

Thank you all.

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Doesn't it suffice to check that your mesh has only one boundary curve? – lhf Apr 28 '11 at 19:16
1 boundary component + Euler characteristic equal to $1$ – user8268 Apr 28 '11 at 19:23
How about connected and Euler-Characteristic 1 – Alexander Thumm Apr 28 '11 at 19:26
thanks all of you guys ;) – Gatsu Apr 28 '11 at 20:27