Efficient determination of orientable manifold polygon meshes

Many polygon mesh processing methods, including compression methods like the Edgebreaker and the Dual- Degree algorithms, require the input mesh to be an orientable 2-manifold. A polygon mesh is orientable if all faces in the mesh have compatible orientations and is 2-manifold if there is a unique face-fan around each vertex in the mesh. Based on these definitions, we developed an efficient algorithm to determine whether a polygon mesh - or any of its connected components (CCs) - is an orientable 2-manifold: the orientability is determined by checking if there are duplicated half-edges in the mesh or CC, and the manifoldness is determined by checking if there is a unique face-fan around each vertex in the mesh or CC. To show its effectiveness in polygon mesh compression, we applied the proposed method to adaptively select connectivity coding algorithms for different CCs in the input mesh. The candidate algorithms for selection are the dual-degree algorithm, which assumes the input mesh or CCs being 2-manifold, and the polygon-fan algorithm, which does not require the manifold assumption. For evaluation, we used the test dataset from the Call for Proposals on Static Polygonal Mesh Coding technology organized by the Volumetric Visual Media Working Group of the Alliance for Open Media. The experimental results show that the proposed method achieved an average total coding gain of 2.11%.