Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Incremental and Transitive Discrete Rotations   A discrete rotation algorithm can be apprehended as a parametric application
$f\_\alpha$ from $\ZZ[i]$ to $\ZZ[i]$, whose resulting permutation ``looks
like'' the map induced by an Euclidean rotation. For this kind of algorithm, to
be incremental means to compute successively all the intermediate rotate d
copies of an image for angles in-between 0 and a destination angle. The di
scretized rotation consists in the composition of an Euclidean rotation with a
discretization; the aim of this article is to describe an algorithm whic h
computes incrementally a discretized rotation. The suggested method uses o nly
integer arithmetic and does not compute any sine nor any cosine. More pr
ecisely, its design relies on the analysis of the discretized rotation as a
step function: the precise description of the discontinuities turns to be th e
key ingredient that will make the resulting procedure optimally fast and e
xact. A complete description of the incremental rotation process is provided,
also this result may be useful in the specification of a consistent set of
defin itions for discrete geometry.

24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int