# Tangential Distance Field Methods

We introduce a novel class of distance ﬁelds for a given surface based on tangent-space representations. At each point in space, we assign a scalar value which is a weighted sum of distances to the tangent planes of the surface. We call the resulting scalar ﬁeld a tangential distance ﬁeld or TDF. When applied to triangle mesh models, the tangent planes become supporting planes of the mesh triangles. The weighting scheme used to construct a TDF for a given mesh and the way the TDF is utilized can be closely tailored to a speciﬁc application. At the same time, the TDFs are continuous, lending themselves to standard optimization techniques, such as greedy local search, thus leading to efﬁcient algorithms.