C-B样条曲线的分割和拼接

Arbitrary Subdivision Algorithm and Joining of C-B-Spline

曲线曲面造型中设计复杂的自由曲线时,单段曲线已不能满足外形设计的要求,因而在实际造型中,经常采用曲线的分割和拼接。C-B样条理论是曲线曲面造型的一项重要内容。在对C-B样条基函数及曲线端点特性分析的基础上,提出了C-B样条曲线的任意分割算法,并对C-B样条曲线间进行了G1拼接,给出了B样条曲线和C-B样条曲线G1和G2光滑拼接的几何条件。采用分割和拼接技术会增加C-B样条曲线的灵活性,所得结论具有明确的几何意义,并可以进一步推广到C-B样条曲面造型中。

The single curve already can＇t satisfy the requirements of shape design when designing complex free curve in curve/surface modeling.Thus in the actual modeling,C-B-spline theory is an important content of curve/surface modeling.Propose the algorithm of arbitrarily divided when analysing C-B-spline basis functions,then splicing between two C-B-spline.In addition,give geometry conditions about B-spline curves and C-B-spline curves.The results are benefit for the shape modification,and they can also be extended to surface modeling with C-B-spline.