Abstract: A practical algorithm for B-spline curve approximation to a dense and noisy sectional data point set is proposed. The redundant points are eliminated and the point set is resampled by using the equal-arc-length method. The discrete curvature and the first-order difference of each point are calculated. Almost all the feature points, including crease points, inflection points and curvature extrema value points, are identified automatically. A B-spline curve is constructed to interpolate all the feature points and one new interpolation point is inserted at the place where the maximum fitting error occurs. This process is repeated until the maximum fitting error is less than the given error bound. A few examples are presented to show that the curve can reconstruct the small features of the sectional profile well, and both the number and the location of the knots are reasonable. The algorithm is feasible and efficient, and it can be widely used to deal with sectional profile fitting problems.

Key words: Curve approximation, Discrete curvature, Equal-arc-length resampling, Feature points, Error compensation, Error identification, Error modeling, Positioning accuracy, Five-axis machine tools