The Alfeld split is obtained by subdividing a simplex in Rs into s+1 subsimplices with the barycenter as one of their vertices. On this split, we consider the space of C1 splines of degree d (d >= s+1), for which we construct a basis of simplex-splines with knots at the barycenter and the vertices of the simplex. The basis consists of two types of simplex-splines: firstly Bernstein polynomials with domain points on the facets of the simplex and secondly certain simplex-splines with at least one knot at the barycenter. Partition of unity, Marsden-like identities, and domain points are shown. We also provide C1 smoothness conditions across a facet between two simplices.
Lyche, T., Merrien, J.-., Speleers, H. (2025). A C1 simplex-spline basis for the Alfeld split in Rs. COMPUTER AIDED GEOMETRIC DESIGN, 117 [10.1016/j.cagd.2025.102412].
A C1 simplex-spline basis for the Alfeld split in Rs
Speleers H.
2025-01-01
Abstract
The Alfeld split is obtained by subdividing a simplex in Rs into s+1 subsimplices with the barycenter as one of their vertices. On this split, we consider the space of C1 splines of degree d (d >= s+1), for which we construct a basis of simplex-splines with knots at the barycenter and the vertices of the simplex. The basis consists of two types of simplex-splines: firstly Bernstein polynomials with domain points on the facets of the simplex and secondly certain simplex-splines with at least one knot at the barycenter. Partition of unity, Marsden-like identities, and domain points are shown. We also provide C1 smoothness conditions across a facet between two simplices.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
