Cubic B\'{e}zier-Spline Curves: Interpolation and Maximum Curvature

TL;DR

This paper introduces a closed-form solution for inverse interpolation of periodic uniform B-spline curves and applies it to determine their maximum curvature, supported by computational examples.

Contribution

It provides a novel closed-form solution for inverse interpolation of periodic uniform B-spline curves and calculates their maximum curvature.

Findings

Closed-form inverse solution for periodic uniform B-spline curves

Method to determine maximum curvature of Bézier-spline curves

Computational and graphical validation using Maple

Abstract

In this paper, we propose a closed-form solution to the inverse problem in interpolation with periodic uniform B-spline curves. This solution is obtained by modifying the one we have established to a similar problem with relaxed uniform B-spline curves. Then we use these solutions to determine the maximum curvature of a B\'{e}zier-spline curve. Our computational and graphical examples are presented with the aid of Maple procedures.