A Group of Orthogonal Basis Based on UE-Bézier Basis

UE-Bezier (unified and extended Bezier) basis is the unified form of Bezier-like bases, including polynomial Bezier basis, trigonometric polynomial and hyperbolic polynomial Bezier basis. Similar to the original Bezier-like bases, UE-Bezier basis functions are not orthogonal. In this paper, a group of orthogonal basis is constructed based on UE-Bezier basis. The transformation matrices between UE-Bezier basis and the proposed orthogonal basis are also solved. As an example, we apply the proposed orthogonal basis and the transformation into the approximation of an inverse function by an UE-Bezier polynomial.