通过节点调整和约束优化近似拼接两B样条曲线

Approximate uniting of two adjacent B-spline curves through knot adjustment and constrained optimization

研究了两相邻B样条曲线近似拼接成 1条B样条曲线的问题,基本出发点是寻找精确拼接两曲线的条件,然后通过约束优化目标,重新调整曲线的控制点以满足此条件;为了获得这样的曲线而不用多余的节点,提出了一种调整某 1条k次曲线的后k个节点,且不改变其形状的新算法;同时讨论了更一般的曲线拼接问题,即让拼接曲线通过某些目标点。

This paper explains the problem of approximate joining two adjacent B-spline curves into one B-spline curve. The basic idea of the approach is to find the conditions for precise joining of two B-spline curves, and readjusts the control points of the curves by constrained optimization in order to satisfy these conditions. To obtain a joined curve without superfluous knots, we present a new knot adjustment algorithm for adjusting the end k knots of a kth order B-spline curve without changing its shape. The more general problem of joining curves to pass through some goal points is also discussed.