Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Building geometrically continuous splines   With the renewed and growing interest in geometric continuity in mind, this
article gives a general definition of geometrically continuous polygonal
surfaces and geometrically continuous spline functions on them. Polynomial
splines defined by G1 gluing data in terms of rational functions are analyzed
further. A general structure for a spline basis is defined, and a dimension
formula is proved for spline spaces of bounded degree on polygonal surfaces
made up of rectangles and triangles. Lastly, a comprehensive example is
presented, and practical perspectives of geometric continuity are discussed.
The whole objective of the paper is to put forward a modernized, practicable
framework of modeling with geometric continuity.

10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph