LAUSR

This paper analyzes the curvature distributions of cubic B-spline curves. Firstly, a sufficient geometric condition is presented to guarantee that the curvature of a B-spline curve is monotonic. Then, a design algorithm is developed for cubic B-spline curves with monotonic curvature, as well as an algorithm for curve interpolation with monotonic curvature. Finally, examples are given to demonstrate the effectiveness and efficiency of the new design approach. Compared to Euler curves, the proposed algorithm is easier to compute; it also has an exact solution with boundary conditions. Furthermore, it is compatible with existing commercial CAD software.