Fitting a spatial arc to noisy point clouds with high accuracy and reproducibility is challenging, although it is important in many applications, such as precise measurement, computerized numerical control machining and robotic path planning. In optical measuring applications, an arc-shaped object is usually first scanned as point clouds by a 3D camera or multiple charge-coupled device cameras, and arc fitting is then invoked to fit these point clouds, obtaining the measuring radius and center. The accuracy of the arc-fitting algorithm plays an important role in the arc-measuring precision. In this paper, a novel algorithm is proposed to fit a spatial arc of high accuracy and reproducibility to noisy point clouds. This method combines the repeated least trimmed squares idea with the smoothing fairness function, i.e. discrete curvature, to devise the objective function, which is solved iteratively. This algorithm can successfully filter noise and fit a highly accurate arc to noisy point clouds with high reproducibility. Seven popular arc-fitting algorithms are implemented as benchmarks and both simulated and real data scanned from physical objects are tested to validate that the proposed algorithm performs best. The proposed algorithm is efficient and can be easily implemented in industrial applications.

以高精度和可重复性将空间弧拟合到嘈杂的点云是具有挑战性的，尽管它在许多应用中很重要，例如精确测量、计算机数控加工和机器人路径规划。在光学测量应用中，弧形物体通常首先被3D相机或多个电荷耦合器件相机扫描为点云，然后调用弧形拟合来拟合这些点云，获得测量半径和中心。弧拟合算法的精度对弧测量精度起着重要作用。在本文中，提出了一种新算法来拟合具有高精度和可重复性的空间弧到嘈杂的点云。这种方法结合了重复最小修整的思想和平滑公平函数，即离散曲率，设计目标函数，迭代求解。该算法可以成功过滤噪声，并以高重现性将高精度弧拟合到噪声点云中。七种流行的弧拟合算法被实现为基准，并测试从物理对象扫描的模拟和真实数据，以验证所提出的算法性能最佳。所提出的算法是有效的，并且可以很容易地在工业应用中实现。