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- A Bivariate C1 Cubic Spline Space on Wang's Refinement - IEEE Conference Publication
Schumaker, Spaces of bivariate splines on triangulations with holes, J. Theory Appl. Chou, L.
Su, and R. Wang, The dimensions of bivariate spline spaces over triangulations, Int. Chui and D. Chui and T. He, Bivariate C1 quadratic finite elements and vertex splines, Math. Chui and R. Wang, Multivariate spline spaces, J.
Wang, On smooth multivariate spline functions, Math. Diener, Instability in the dimension of spaces of bivariate piecewise polynomials of degree 2r and smoothness r, SIAM J. Diener, Geometry dependence of the dimension of spaces of piecewise polynomials on rectilinear partitions, Computer Aided Geometric Design 14, 43—50 Mathematical Research and Exposition 14, — Schempp and K. Zeller, eds. Hong, Spaces of bivariate spline functions over triangulations, Approx. Theory and Appl.
MR 92f Varma, N. Govil et al. Hong and H. Jia, Lower bounds on the dimension of spaces of bivariate splines, in Multivariate Approximation and Interpolation, W. Haussmann and K.
Spline functions on triangulations
Jetter, eds. Liu, An integral representation of bivariate splines and the dimension of quadratic spline spaces over stratified triangulations, Acta Math. Sinica 37, — Liu, The dimension of cubic spline space over stratified triangulations, J.
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Mathematical Research and Exposition 16, — Manni, On the dimension of bivariate spline spaces on generalized quasi-cross-cut partitions, J. Theory 69, — Morgan and R. Scott, The dimension of piecewise polynomials, Manuscript Powell and M.
A Bivariate C1 Cubic Spline Space on Wang's Refinement - IEEE Conference Publication
Software 3, — Schumaker, On the dimension of spaces of piecewise polynomials in two variables, in Multivariable Approximation Theory, W. Strang, Piecewise polynomials and the finite elements method, Bull. Strang, The dimension of piecewise polynomials, and one-sided approximation, in Proc.
Numerical Solution of Differential Equations, Dundee pp. Wang, The structural characterization and interpolation for multivariate splines, Acta Math.
Sinica 18, 91— Ye, Some problems for the bivariate C1 cubic splines, Approx. Related Papers.
By Don Hong. Some new formulations of smoothness conditions and conformality conditions for bivariate splines. Some smoothness conditions and conformality conditions for bivariate quartic and quintic splines. Download pdf.
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In the present paper we compute for the first time Beta-function B-splines BFBS achieving Hermite interpolation up to third partial derivatives at the vertices of the triangulation. We consider examples of BFBS with uniform and variable order of the Hermite interpolation at the vertices of the triangulation, for possibly non-convex star-1 neighbourhoods of these vertices. We also discuss the conversion of the local functions from Taylor monomial bases to appropriately shifted and scaled Bernstein bases, thereby converting the Hermite interpolatory form of the linear combination of BFBS to a new, Bezier-type, form.
This conversion is fully parallelized with respect to the vertices of the triangulation and, for Hermite interpolation of uniform order, the load of the computations for each vertex of the computation is readily balanced. Springer Professional. Back to the search result list.