A selective eraser of curvature extrema for B-spline curves

摘要

This paper provides a selective eraser of curvature extrema for B-spline curves. It is introduced as an extension to the standard least squares method for approximating a series of points using a B-spline. The extension consists in adding constraints to produce segments of curve with monotone increase or decrease of curvature. The primal-dual interior point method is used to solve the constrained optimization problem. The method requires gradients that are computed using B-spline symbolic operators. Therefore, the algorithm relies on the arithmetic and differential properties of B-splines. The variation-diminishing property of B-splines is also exploited to apply the constraints.