Recurrence relations for multivariate $B$-splines
نویسندگان
چکیده
منابع مشابه
On real-analytic recurrence relations for cardinal exponential B-splines
Let LN+1 be a linear differential operator of order N + 1 with constant coefficients and real eigenvalues 1, . . . , N+1, let E( N+1) be the space of all C∞-solutions of LN+1 on the real line. We show that for N 2 and n = 2, . . . , N , there is a recurrence relation from suitable subspaces En to En+1 involving real-analytic functions, andwithEN+1=E( N+1) if and only if contiguous eigenvalues a...
متن کاملA recurrence relation for rational B-splines
In this note a recurrence relation for rational B-splines is presented. Using this formula, it is possible to write a rational spline in terms of normalized rational B-splines of lower order, with certain rational coeecients; these coincide with that generated by the well-known "rational version of the de Boor algorithm" based on knot-insertion Farin '88], Farin '89]. A modiied relation is pres...
متن کاملMultivariate 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 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 کاملMultivariate Splines with Convex B Patch Control Nets are Convex
In this paper results from a forthcoming paper are presented concerning the convexity of multivariate spline functions built from B patches Conditions are given under which it is possible to de ne a control net for such spline functions The control net is understood as a piecewise linear function If it is convex then so is the underlying spline
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: Proceedings of the American Mathematical Society
سال: 1982
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1982-0656111-8