Pseudo--Normals for Signed Distance Computation

The face normals of triangular meshes have long been used to determine whether a point is in- or outside of a given mesh. However, since normals are a differential entity they are not defined at the vertices and edges of a mesh. The latter causes problems in general algorithms for determining the relation of a point to a mesh. At the vertices and edges of a triangle mesh, the surface is not \$C\^1\$ continuous. Hence, the normal is undefined at these loci. Thürmer and Wüthrich proposed the \$\backslash\$emph{angle weighted pseudo--normal} as a way to deal with this problem. In this paper, we undertake showing that the angle weighted pseudo--normal has an important property, namely that it allows us to discriminate between points that are inside and points that are outside the mesh. This result is used for proposing a simple and efficient algorithm for computing the signed distance field from a mesh. Moreover, our result is an additional argument for the angle weighted pseudo--normals being the natural extension of the face normals.