Circular Arc Approximation by Quartic H-Bézier Curve

The quartic H-Bézier curve is used for the approximation of circular arcs. It has five control points and one positive real free parameter. The four control points are carried out b

The best quintic Chebyshev approximation of circular arcs of order ten

Mathematically, circles are represented by trigonometric parametric equations and implicit equations. Both forms are not proper for computer applications and CAD systems. In this paper, a quintic polynomial approximation for a circular arc is presented. This approximation is set so that the error function is  of degree $10$ rather than $6$; the Chebyshev error function equioscillates $11$ times rather than $7$; the approximation order is $10$ rather than $6$. The method approximates more than the full circle with Chebyshev   uniform error  of  $1/2^{9}$. The examples show the competence and simplicity of the proposed approximation, and that it can not be improved

Circular Arc Approximation by Quartic H-Bézier Curve

The quartic H-Bézier curve is used for the approximation of circular arcs. It has five control points and one positive real free parameter. The four control points are carried out b

GCS approximation

The discipline of Computer Aided Geometric Design (CAGD) deals with the computational aspects of geometric objects. This thesis is concerned with the construction of one of the most primitive geometric objects, curves. More specifically, it relates to the construction of a high quality planar curve. The Generalised Cornu Spiral (GCS) is a high quality planar curve that is beginning to show value in Computer Aided Design (CAD) and Computer Aided Manufacture (CAM) applications. However in its current form it is incompatible with current CAD/CAM systems. This thesis addresses the issue with the development of a robust and efficient polynomial replacement for the GCS