Shape controlled interpolatory ternary subdivision (Q734841)

Ternary subdivision schemes compare favorably with their binary analogues because they are able to generate limit functions with the same (or higher) smoothness but smaller support. This work is a continuation of some previous works of the same authors. An interpolating 4-point subdivision method is presented which unifies the locally controlled \(C^2\) scheme using local tension control [Comput. Aided Geom. Des. 24, No.~4, 210--219 (2007; Zbl 1171.65326)] with another interpolation scheme reproducing exactly conic sections as limit curves [Comput. Aided Geom. Des. 24, No.~1, 1--9 (2007; Zbl 1171.65325)]. The key point of the unification of both schemes is the use of local shape parameters associated with the initial polyline edges.