C-shaped G2G2 Hermite interpolation with circular precision based on cubic PH curve interpolation

Based on the technique of C-shaped G1G1 Hermite interpolation by a cubic Pythagorean-hodograph (PH) curve, we present a simple method for C-shaped G2G2 Hermite interpolation by a rational cubic Bézier curve. The method reproduces a circular arc when the input data come from it. Both the Bézier control points, which have a well-understood geometrical meaning, and the weights of the resulting rational cubic Bézier 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.

► The method reproduces a circular arc when the input data come from it.
► The Bézier control points have a well-understood geometrical meaning.
► Both the Bézier control points and the weights of the resulting rational cubic Bézier curve are expressed in explicit form.
► The upper limit of the tangential angle between the given tangent vector and the line joining the two end points is now increased to be no more than ππ.