Converting sets of polygons to manifold surfaces by cutting and stitching

Abstract

Many real-world polygonal surfaces contain topological singularies that represent a challenge for processes such as simplification, 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, multiply singular vertices, 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 manifold. We study two different stitching strategies called `edge pinching' 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 geometry). 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.