Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: B-spline-like bases for $C^2$ cubics on the Powell-Sabin 12-split   For spaces of constant, linear, and quadratic splines of maximal smoothness
on the Powell-Sabin 12-split of a triangle, the so-called S-bases were recently
introduced. These are simplex spline bases with B-spline-like properties on the
12-split of a single triangle, which are tied together across triangles in a
B\'ezier-like manner.
  In this paper we give a formal definition of an S-basis in terms of certain
basic properties. We proceed to investigate the existence of S-bases for the
aforementioned spaces and additionally the cubic case, resulting in an
exhaustive list. From their nature as simplex splines, we derive simple
differentiation and recurrence formulas to other S-bases. We establish a
Marsden identity that gives rise to various quasi-interpolants and domain
points forming an intuitive control net, in terms of which conditions for
$C^0$-, $C^1$-, and $C^2$-smoothness are derived.

16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio