Scattered Points Interpolation with Globally Smooth B-Spline Surface using Iterative Knot Insertion

We introduce a new method to interpolate scattered 3D data points with a single B-spline surface patch which is globally smooth. Given a set of scattered 3D data points and their corresponding parametrization, our method first constructs a set alpha of B-spline bases using a weighted strategy, and inserts knots to the knot vectors based on alpha. Then, the knot insertion procedure is iterated until a set beta of B-spline bases exists, which indicates the existence of the interpolation surface. Finally, by applying the fairing energy minimizing with interpolation constraints, a globally smooth B-spline surface which interpolates the data points can be produced. Experimental results demonstrate that the generated Bspline surfaces often have fewer control points than those of traditional methods, while keeping the scattered data points interpolated accurately. The implementation of our algorithm and the scripts to reproduce all the results are available at https://github.com/wangbolun300/sparse_data. (c) 2022 Elsevier Ltd. All rights reserved.