Construction Of B-Basis For A Kind Of Mixed Function Space

Bernstein basis is a basis for the space of degree-n algebraic polynomials T = span{1,t,t2,…,tn} with the good properties of shape preserving and evaluation,etc.However,the transcendental curve,such as the helix and the cycloid,can not be represented by algebraic polynomial.In order to represent a curve with intrinsic properties and harmonic properties,we construct normalized B-bases for a class of mixed function Spaces and define curves.First,we review the basic definition and basic properties of B-bases,and introduce the general method of constructing B-bases by the endpoint condition.Secondly,the mixing function space for trigonometric functions and polynomial:T1 =span{1,sint,cost,t sint,t cost},T2 = span{1,sin t,cost,t sint,t cost,t2 sin t,t2 cost},T3 = span{1,sint,cost,t sint,tcost,tsint,t cost,t3sint,t3cost}.We construct their normalized B-basis.Finally,we give the definition of the Bezier-like curve in the space T1,T2,T3,which satisfies the endpoint interpolation and the convex hull property.At the same time,the integral curve of a class of intrinsic definition and its equidistant line in the form of Bezier-like are given.