带约束的B样条曲线曲面延伸技术

B-spline Curves and Surfaces Extension with Constraints

论文提出了一种带光滑有序点列约束的B样条曲线延伸方法。该算法能够根据约束点列的情况对曲线延伸部分所对应的节点值进行优化,通过插值尽量少的约束点,使得延伸曲线与约束点列之间的最大距离小于预先给定的误差值,并且延伸曲线与原始曲线之间自然达到最大阶连续。该方法也同样适用于带曲线约束的B样条曲面延伸。实例表明,所提出的算法是可行且有效的。

An algorithm for extending B-spline curves with a sequence of ordered points constraint is presented based on the curve unclamping algorithm.The most important feature of this algorithm is the ability to optimize the knots of the extended curve segment according to the ordered points.Thus,with minimum number of interpolation points,the maximum deviation of the extended curve segment from the ordered points is less than the given tolerance.The extended curve segment connects to the original curve with maximum continuity intrinsically.Further more,this algorithm can be applied to the extension of B-spline surfaces with the constraints of a sequence of B-spline curves.Several experimental results have shown the validity and applicability of the proposed algorithm.