Curvature continuous offset approximation based on circle approximation using quadratic Bézier biarcs

We present a method for G2G2 end-point interpolation of offset curves using rational Bézier curves. The method is based on a G2G2 end-point interpolation of circular arcs using quadratic Bézier biarcs. We also prove the invariance of the Hausdorff distance between two compatible curves under convolution. Using this result, we obtain the exact Hausdorff distance between an offset curve and its approximation by our method. We present the approximation algorithm and give numerical examples.

► An algorithm is presented for G2G2 approximation of offsets using rational splines.
► G2G2 end-point interpolation of circular arcs is developed using quadratic Bezier Biarcs.
► The curvature-continuous offset approximation is based on this circle approximation.
► Invariance of the Hausdorff distance between two curves under convolution is proved.
► The exact Hausdorff distance between offset curve and approximant curve is so obtained.