Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamic evaluation of exponential polynomial curves and surfaces via
  basis transformation   It is shown in "SIAM J. Sci. Comput. 39 (2017):B424-B441" that free-form
curves used in computer aided geometric design can usually be represented as
the solutions of linear differential systems and points and derivatives on the
curves can be evaluated dynamically by solving the differential systems
numerically. In this paper we present an even more robust and efficient
algorithm for dynamic evaluation of exponential polynomial curves and surfaces.
Based on properties that spaces spanned by general exponential polynomials are
translation invariant and polynomial spaces are invariant with respect to a
linear transform of the parameter, the transformation matrices between bases
with or without translated or linearly transformed parameters are explicitly
computed. Points on curves or surfaces with equal or changing parameter steps
can then be evaluated dynamically from a start point using a pre-computed
matrix. Like former dynamic evaluation algorithms, the newly proposed approach
needs only arithmetic operations for evaluating exponential polynomial curves
and surfaces. Unlike conventional numerical methods that solve a linear
differential system, the new method can give robust and accurate evaluation
results for any chosen parameter steps. Basis transformation technique also
enables dynamic evaluation of polynomial curves with changing parameter steps
using a constant matrix, which reduces time costs significantly than computing
each point individually by classical algorithms.

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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: supr-con
7
The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
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The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph