Algorithmic computation of the bishop frame of the rational Bezier curves with augmented reality applications

Purpose Bezier curves are widely used in computer-aided geometric design (CAGD) for modeling objects such as aircraft, cars and ships. Augmented reality applications are an important type of new-generation technology that is increasingly being used in simulations in education, military fields and gaming fields. Our study aims to provide a different approach with Augmented reality applications, one of the new generation technologies, by examining some geometric properties of Bezier curves, which have an important place in the design world. In our study, the Bishop frame, curvatures, derivative formulas and the Darboux vector of the Bishop frame have been computed by the algorithm method for the whole points of the rational Bezier curves. In the last part, some numerical examples and augmented reality applications have been given for the rational and polynomial Bezier curves in the GeoGebra program. Firstly, geometric computations related to rational Bezier curves were made in the GeoGebra program, and then drawing algorithms of rational Bezier curves were demonstrated with videos in the GeoGebra Ar program. Design/methodology/approach In this study, the theoretical method used is the algorithmic computation of the Bishop frame of Rational Bezier curves. The design application involved creating some three-dimensional Bezier curve and their augmented reality application. Findings Using the algorithmic method, the Bishop frame of Rational Bezier curves was calculated, the curvatures of the curve's Bishop frame were determined and various properties were computed. Originality/value The originality of this study lies in the algorithmic computation of the Bishop frame of rational Bezier curves, which has not been previously addressed in the literature, as well as the calculation of certain properties related to the curvatures of the Bishop frame. Additionally, a boat design was created using Bezier curves, which are widely used in object design, and an augmented reality application was implemented. Another advantage of this study is that it is expected to help in the more effective use of Bezier curves in the gaming industry.