Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Consistent digital line segments   We introduce a novel and general approach for digitalization of line segments
in the plane that satisfies a set of axioms naturally arising from Euclidean
axioms. In particular, we show how to derive such a system of digital segments
from any total order on the integers. As a consequence, using a well-chosen
total order, we manage to define a system of digital segments such that all
digital segments are, in Hausdorff metric, optimally close to their
corresponding Euclidean segments, thus giving an explicit construction that
resolves the main question of Chun et al.

20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn