$C^1$ Interpolatory Subdivision with Shape Constraints for Curves
Résumé
We derive two reformulations of the $C^1$ Hermite subdivision scheme introduced in [12]. One where we separate computation of values and derivatives and one based of refinement of a control polygon. We show that the latter leads to a subdivision matrix which is totally positive. Based on this we give algorithms for constructing subdivision curves that preserve positivity, monotonicity, and convexity.