test if a polygon-surface is closed (+ additional nice-to-have requirements)

I have a 3D object bounded by Polygons. Is there a standard algorithm that tests if the volume is closed e.g. no polygon is missing?

Example: I have a cube bounded by six squares. The algorithm should detect if one of those squares is missing.

It would be perfect, if also the minimal surface could be calculated to complement an existing (open) surface to a closed one.

It would be even more perfect if that minimal surface could be returned in terms of a minimal set of convex polygons.

• What data does the algorithm have to work with, in particular: how is the set of existing polygons given? – Klaus Draeger Oct 15 '13 at 14:51
• the (ordered) coordinates of the edges are given – Simon Fromme Oct 15 '13 at 21:15
• That's all I should add. Which polygon is linked to which, etc. is not specified. – Simon Fromme Oct 17 '13 at 2:39
• I suppose that this is what the algorithm would need to determine first, i.e. determine which edges are common to two of the polygons. Your object is closed iff this is the case for all edges. – Klaus Draeger Oct 17 '13 at 11:16