The dimension of bivariate spline spaces of smoothness r for degree \(d\geq 4r+1\)
From MaRDI portal
Publication:1103799
DOI10.1007/BF01890563zbMath0646.41008MaRDI QIDQ1103799
Peter Alfeld, Larry L. Schumaker
Publication date: 1987
Published in: Constructive Approximation (Search for Journal in Brave)
Numerical computation using splines (65D07) Multidimensional problems (41A63) Spline approximation (41A15)
Related Items
Macro-elements and stable local bases for splines on Powell-Sabin triangulations, A \(C^ 2\) finite element and interpolation, The dimension of a class of bivariate spline spaces, Recursive computation of bivariate Hermite spline interpolants, Multivariate splines and the Bernstein-Bézier form of a polynomial, Algebraic methods in approximation theory, Piecewise polynomials on polyhedral complexes, The Dimension of the Space of Smooth Splines of Degree 8 on Tetrahedral Partitions, Local cohomology of bivariate splines, Dual bases for spline spaces on cells, A family of ideals of minimal regularity and the Hilbert series of \(C^r(\widehat\Delta)\), A spectral sequence for splines, Local Lagrange interpolations using bivariate \(C^2\) splines of degree seven on triangulated quadrangulations, Minimally supported bases for spaces of bivariate piecewise polynomials of smoothness r and degree \(d\geq 4r+1\), On convexity of piecewise polynomial functions on triangulations, On multi-level bases for elliptic boundary value problems, The bivariate quadratic \(C^1\) spline spaces with stable dimensions on the triangulations, Spline spaces with mixed orders of continuity over T-meshes, Dimension of polynomial splines of mixed smoothness on T-meshes, Lattice-supported splines on polytopal complexes, \(G^1\) spline functions for point cloud fitting, A lower bound for the dimension of tetrahedral splines in large degree, Dimension of mixed splines on polytopal cells, Multivariate polynomial splines on generalized oranges, Generalized splines on graphs with two labels and polynomial splines on cycles, Frames for vector spaces and affine spaces, Multivariate vertex splines and finite elements, Smooth interpolation to scattered data by bivariate piecewise polynomials of odd degree, On the dimensions of bivariate spline spaces and the stability of the dimensions, Construction of quintic Powell-Sabin spline quasi-interpolants based on blossoming, Splines with boundary conditions, Super spline spaces of smoothness \(r\) and degree \(d\geq{} 3r+2\), A normalized basis for \(\mathcal{C}^1\) cubic super spline space on Powell-Sabin triangulation, On structure of bivariate spline space of lower degree over arbitrary triangulation, A new bound for smooth spline spaces, On the dimension of bivariate spline spaces on generalized quasi-cross- cut partitions, A new finite element of \(C^ 1\) cubic splines, On dimension and existence of local bases for multivariate spline spaces, On the complexity of isolating real roots and computing with certainty the topological degree, Polynomial splines of non-uniform degree on triangulations: combinatorial bounds on the dimension, Dimensions of spline spaces over unconstricted triangulations, Dimensions of spline spaces over T-meshes, Structure and dimension of multivariate spline space of lower degree on arbitrary triangulation, On the dimension of bivariate spline spaces of smoothness r and degree \(d=3r+1\), A dimension series for multivariate splines, Counting the dimension of splines of mixed smoothness. A general recipe, and its application to planar meshes of arbitrary topologies, Associated primes of spline complexes, A bivariate \(C^1\) cubic super spline space on Powell-Sabin triangulation, An explicit local basis for \(C^{1}\) cubic spline spaces over a triangulated quadrangulation, The generic dimensions of the space of smooth splines of degree 7 on tetrahedral partitions, Graphs admitting only constant splines, On \(C^ 2\) quintic spline functions over triangulations of Powell-Sabin's type, Homology of Smooth Splines: Generic Triangulations and a Conjecture of Strang, A B-spline-like basis for the Powell-Sabin 12-split based on simplex splines, Bivariate spline spaces and minimal determining sets, Interpolation by spline spaces on classes of triangulations, A counter-example to the Schenck-Stiller ``\(2r + 1\) conjecture, A Lower Bound for Splines on Tetrahedral Vertex Stars, Developments in bivarite spline interpolation, Quasi-splines and their moduli, Module and vector space bases for spline spaces, Multivariate weak spline function space
Cites Work
- Unnamed Item
- Unnamed Item
- Bounds on the dimension of spaces of multivariate piecewise polynomials
- A survey of curve and surface methods in CAGD
- Minimally supported bases for spaces of bivariate piecewise polynomials of smoothness r and degree \(d\geq 4r+1\)
- Interpolation polynomials on the triangle
- A Nodal Basis for C 1 Piecewise Polynomials of Degree n ≥5