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

Abstract

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 α of B-spline bases using a weighted strategy, and inserts knots to the knot vectors based on α . Then, the knot insertion procedure is iterated until a set β 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 B-spline 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 . • An iterative knot insertion algorithm is introduced to guarantee the existence of B-spline interpolation surfaces when fitting scattered 3D data points. • The generated B-spline surfaces often use fewer control points than those of tranditional interpolation methods. • A novel parameter δ is introduced to improve the stability of control point solving. • The control points can be solved by a global fairing energy minimization procedure with strict interpolation constraints. Thus, the generated B-spline surface is globally smooth.