کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
440620 | 691195 | 2013 | 18 صفحه PDF | دانلود رایگان |
We present the construction of a multivariate normalized B-spline basis for the quadratic C1C1-continuous spline space defined over a triangulation in RsRs (s⩾1s⩾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.
► We construct a normalized basis for multivariate quadratic Powell–Sabin splines.
► A geometric interpretation is given in terms of simplices containing certain points.
► We also discuss a family of multivariate quasi-interpolants.
Journal: Computer Aided Geometric Design - Volume 30, Issue 1, January 2013, Pages 2–19