Sentence examples for basis functions of degree from inspiring English sources

A class of new polynomial basis functions with n − 1 local shape control parameters is presented here to allow the construction of Bézier curves with n local shape control parameters, which is an extension to the classical Bernstein basis functions of degree n.

Specifically, when the shape parameters are (lambda_{i} = 0) ((i = 1,2, ldots,n)), the generalized Bernstein basis functions of degree n degenerate into the classical Bernstein basis functions of degree n.

The generalized Bernstein basis functions of degree n, as shown in (1), associated with the shape parameters (lambda_{i}) ((i = 1,2, ldots,n)), are linearly independent.

where w i is the weights, P i is the control points (vector), and N i,k is the normalized B-spline basis functions of degree k.

Since the Bernstein basis functions of degree (n+1) are linearly independent, we obtain (beta_{i} = 0) ((i = 0,1, ldots,n + 1)).

The spatially coherent transient deformation field is expanded in Deslauriers-Dubuc (DD) interpolating wavelet basis functions of degree 3 as in Ohtani et al. (2010); only the horizontal components of the GPS time series are analyzed because of significantly larger colored noise in the vertical.

(J_{n,k}(x)) is the Bézier basis function of degree n.

If a knot appears i times, the continuity of a NURBS basis function of degree p at that knot is C p - i.

Growth rates for resistive tearing modes with experimentally relevant Lundquist number are computed accurately with time-steps that are large with respect to the global Alfvén time and moderate spatial resolution when the finite elements have basis functions of polynomial degree (p) two or larger.

In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees.

Thus, the Shannon number of basis functions to degree N = 360 is K ≈ 6104 for the 25°-radius spherical cap centered on Australia in this study.