Sweeping Surfaces of Polynomial Curves in Euclidean 3-space

Abstract In this study, we investigate the surfaces created by the movement of the profile curves through the regular polynomial spine curves. To overcome the restrictions of establishing a frame of the polynomial curves at the points where the second and higher-order derivatives vanish, the Frenet-like curve (Flc) frame is considered. In this way, by introducing sweeping surfaces defined based on the Flc frame, we analyze their parameter curves to determine conditions to be geodesics, asymptotics, and principal curvature lines. Furthermore, we derive conditions of these sweeping surfaces to be minimal, developable, and Weingarten surfaces. Lastly, we provide some examples of these sweeping surfaces and illustrate their graphical representations.