Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterisation of rational and NURBS developable surfaces in Computer
  Aided Design   In this paper we provide a characterisation of rational developable surfaces
in terms of the blossoms of the bounding curves and three rational functions
$\Lambda$, $M$, $\nu$. Properties of developable surfaces are revised in this
framework. In particular, a closed algebraic formula for the edge of regression
of the surface is obtained in terms of the functions $\Lambda$, $M$, $\nu$,
which are closely related to the ones that appear in the standard decomposition
of the derivative of the parametrisation of one of the bounding curves in terms
of the director vector of the rulings and its derivative. It is also shown that
all rational developable surfaces can be described as the set of developable
surfaces which can be constructed with a constant $\Lambda$, $M$, $\nu$ . The
results are readily extended to rational spline developable surfaces.

29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics