A quadratic spline is a differentiable piecewise quadratic function. Many problems in numerical analysis and optimization literature can be reformulated as unconstrained minimizations of quadratic splines. However, only special cases of quadratic splines are studied in the existing literature, and algorithms are developed on a case by case basis. There lacks an analytical representation of a ge...

To describe the tool path of a CNC machine, it is often necessary to approximate curves by G arc splines with the number of arc segments as small as possible. Ahn et al. have proposed an iterative algorithm for approximating quadratic Bézier curves by G arc splines with fewer arc segments than the biarc method. This paper gives the formula of the upper bound for arc segments used by their algor...

in the present research, implementations of different computational geometry technologies in isogeometric analysis framework for computational fracture mechanics are investigated. nurbs and t-splines are two different computational geometry technologies which are studied in this work. among features of b-spline basis functions the possibility of enhancing a b-spline basis with discontinuities b...

Powell-Sabin splines are piecewise quadratic polynomials with global C-continuity. They are defined on conformal triangulations of two-dimensional domains, and admit a compact representation in a normalized B-spline basis. Recently, these splines have been used successfully in the area of computer-aided geometric design for the modelling and fitting of surfaces. In this paper, we discuss the ap...

We investigated the benefit of incorporating a negativity penalty into a least-squares criterion used to reconstruct 3-D radiotracer distributions in cardiac SPECT studies. B-spline spatial basis functions were used to provide a continuous model for the 3-D tracer distribution. Spline coefficients that tended to have negative values were identified and were constrained to stay near zero with us...

Bivariate cubic L1 smoothing splines are introduced. The coefficients of a cubic L1 smoothing spline are calculated by minimizing the weighted sum of the L1 norms of second derivatives of the spline and the 1 norm of the residuals of the data-fitting equations. Cubic L1 smoothing splines are compared with conventional cubic smoothing splines based on the L2 and 2 norms. Computational results fo...

In this paper, we present a discussion of the proper orthogonal decomposition (POD) as applied to simulation and feedback control of the one dimensional heat equation. We provide two examples of input collections to which the POD process is applied. First, we apply POD directly to the nite element basis of linear B-splines. Next we additionally include time snapshots. We show that although the ...

the aim of the present study was the estimation of (co) variance components and genetic parameters for body weight of moghani sheep, using random regression models based on b-splines functions. the data set included 9165 body weight records from 60 to 360 days of age from 2811 moghani sheep, collected between 1994 to 2013 from jafar-abad animal research and breeding institute, ardabil province,...

This paper introduces a grammar-based model for developing a multi-thread multi-frontal parallel direct solver for onedimensional isogeometric finite element method. The model includes the integration of B-splines for construction of the element local matrices and the multi-frontal solver algorithm. The integration and the solver algorithm are partitioned into basic indivisible tasks, namely th...

Hierarchical Powell-Sabin splines are C-continuous piecewise quadratic polynomials defined on a hierarchical triangulation. The mesh is obtained by partitioning an initial conforming triangulation locally with a triadic split, so that it is no longer conforming. We propose a normalized quasi-hierarchical basis for this spline space. The B-spline basis functions have a local support, they form a...