Multivariate complex B-splines and Dirichlet averages
نویسندگان
چکیده
منابع مشابه
Multivariate complex B-splines and Dirichlet averages
The notion of complex B-spline is extended to a multivariate setting by means of ridge functions employing the known geometric relationship between ordinary B-splines and multivariate B-splines. To derive properties of complex B-splines in R, 1 < s ∈ N, the Dirichlet average has to be generalized to include infinite dimensional simplices △∞. Based on this generalization several identities of mu...
متن کاملMultivariate Complex B-Splines, Dirichlet Averages and Difference Operators
For the Schoenberg B-splines, interesting relations between their functional representation, Dirichlet averages and difference operators are known. We use these relations to extend the B-splines to an arbitrary (infinite) sequence of knots and to higher dimensions. A new Fourier domain representation of the multidimensional complex B-spline is given. 1. Complex B-Splines Complex B-splines are a...
متن کاملDouble Dirichelet Averages and Complex B-Splines
A relation between double Dirichlet averages and multivariate complex B-splines is presented. Based on this reationship, a formula for the computation of certain moments of multivariate complex B-splines is derived.
متن کاملComplex B - splines
We propose a complex generalization of Schoenberg’s cardinal splines. To this end, we go back to the Fourier domain definition of the B-splines and extend it to complex-valued degrees. We show that the resulting complex B-splines are piecewise modulated polynomials, and that they retain most of the important properties of the classical ones: smoothness, recurrence, and two-scale relations, Ries...
متن کاملModelling robot manipulators with multivariate B-splines
In programming robot manipulators to carry out a wide variety of tasks it would be desirable to create a cad system in which these tasks can be programmed at the task level, leaving the ne-grained detail of path planning and collision detection to the system. This paper describes the theoretical background to such a system, by providing a model in which robot motions are represented using multi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2010
ISSN: 0021-9045
DOI: 10.1016/j.jat.2009.05.002