Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Certified Approximation of Parametric Space Curves with Cubic B-spline
  Curves   Approximating complex curves with simple parametric curves is widely used in
CAGD, CG, and CNC. This paper presents an algorithm to compute a certified
approximation to a given parametric space curve with cubic B-spline curves. By
certified, we mean that the approximation can approximate the given curve to
any given precision and preserve the geometric features of the given curve such
as the topology, singular points, etc. The approximated curve is divided into
segments called quasi-cubic B\'{e}zier curve segments which have properties
similar to a cubic rational B\'{e}zier curve. And the approximate curve is
naturally constructed as the associated cubic rational B\'{e}zier curve of the
control tetrahedron of a quasi-cubic curve. A novel optimization method is
proposed to select proper weights in the cubic rational B\'{e}zier curve to
approximate the given curve. The error of the approximation is controlled by
the size of its tetrahedron, which converges to zero by subdividing the curve
segments. As an application, approximate implicit equations of the approximated
curves can be computed. Experiments show that the method can approximate space
curves of high degrees with high precision and very few cubic B\'{e}zier curve
segments.

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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th