An Improved Parameterized Interpolation Method Based on Modified Chord Length

Abstract

Aiming at the problem of smoothness of the B-spline curve interpolation, an improved parameterized interpolation method based on modified chord length is proposed. We construct a series of interpolation arcs using the relationship between the chord length and chord angle of given data points and then calculate the global knot parameters by replacing the chord length with the arc length. In addition, we propose curve smoothness index based on the relationship between the radius of curvature and the cumulative curve length and compare it with other classical methods to construct cubic B-spline curves in the tests; at the same time, the deviation error is used to evaluate the swing of the curve. Furthermore, two sets of point cloud data are used to test the surface interpolation for different parameterization methods, and the Gauss curvature map is used to evaluate the smoothness of interpolated surfaces. As a result, the proposed method performs better than other methods; the constructed curves and surfaces maintain a good performance.