Caputo Fabrizio Bézier Curve with Fractional and Shape Parameters

Abstract

In recent research in computer-aided geometric design (CAGD), one of the most popular concerns has been the creation of new basis functions for the Bézier curve. Bézier curves with high degrees often overshoot, which makes it challenging to maintain control over the ideal length of the curved trajectory. To get around this restriction, free-form surfaces and curves can be created using the Caputo Fabrizio basis function. In this study, the Caputo Fabrizio fractional order derivative is used to construct the Caputo Fabrizio basis function, which contains fractional parameter and shape parameters. The Caputo Fabrizio Bézier curve and surface are defined using the Caputo Fabrizio basis function, and their geometric properties are examined. Using fractional and shape parameters in the implementation of the Caputo Fabrizio basis function offers an alternative perspective on how the Caputo Fabrizio basis function can construct complicated curves and surfaces beyond a limited formulation. Curves and surfaces can have additional shape and length control by adjusting a number of fractional and shape parameters without affecting their control points. The Caputo Fabrizio Bézier curve’s flexibility and versatility make it more effective in creating complex engineering curves and surfaces.