Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction of $G^2$ planar Hermite interpolants with prescribed arc
  lengths   In this paper we address the problem of constructing $G^2$ planar
Pythagorean--hodograph (PH) spline curves, that interpolate points, tangent
directions and curvatures, and have prescribed arc-length. The interpolation
scheme is completely local. Each spline segment is defined as a PH biarc curve
of degree $7$, which results in having a closed form solution of the $G^2$
interpolation equations depending on four free parameters. By fixing two of
them to zero, it is proven that the length constraint can be satisfied for any
data and any chosen ratio between the two boundary tangents. Length
interpolation equation reduces to one algebraic equation with four solutions in
general. To select the best one, the value of the bending energy is observed.
Several numerical examples are provided to illustrate the obtained theoretical
results and to numerically confirm that the approximation order is $5$.

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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
3
The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio