Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Curvature line parametrized surfaces and orthogonal coordinate systems.
  Discretization with Dupin cyclides   Cyclidic nets are introduced as discrete analogs of curvature line
parametrized surfaces and orthogonal coordinate systems. A 2-dimensional
cyclidic net is a piecewise smooth $C^1$-surface built from surface patches of
Dupin cyclides, each patch being bounded by curvature lines of the supporting
cyclide. An explicit description of cyclidic nets is given and their relation
to the established discretizations of curvature line parametrized surfaces as
circular, conical and principal contact element nets is explained. We introduce
3-dimensional cyclidic nets as discrete analogs of triply-orthogonal coordinate
systems and investigate them in detail. Our considerations are based on the Lie
geometric description of Dupin cyclides. Explicit formulas are derived and
implemented in a computer program.

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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con