Fitting and fairing Hermite-type data by matrix weighted NURBS curves. (September 2018) - Yang, Xunnian
Abstract: This paper proposes techniques to fit and fair sequences of points together with normals or tangents at the points by matrix weighted NURBS curves. Given a set of Hermite-type data, a matrix weighted NURBS curve is constructed by choosing the input points as control points and computing the weight matrices using the normals or tangents. Unlike traditional B-spline or NURBS curves that have only linear precision, matrix weighted NURBS curves with point-normal or point-tangent control pairs have almost circular or helical precision. Matrix weighted NURBS curves constructed from Hermite-type data can be fair and fit the input points closely when the original data were regularly sampled from curves with smoothly varying tangents and curvatures. If the original data are non-uniformly spaced or noisy, fair fitting curves can still be obtained by repeatedly sampling points from previously constructed curves and constructing new matrix weighted NURBS curves using the resampled data. Highlights: Weight matrices for matrix weighted NURBS curves are robustly computed. Matrix weighted NURBS curves with point-tangent control pairs are defined. Algorithm for fitting Hermite-type data by matrix weighted NURBS curves is given. Algorithm for fairing Hermite-type data by repeatedly curve fitting is proposed.