Data reduction using cubic rational B-splines

摘要

A geometric method for fitting rational cubic B-spline curves to data representing smooth curves, such as intersection curves or silhouette lines, is presented. The algorithm relies on the convex hull and on the variation diminishing properties of Bezier/B-spline curves. It is shown that the algorithm delivers fitting curves that approximate the data with high accuracy even in cases with large tolerances. The ways in which the algorithm computes the end tangent magnitudes and inner control points, fits cubic curves through intermediate points, checks the approximate error, obtains optimal segmentation using binary search, and obtains appropriate final curve form are discussed.