Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the one method of a third-degree bezier type spline curve
  construction   A method is proposed for constructing a spline curve of the Bezier type,
which is continuous along with its first derivative by a piecewise polynomial
function. Conditions for its existence and uniqueness are given. The
constructed curve lies inside the convex hull of the control points, and the
segments of the broken line connecting the control points are tangent to the
curve. To construct the curve, we use the approach proposed earlier for
constructing a parabolic spline. The idea is to use additional points with
unknown values of some function. Additional points are used as spline nodes,
and the function values are determined from the condition of the first
derivative continuity of a piecewise polynomial curve. In multiple
interpolation nodes, the function takes the given values and the values of the
first derivative, which are determined by the control points. Examples of
constructing a spline curve are given.

30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex