Curves and Surfaces Construction Based on New Basis with Exponential Functions
By incorporating two exponential functions into the cubic Bernstein basis functions, a new class of ??-Bernstein basis functions is constructed. Based on these ??-Bernstein basis functions, a kind of ??-Bzier-like curve with two shape parameters, which include the cubic Bernstein-Bzier curve, is proposed. The C 1 and C 2 continuous conditions for joining two ??-Bzier-like curves are given. By using tensor product method, aclass of rectangular Bzier-like patches with four shape parameters is shown. The G 1 and G 2 continuous conditions for joining two rectangular Bzier-like patches are derived. By incorporating three exponential functions into the cubic Bernstein basis functions over triangular domain, a new class of ???-Bernstein basis functions over triangular domain is also constructed. Based on the ???-Bernstein basis functions, a kind of triangular ???-Bzier-like patch with three shape parameters, which include the triangular Bernstein-Bzier cubic patch, is presented. The conditions for G 1 continuous smooth joining two triangular ???-Bzier-like patches are discussed. The shape parameters serve as tension parameters and have a predictable adjusting role on the curves and patches.
bernstein basis shape parameter bernstein-bzier curve triangular bernstein-bzier patch geometric continuity 65d07 65d17