A note on robust biarc computation

A robust algorithm for the numerical computation of biarcs, i.e. G1 curves com- posed of two arcs of circle, is presented. Many algorithms exist, but are based on geometric constructions, which must consider dierent geometrical congurations. The proposed algorithm uses an analytic construction, which explicitly states the solution and does not require the identication of geometric cases. Moreover, singular angles congurations are treated smoothly. The proposed algorithm is compared with the Matlab's routine rscvn that solves geo- metrically the same problem. Numerical experiments show that Matlab's routine sometimes fails near quasi singular congurations. Moreover, Matlab's routine has a non natural choice of the solution for large angles. Finally, the proposed solution depends smoothly on the geometrical parameters, so that it can be easily included in more complex algorithms involving splines of biarcs or least squares data tting.