A New Method to Design Cubic Pythagorean-Hodograph Spline Curves with Control Polygon

Abstract

A new method to design a cubic Pythagorean-hodograph (PH) spline curve from any given control polygon is proposed. The key idea is to suitably choose a set of auxiliary points associated with the edges of the given control polygon to guarantee the constructed PH spline has $G^1$ continuity or curvature continuity. The method facilitates intuitive and efficient construction of open and closed cubic PH spline curves that typically agrees closely with the same friendly interface and properties as B-splines, for example, the convex hull and variation-diminishing properties.

Keywords

Cubic pythagorean-hodograph (PH) curve / Control polygon / Interactive design / $G^1$ continuity')">$G^1$ continuity / Curvature continuity