Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of a method to parameterize planar curves immersed in
  triangulations   We prove that a planar $C^2$-regular boundary $\Gamma$ can always be
parameterized with its closest point projection $\pi$ over a certain collection
of edges $\Gamma_h$ in an ambient triangulation, by making simple assumptions
on the background mesh. For $\Gamma_h$, we select the edges that have both
vertices on one side of $\Gamma$ and belong to a triangle that has a vertex on
the other side. By imposing restrictions on the size of triangles near the
curve and by requesting that certain angles in the mesh be strictly acute, we
prove that $\pi:\Gamma_h\rightarrow\Gamma$ is a homeomorphism, that it is $C^1$
on each edge in $\Gamma_h$ and provide bounds for the Jacobian of the
parameterization. The assumptions on the background mesh are both easy to
satisfy in practice and conveniently verified in computer implementations. The
parameterization analyzed here was previously proposed by the authors and
applied to the construction of high-order curved finite elements on a class of
planar piecewise $C^2$-curves.

30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat