Curvature comparison of Bézier curve, ball curve and trigonometric curve in preserving the positivity of real data

Abstract

The curvature of a curve is important in designing roads, construction of smooth surfaces, or grinding workpieces. Curvature is the tool to measure the smoothness of curves and surfaces. Therefore, in this paper, the curvature profile of three functions will be compared where these three functions also preserved the positivity of the data. These three functions are a rational cubic Bézier curve, a rational cubic Ball curve, and a cubic trigonometric Bézier curve. Conditions were imposed to preserve the positivity of the data and the results are presented. Then, the curvature profile of the curves are compared and analysed. It was found that the interpolated curve by cubic Bézier curve is the best among those three types of curves based on the lowest amplitude value of curvature. However, for all three curves, the curvatures are not continuous since the interpolated curves represent C1 continuity only.