Geometric approximation scheme for parabolic arcs

Abstract

A cubic H-Bézier geometric approximation scheme with one free parameter τis introduced for parabolic arcs. It has four control points. The control points are computed by matching the end points and end unit tangents of the two curves and provide two more free parameters. These free parameters are computed by curvature continuity constraints. Optimal value of τ is obtained by minimizing the maximum value of the distance between the cubic H-Bézier curve and the concerned parabolic arc. The method is illustrated using different numerical examples which show that the proposed method is economical, reliable and efficient.

Keywords

• 68U05
• 65D05
• 65D07
• 65D18