$C^1$ analysis of 2D subdivision schemes refining point-normal pairs with the circle average.

This article continues the investigation started in [9] on subdivisionschemes refining 2D point-normal pairs, obtained by modifying linearsubdivision schemes using the circle average. While in [9] the convergence ofthe Modified Lane-Riesenfeld algorithm and the Modified 4-Point schemes isproved, here we show that the curves generated by these two schemes are $C^1$.