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\begin{document}

\title{An Iterative Algorithm for Determining the Arc Length of a High Order
Flat Bezier Curve}



\author[1]{Dmitry TARASOV}%
\author[1]{Oleg Milder}%
\affil[1]{Ural Federal University named after the first President of Russia B N Yeltsin}%


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  \date{May 26, 2024}


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\begin{abstract}
Quantifying the spatial characteristics of information stored and
disseminated electronically is a complex computational challenge. Flat
vector objects such as symbols, tracks, routes, etc. are described using
the mathematical apparatus of Bezier curves. Finding the perimeters of
such objects, especially in the case of curves of order higher than the
third, is associated with certain difficulties. Reducing the order of
curves by dividing or splitting them into sub-curves of lower orders,
accompanied by some decrease in the accuracy of the estimate, is a
convenient method for fast calculating the perimeters of plane figures
described by Bezier curves. In this work, we propose an iterative
algorithm for determining the arc length of a Bezier curve, which
compares different criteria for splitting a curve into sub-curves.%
\end{abstract}%



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