Constructing a quasi-Legendre basis based on the C-Bézier basis

In the spaceГn = span{sint, cost, 1, t, t2, …, tn- 2, a C-Bezier basis is constructed by an integral approach. However, the C-Bezier basis is not orthogonal. For some applications, we construct an orthogonal basis based on the C-Bezier basis, which has remarkable properties similar to that of the Legendre basis. Then we derive the transformation matrices that convert the C-Bezier basis and the orthogonal basis into each other. As an example of application, we apply this orthogonal basis to the degree reduction approximation of the C-Bezier curves.