High-quality point sampling for B-spline fitting of parametric curves with feature recognition

Abstract

Determining a sequence of points from parametric curves is essential for the construction of least-squares B-spline fitting curves in geometric modeling and related applications. Uniform sampling methods always determine points uniformly in arc length, curvature or a weighted form, but feature points intuitively indicating the curve profile are generally ignored. In this paper, we focus on high-quality point sampling so as to better capture the original curve shape. Firstly, all the feature points (inflection points and extreme curvature points) on the curve are recognized by a parabolic interpolation method. Then more auxiliary points are adaptively added according to the characteristic function defined as a weighted sum of arc length and total curvature characteristics. By adjusting the weight in the characteristic function, it provides more flexibility and controllability to obtain auxiliary points. Finally, we convert the original curve into a B-spline curve by interpolating these feature points and auxiliary points using the progressive–iterative approximation method. Numerical examples demonstrate the effectiveness and high quality of our proposed method.