We present the construction of a multivariate normalized B-spline basis for the quadratic C1-continuous spline space defined over a triangulation in Rs (s≥1) with a generalized Powell-Sabin refinement. The basis functions have a local support, they are nonnegative, and they form a partition of unity. The construction can be interpreted geometrically as the determination of a set of s-simplices that must contain a specific set of points. We also propose a family of quasi-interpolants based on this multivariate Powell-Sabin B-spline representation. Their spline coefficients only depend on a set of local function values. The multivariate quasi-interpolants reproduce quadratic polynomials and have an optimal approximation order.
Speleers, H. (2013). Multivariate normalized Powell-Sabin B-splines and quasi-interpolants. COMPUTER AIDED GEOMETRIC DESIGN, 30(1), 2-19 [10.1016/j.cagd.2012.07.005].
Multivariate normalized Powell-Sabin B-splines and quasi-interpolants
Speleers H.
2013-01-01
Abstract
We present the construction of a multivariate normalized B-spline basis for the quadratic C1-continuous spline space defined over a triangulation in Rs (s≥1) with a generalized Powell-Sabin refinement. The basis functions have a local support, they are nonnegative, and they form a partition of unity. The construction can be interpreted geometrically as the determination of a set of s-simplices that must contain a specific set of points. We also propose a family of quasi-interpolants based on this multivariate Powell-Sabin B-spline representation. Their spline coefficients only depend on a set of local function values. The multivariate quasi-interpolants reproduce quadratic polynomials and have an optimal approximation order.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
