C1 Interpolatory Subdivision with Shape Constraints for Curves

We derive two reformulations of the C1 Hermite subdivision scheme introduced by Merrien. 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.

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