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Title: Multivariate normalized Powell-Sabin B-splines and quasi-interpolants
Authors: Speleers, Hendrik # ×
Issue Date: Jan-2013
Publisher: North-Holland
Series Title: Computer Aided Geometric Design vol:30 issue:1 pages:2-19
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.
ISSN: 0167-8396
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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