Orthogonalization of unified and extended B~zier basis and its transformation matrix

摘要

UE-Bézier (unified and extended Bézier) basis is the unified form of Bézier-like bases,including polynomial Bézier basis,trigonometric polynomial and hyperbolic polynomial Bézier basis.Similar to the original Bézier-like bases,UE-Bézier basis functions are not orthogonal.In this paper,a group of orthogonal basis is constructed based on UE-Bézier basis.The transformation matrices between UE-Bézier basis and the proposed orthogonal basis are also solved.