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 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.

Computer-Aided Design 148, 103244