C-shaped G~2 Hermite interpolation with circular precision based on cubic PH curve interpolation

摘要

Based on the technique of C-shaped G~1 Hermite interpolation by a cubic Pythagorean-hodograph (PH) curve, we present a simple method for C-shaped G~2 Hermite interpolation by a rational cubic Bezier curve. The method reproduces a circular arc when the input data come from it. Both the Bezier control points, which have a well-understood geometrical meaning, and the weights of the resulting rational cubic Bezier curve are expressed in explicit form. We test our method with many numerical examples, and some of them are presented here to demonstrate the properties of our method. The comparison between our method and a previous method is also included.