Results 1  10
of
222
On the evaluation of box splines
"... The first (and for some still the only) multivariate Bspline is what today one would call the simplex spline, since it is derived from a simplex, and in distinction to other polyhedral splines, such as the cone spline and the box spline. The simplex spline was first talked about in 1976. However, i ..."
Abstract

Cited by 201 (8 self)
 Add to MetaCart
The first (and for some still the only) multivariate Bspline is what today one would call the simplex spline, since it is derived from a simplex, and in distinction to other polyhedral splines, such as the cone spline and the box spline. The simplex spline was first talked about in 1976. However
Stable Evaluation of Box Splines
 Numerical Algorithms
, 1996
"... The most elegant way to evaluate boxsplines is by using their recursive definition. However, a straightforward implementation reveals numerical difficulties. A careful analysis of the algorithm allows a reformulation which overcomes these problems without losing efficiency. A concise vectorized MAT ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
The most elegant way to evaluate boxsplines is by using their recursive definition. However, a straightforward implementation reveals numerical difficulties. A careful analysis of the algorithm allows a reformulation which overcomes these problems without losing efficiency. A concise vectorized
to Box Spline Theory
"... We investigate the relation between an ideal I of finite codimension in the space Π of multivariate polynomials and ideals which are generated by lower order perturbations of some generators for I. Of particular intereest are the codimension of these ideals and the local approximation order of their ..."
Abstract
 Add to MetaCart
of their kernels. The discussion, stimulated by recent results in approximation theory, allows us to provide a simple analysis of the polynomial and exponential spaces associated with box splines. We describe their structure, dimension, local approximation order and an algorithm for their construction
Quasiinterpolation projectors for box splines
, 2008
"... We consider box spline quasiinterpolants based on local linear functionals of point evaluator and integral type. The approximations are easy to compute, and reproduce the whole spline space in question. ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
We consider box spline quasiinterpolants based on local linear functionals of point evaluator and integral type. The approximations are easy to compute, and reproduce the whole spline space in question.
Biorthogonal Box Spline Wavelet Bases
"... Some specific box splines are refinable functions with respect to n x n expanding integer scaling matrices M satisfying M^n = 2I. Therefore they can be used to define a multiresolution analysis and a wavelet basis associated with these scaling matrices. In this paper, we construct biorthogonal wavel ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Some specific box splines are refinable functions with respect to n x n expanding integer scaling matrices M satisfying M^n = 2I. Therefore they can be used to define a multiresolution analysis and a wavelet basis associated with these scaling matrices. In this paper, we construct biorthogonal
Deriving BoxSpline Subdivision Schemes
"... Abstract. We describe and demonstrate an arrow notation for deriving boxspline subdivision schemes. We compare it with the ztransform, matrix, and mask convolution methods of deriving the same. We show how the arrow method provides a useful graphical alternative to the three numerical methods. We ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Abstract. We describe and demonstrate an arrow notation for deriving boxspline subdivision schemes. We compare it with the ztransform, matrix, and mask convolution methods of deriving the same. We show how the arrow method provides a useful graphical alternative to the three numerical methods. We
BoxSpline Tilings
, 1989
"... We describe a simple method for generating tilings of IR d . The basic tile is defined as# := {x # IR d : f(x) < f(x + j) #j # ZZ d \0}, with f a real analytic function for which f(x + j) # # as j # # for almost every x. ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
We describe a simple method for generating tilings of IR d . The basic tile is defined as# := {x # IR d : f(x) < f(x + j) #j # ZZ d \0}, with f a real analytic function for which f(x + j) # # as j # # for almost every x.
Scattered data interpolation by box splines
, 2007
"... Given scattered data in IR s, interpolation from a dilated box spline space SM(2 k ·) is always possible for a fine enough scaling. For example, for the Lagrange function of a point θ one could take any shifted dilate M(2 k · −j) which is nonzero at θ and zero at the other interpolation points. Howe ..."
Abstract
 Add to MetaCart
Given scattered data in IR s, interpolation from a dilated box spline space SM(2 k ·) is always possible for a fine enough scaling. For example, for the Lagrange function of a point θ one could take any shifted dilate M(2 k · −j) which is nonzero at θ and zero at the other interpolation points
Results 1  10
of
222