..., 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...

... are generally used in curve theory. However, the Serret-Frenet frame does not work when the second derivative is zero. In order to eliminate this problem, the quasi-frame was obtained. In this study, the quasi frames of the polynomial and rational Bezier curves are calculated by an algorithmic method. Thus...