C-curves: An extension of cubic curves Original Research Article

A linearly parametrized set of curves, named C-curves, is suggested with basis sin t, cos t, t, and 1. C-curves are an extension of cubic curves, they depend on a parameter α > 0, and their limiting case for α → 0 is a cubic curve. They can deal with free form curves and surfaces, and provide exact reproduction of circles and cylinders. So, they could be used to unify the representation and processing of both free and normal form curves and surfaces in engineering.