A New Method to Design Cubic Pythagorean-Hodograph Spline Curves with Control Polygon
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 G1 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.
Publication Source (Journal or Book title)
Communications in Mathematics and Statistics
Kang, H., & Li, X. (2019). A New Method to Design Cubic Pythagorean-Hodograph Spline Curves with Control Polygon. Communications in Mathematics and Statistics, 7 (3), 363-381. https://doi.org/10.1007/s40304-018-0158-5