Composite finite elements of class Ck
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In this paper, the Hermite problem Hk(A, V) is solved in V = Pkn(D, τ) iff n ⩾ 4k+1 (Ženisek).About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 1985-05-01 and is currently open access. It has received 41 citations till now.read more
Citations
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Journal ArticleDOI
Triangular Berstein-Be´zier patches
TL;DR: The C’ Powell-Sabin interpolants and the Clough-Tocher split are described, respectively, as well as the general case, Split Triangle Interpolants and Split Triangle square interpolants, which are described as follows:.
Journal ArticleDOI
Fitting scattered data on sphere-like surfaces using spherical splines
TL;DR: In this paper, the authors propose a space of polynomial splines defined on planar traingulations for fitting scattered data in the plane, using macro-element and minimal energy splines.
Journal ArticleDOI
Developments in bivariate spline interpolation
TL;DR: In this paper, a survey of the field of interpolation by bivariate splines is presented, where the authors summarize results on the dimension and the approximation order of the spline spaces, and describe interpolation methods for these spaces.
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Construction of Normalized B-Splines for a Family of Smooth Spline Spaces Over Powell–Sabin Triangulations
TL;DR: A suitable B-spline representation for a family of bivariate spline functions with smoothness r≥1 and polynomial degree 3r−1 is constructed and an efficient and stable computation of the Bernstein–Bézier form is provided.
References
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Journal ArticleDOI
Triangular Berstein-Be´zier patches
TL;DR: The C’ Powell-Sabin interpolants and the Clough-Tocher split are described, respectively, as well as the general case, Split Triangle Interpolants and Split Triangle square interpolants, which are described as follows:.
Journal ArticleDOI
Piecewise Quadratic Approximations on Triangles
M. J. D. Powell,M. A. Sabin +1 more
TL;DR: Two methods of constructing piecewise quadratic approximations are described which have the property that, if they are applied on each triangle of a triangulation, then ~(x, y) and its first derivatives are continuous everywhere.
Book ChapterDOI
Mathematical and practical possibilities of unisurf
TL;DR: The UNISURF system as mentioned in this paper was designed to help car body design and tooling and mainly to cut down delay and increase accuracy and smoothness, but it was not intended for nonmathematicians.
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C1 quintic interpolation over triangles: Two explicit representations
R. E. Barnhill,G. Farin +1 more
TL;DR: In this paper, two explicit representations of a C1 quintic interpolant over triangles are derived by generalization of Coons' methods and Bernstein-Bezier methods, respectively.