Abstract: This paper proposes a new implicit B-spline curve reconstruction algorithm based on direct Greville ordinates. For a given point cloud, it creates signed distance field first and lets them to be the Greville ordinates of B-spline function, and then optimizes Greville ordinates according to average algebraic error of raw points in high influence region. Finally, an implicit curve is obtained which is the zero level set of B-spline function. The proposed algorithm has benefits of simple model, fast speed, additional branch free, and being without manual tuning any parameters. Experimental results demonstrate that the reconstructing efficiency is higher than point fitting method as well as ordinary field fitting method, and the reconstruction accuracy expressed in geometric errors is better than ordinary field fitting method.

Key words: B-spline, implicit curve, curve reconstruction, Greville ordinate, field fitting

摘要： 提出了一种以隐式B-样条曲线为表达形式，基于直接Greville纵标的曲线重建方法。根据点云建立有向距离场，并作为B-样条函数的Greville纵标，然后根据高影响区内的平均代数误差优化Greville纵标；得到一个隐式B-样条函数，该函数的零点集即为重建曲线。该方法具有模型简单，重建速度快，无多余分支，无需手工调节任何参数的优点。实验结果证实了该直接法的效率明显高于点拟合法和普通场拟合法，以几何误差为准则的精度亦优于普通场拟合方法。

关键词: B-样条, 隐式曲线, 曲线重建, Greville纵标, 场拟合