Finding a basis 〈φ1,… ,φd 〉 for a d-dimensional vector space of cubic splines allows us to express any element x of the vector space as x = α1φ1 +… +αd φd where α1,… , αd ∈ R. For the case of a vector space of cubic spline functions, some basis sets can ...
The cubic B-spline functions S(t) is constructed as a weighted sum of m+2 cubic B-spline basis functions Bi(t), namely (20)S(t)=∑i=−1mciBi(t) where ci are the unknown parameters of the cubic B-spline basis functions Bi(t). It is possible to approximate the unknown gust w...
UniformCubicB-splineon[0,1)•Fourcontrolpointsarerequiredtodefinethecurvefor0t<1(tistheparameter)–Notsurprisingforacubiccurvewith4degreesoffreedom •TheequationlooksjustlikeaBeziercurve,butwithdifferentbasisfunctions –Alsocalledblendingfunctions-theydescribehowtoblendthecontrolpointstomakethecurve x(t)...
Cubic Spline: A cubic spline is a function defined by multiple sub-functions. Each function has a sub-domain where is part of whole domains. A cubic spline has to guarantee the continuity at the data points in the full domain. The function is continue only if the first and second derivati...
cubic spline [′kyü·bik ′splīn] (mathematics) One of a collection of cubic polynomials used in interpolating a function whose value is specified at each of a collection of distinct ordered values,Xi(i=1, …,n), and whose slope is specified atX1andXn; one cubic polynomial is found for...
摘要: In this paper, using the cubic spline function, we establish the formula of approximate integration for Cauchy type singular integrals, give the estimations of approximate error.关键词: Cubic Spline Functions Hilbert Subspace Reproducing Kernel Cauehy-Type Singular Integral Quadrature Formula 被引...
The phase curve is approximated with the cubic spline function with a fixed number of characteristic points equidistantly distributed phase. Because such a smoothing function depends on the value of the initial epoch it is proposed to use the mean of some spline curves corresponding to various ...
The given equation is decomposed into a system of equations and modified cubic B-spline basis functions have been used for spatial variable and its derivatives, which gives results in amenable system of ordinary differential equations. The resulting system of equation has subsequently been solved by ...
This study develops an improved Feldkamp–Davis–Kress (FDK) reconstruction algorithm using non-local total variation (NLTV) denoising and a cubic B-spline interpolation-based backprojector to enhance the image quality of low-dose cone-beam computed tomography (CBCT). The NLTV objective function is...
Spline theoryPublisher's description: Spline functions arise in a number of fields: statistics, computer graphics, programming, computer-aided design technology, numerical analysis, and other areas of applied mathematics. Much work has focused on approximating splines such as B-splines and B茅zier ...