# An Approximation of Bézier Curves by a Sequence of Circular Arcs

## DOI:

https://doi.org/10.5755/j01.itc.50.2.25178## Keywords:

Bézier Curves;, Circular arc Approximation;, Analytic geometric of circle;, Arbitrary degree## Abstract

Some researches have investigated that a Bézier curve can be treated as circular arcs. This work is to propose

a new scheme for approximating an arbitrary degree Bézier curve by a sequence of circular arcs. The sequence

of circular arcs represents the shape of the given Bézier curve which cannot be expressed using any other algebraic

approximation schemes. The technique used for segmentation is to simply investigate the inner angles

and the tangent vectors along the corresponding circles. It is obvious that a Bézier curve can be subdivided into

the form of subcurves. Hence, a given Bézier curve can be expressed by a sequence of calculated points on the

curve corresponding to a parametric variable t. Although the resulting points can be used in the circular arc

construction, some duplicate and irrelevant vertices should be removed. Then, the sequence of inner angles are

calculated and clustered from a sequence of consecutive pixels. As a result, the output dots are now appropriate

to determine the optimal circular path. Finally, a sequence of circular segments of a Bézier curve can be approximated

with the pre-defined resolution satisfaction. Furthermore, the result of the circular arc representation

is not exceeding a user-specified tolerance. Examples of approximated nth-degree Bézier curves by circular arcs

are shown to illustrate efficiency of the new method.

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