@CONFERENCE\{IMM2003-02525,
author = "H. Aan{\ae}s and J. A. B{\ae}rentzen",
title = "Pseudo--Normals for Signed Distance Computation",
year = "2003",
booktitle = "Vision, Modeling, and visualization 2003, Munich, Germany",
volume = "",
series = "",
editor = "",
publisher = "",
organization = "",
address = "",
url = "http://www2.compute.dtu.dk/pubdb/pubs/2525-full.html",
abstract = "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."
}