ConicCurv is a new derivative-free algorithm to estimate the curvature of a plane curve from a sample of data points. It is based on a known tangent estimator method grounded on classic results of Projective Geometry and B\'ezier rational conic curves. The curvature values estimated by ConicCurv are invariant to Euclidean changes of coordinates and reproduce the exact curvature values if the data are sampled from a conic. We show that ConicCurv< has convergence order $3$ and, if the sample points are uniformly arc-length distributed, the convergence order is $4$. The performance of ConicCurv is compared with some of the most frequently used algorithms to estimate curvatures and its performance is illustrated in the calculation of the elastic energy of subdivision curves and the location of L-curves corners.

翻译：ConicCurv 是一种新的无导数算法，用于从数据点样本中估计平面曲线的曲率。该算法基于一种已知的切线估计方法，该方法建立在经典射影几何与有理二次 Bézier 曲线理论的基础之上。ConicCurv 估计的曲率值在欧几里得坐标变换下具有不变性，并且当数据采样自圆锥曲线时，能够精确重现其曲率值。我们证明 ConicCurv 具有 $3$ 阶收敛精度，若采样点呈均匀弧长分布，则收敛精度可达 $4$ 阶。本文对比了 ConicCurv 与几种常用曲率估计算法的性能，并通过细分曲线的弹性能量计算以及 L-曲线拐点定位等实例展示了其应用效果。