Normalized C-Basis and C-Curves
An alternative to the rational Bézier model is mixed algebraic and trigonometric curves named helix splines or C-curves (C for cycloidal). The basis of the C-curves space, named C-basis, is determined in order to retain some properties of the Bernstein bases.
An alternative to the Bézier model (see the related link) is the -order space of mixing algebraic and trigonometric polynomials . For example, the space allows exact representations of circles, ellipses, and cycloids. In , it is determined that the corresponding normalized C-basis for is defined by:
In this Demonstration, you can vary the value of . The corresponding curves are determined by the control points, which you can drag.
 E. Mainar, J. M. Peña, and J. Sánchez-Reyes, "Shape Preserving Alternatives to the Rational Bézier Model," Computer Aided Geometric Design, 18(1), 2001 pp. 37–60. doi:10.1016/S0167-8396(01)00011-5.