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Many real-world polygonal surfaces contain topological singu- laries that represent a challenge for processes such as simplifica- tion, compression, smoothing, etc. We present an algorithm for removing such singularities, thus converting non-manifold sets of polygons to manifold polygonal surfaces (orientable if necessary). We identify singular vertices and edges, multipry singular ver- tices, and cut through singular edges. In an optional stitching phase, we join surface boundary edges that were cut, or whose endpoints are sufficiently close, while guaranteeing that the surface is a mani- fold. We study two different stitching strategies called "edge pinch- ing" and "edge snapping"; when snapping, special care is required to avoid re-creating singularities. The algorithm manipulates the polygon vertex indices (surface topology) and essentially ignores vertex coordinates (surface geom- etry). Except for the optional stitching, the algorithm has a linear complexity in the number of vertices edges and faces, and require no floating point operation. Key-words : Polygonal Surface, Manifold, Cutting, Stitching.

Converting sets of polygons to manifold surfaces by cutting and stitching