Dimension elevation is not always corner-cutting

Carolina Vittoria Beccari (1) , Giulio Casciola (1) , Marie-Laurence Mazure (2)

1 Dipartimento di Matematica [Bologna]
2 CVGI - Calcul des Variations, Géométrie, Image

Degree elevation is a typical corner-cutting algorithm. It refers to the process transforming control polygons when embedding a polynomial space of some degree into any polynomial space of higher degree.Dimension elevation similarly refers to the transformation of control polygons when embedding an Extended Chebyshev space possessing a Bernstein basis into another one, of higher dimension. Unlike degree elevation, this cannot always be split into successive (corner-cutting) steps elevating the dimension by one. What happens when it is not possible is investigated here. We shall see that the new control points can even be located outside the initial control polygons, giving evidence that dimension elevation is not always corner-cutting.

Mots clés: Extended Chebyshev spaces; Bernstein bases; dimension elevation; critical length; shape preservation; corner cutting

Domaines: Mathématiques [math]

Carolina Vittoria Beccari, Giulio Casciola, Marie-Laurence Mazure. Dimension elevation is not always corner-cutting. Applied Mathematics Letters, 2020, 109, pp.106529. ⟨10.1016/j.aml.2020.106529⟩. ⟨hal-02482422⟩