This paper shows that, for any given T-spline, the linear independence of its blending functions can be determined by computing the nullity of the T-spline-to-NURBS transform matrix. The paper analyzes the class of Tsplines for which no perpendicular T-node extensions intersect, and shows that the blending functions for any such T-spline are linearly independent.

Analogous to the quadratic B-spline curve, a piecewise quadratic trigonometric polynomial curve is presented in this paper. The quadratic trigonometric polynomial curve has C2 continuity, while the quadratic B-spline curve has C1 continuity. The quadratic trigonometric polynomial curve is closer to the given control polygon than the quadratic B-spline curve.

The non-polynomial spline method is proposed to solve a singular boundary value problems. Some model problems are solved and the numerical results are compared with B-spline approximation and the exact solution. Results obtained by the method indicate the method is simple and effective. Key–Words: Singular point; Singular two-point boundary value problems; Cubic spline

A new algorithm for Computer Aided Geometric Design of least squares (LS) splines with variable knots, named GeDS, is presented. It is based on interpreting functional spline regression as a parametric B-spline curve, and on using the shape preserving property of its control polygon. The GeDS algorithm includes two major stages. For the first stage, an automatic adaptive, knot location algorith...

We study the problem of computing a planar curve, restricted to lie between two given polygonal chains, such that the integral of the square of arc-length derivative of curvature along the curve is minimized. We introduce the Minimum Variation B-spline problem which is a linearly constrained optimization problem over curves defined by Bspline functions only. An empirical investigation indicates...

We proposed the I-spline Smoothing approach for calibrating predictive models by solving a nonlinear monotone regression problem. We took advantage of I-spline properties to obtain globally optimal solutions while keeping the computational cost low. Numerical studies based on three data sets showed the empirical evidences of I-spline Smoothing in improving calibration (i.e.,1.6x, 1.4x, and 1.4x...

B-spline filter kernals have proved useful in many pixel sampling applications. A cubic B-spline filter kernal, having a width of four pixels, is particularly effective. In distribution ray tracing, pixel filters are evaluated implicitly by having the density of sampling proportional to the filter value. In this work we present a simple method to generate random samples having an underlying B-s...

The non-local hyperbolic partial differential equations have many applications in sciences and engineering. A collocation finite element approach based on exponential cubic B-spline and quintic B-spline are presented for the numerical solution of the wave equation subject to nonlocal boundary condition. Von Neumann stability analysis is used to analyze the proposed methods. The efficiency, accu...

The spline collocation method  is employed to solve a system of linear and nonlinear Fredholm and Volterra integro-differential equations. The solutions are collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. We obtain the unique solution for linear and nonlinear system $(nN+3n)times(nN+3n)$ of integro-differential equations. This approximation reduces th...