New Approach to Approximate Circular Arc by Quartic Bezier Curve

Abstract

This paper presents a result of approximation an arc circles by using a quartic Bezier curve. Based on the barycentric coordinates of two and three combination of control points, the interior control points are determined by forcing the curvature at median point as similar as the given curvature at end points. Hausdorff distance is used to investigate the order of accuracy compare to the actual arc circles through central angle of 0 T S d. We found that the optimal approximation order is eight which is somewhat similar to preceding methods in the literatures.

Approximation of circular arcs using quartic Bezier curves with barycentric coordinates satisfying G^2 data

“…Both results have optimal approximation of order 8. Azhar et al [1] proposed a 2 G approximation by applying Barycentric coordinates. Similarly, their approach has the optimal approximation of order 8.…”

“…Fang [5] approximated circular arcs using quintic Bezier curves with seven different approximation methods with k G continuities, where 2,3, 4  k at the joints. This paper proposes numerous improvement of work proposed by Azhar et al [1] to increase the order of approximation of circular arcs. First, we consider quartic Bezier curves that interpolate two points on the circumference of a circle Approximation of circular arcs using quartic Bezier curves 1273 with equal unit vector tangents and curvatures at end points.…”

“…Next section discusses four approaches to obtain parameter  and it's approximation accuracy. The first approach is as shown in Azhar et al [1]…”

An Improved Algorithm for the Approximation of a Cubic Bezier Curve and its Application for Approximating Quadratic Bezier Curve

“…The problems for an opposite task -an approximation of circular arcs by Bezier curves of high degree are widely analyzed and new algorithms are proposed in [13][14][15].…”