Quasi-circular Splines: A Shape-Preserving Approximation

Abstract

The "quasi-circular spline" is introduced as a new method for approximating closed, smooth planar shapes from curvature information. A current application is the measurement of shapes of solid rocket booster cross-sections. Because of the efficiency of the algorithm and its desirable geometric properties, it is also particularly appropriate for computer graphics. The simplicity and efficiency of the quasi-circular spline compare well with previously proposed schemes which are important in graphical applications. It is invariant under the transformations of the Euclidean group. Furthermore, it is shape-preserving in that the quasi-circular spline approximation to a convex planar curve is also convex. Sufficient conditions for convergence are described, and O(h²) approximation to sufficiently smooth curves is demonstrated.