Approximation of circular arcs and offset curves by Bézier curves of high degree

A Novel Method of Offset Approximation along the Normal Direction with High Precision

“…Lee's method [12] is regarded as classical in offset approximation, which is simple and highly precise. Ahn et al made an improvement of their work to reduce the degree of the approximation curve [13]. A comparison is made between our method and their work in terms of the precision in the following.…”

“…The advantage is more obvious after the curve is subdivided, and the results are shown in the third and the fourth rows of Table 1. se. Ahn et al made an improvement of their work to reduce the degree of the approxim [13]. A comparison is made between our method and their work in terms of the precisi llowing.…”

“…Hoschek [9] suggested a least squares solution, Piegl and Tiller [10] employed sample interpolation, and Cheng and Wang [11] used Jacobi series to approximate the offset curve. Lee et al [12] regarded the offset curve as a convolution of a sweeping circle, Ahn et al [13] used conic approximation to approximate the sweeping circle, and Zhao and Wang [14] employed second-order rational polynomials, and achieved high-precision approximation.…”

Quartic approximation of circular arcs using equioscillating error function

“…To approximate the circle c, there is a need to find a parametrically defined polynomial curve p : t → (x(t), y(t)) , 0 ≤ t ≤ 1, where x(t), y(t) are polynomials of degree 4, that approximates c with "minimum" error. Many researchers have tackled this issue using different norms and methods, see [2], [3], [4], [5], [6], [9], [10], [14], [16], [18]. For details and numerical comparisons with these works, see section 6.…”

Normal approximations of regular curves and surfaces

“…Of course, this question is not new, and have been deeply studied in some particular cases (see, for instance, [1] and [2]). But we offer a different approach, with a method which can be used for any kind of regular curve or surface.…”