A Generic Halfedge Mesh Data Structure for .Net

Polygonal meshes are used extensively in computer graphics. A polygonal mesh represents a shape, usually in 3D, by using a set of points, the vertices, connected by edges. Edges form the boundaries of faces. A mesh is convenient to work with because it explicitly represents the surface that one is working with—vertices, edges, and faces are discreetly enumerated and may be manipulated directly. Meshes are often stored by simply keeping a list of points with a list of faces, where each face is a list of vertices, and each vertex of a face is an index into the list of points. While this is simple to implement and manage, many common operations are slow and awkward. It is common to iterate over the neighbors of a mesh element—for example, to compute smooth contours in non-photorealistic rendering, it is necessary to examine faces adjacent to a face to trace contour chains. Another problem is that this mesh representation does not explicitly represent edges. For polyhedral contour rendering, it is necessary to iterate over all edges in a mesh. It is not immediately clear how one would do this without visiting the edges of every face, which means that each edge of a closed manifold mesh would be visited twice.