On a nonlinear version of Lane-Riesenfeld's subdivision schemes converging to piecewise smooth functions preserving high regularity

Lane-Riesenfeld's subdivision schemes provide a versatile tool for generating smooth and detailed curves and surfaces, making them valuable assets in computer graphics and geometric modeling. These schemes offer flexibility in controlling the regularity of the limit function by adjusting some parameters. In this paper, we propose a nonlinear modification of these algorithms for piecewise smooth functions. The new algorithm converge to piecewise smooth limit functions maintaining the high regularity of Lane-Riesenfeld's subdivision schemes in smooth zones. The practical results presented show a very good numerical behavior of the proposed algorithms. • Subdivision scheme converges to piecewise smooth functions if the initial data contains singularities. • Subdivision scheme preserves the high regularity of Lane-Riesenfeld schemes in smooth regions. • Subdivision scheme avoids oscillations near discontinuities .