C-B样条曲线与T-B样条曲线的G^1拼接

G^1 Condition for C-B Spline Curves and T-B Spline Curves

在对T-B样条基函数及曲线端点特性分析的基础上提出了n+1阶T-B样条基函数表达式及求解方法.给出了C-B样条曲线与T-B样条曲线的G1拼接条件.在这种条件下,当C-B样条曲线和T-B样条曲线拼接时,可增加控制顶点使C-B样条曲线通过控制多边形的首末顶点,并与首末边相切.并给出应用实例,即利用T-B样条曲线能精确表示半椭圆弧(半圆弧)的特点,与C-B样条曲线进行G1拼接,从而解决了C-B样条曲面造型中无法精确表示半椭圆弧(半圆弧)的问题.

Based on the analysis of T-B-spline basis functions and the properties of the begin point and end point, the paper presents （ n ＋ 1） th -order uniform T-B-spline basis function and its solution. We also give G^1 blending condition of C-B spline curves and T-B spline curves. Under this condition, when C-B spline and T-B-spline curve blend with each other, we can control the begin point and end point of the controlling vertex through the increased controlling points, thus make the C-B spline curves pass boundary vertexes and render its tangent direction parallel to boundary edges. We also give some examples, i.e. using C-B spline curves to represent the semicircle and semi-ellipse, which overcomes the limitation of C-B spline surface modeling in terms of the accuracy when semicircles and semi-ellipses.