Abstract: Cubic pencils of lines are classified up to projectivities. Explicit formulae for the addition of lines on the set of nonsingular lines of the pencils are given. These formulae can be used for constructing planar generalized principal lattices, which are sets of points giving rise to simple Lagrange formulae in bivariate interpolation. Special attention is paid to the irreducible nons...

In this paper, geometric interpolation by G cubic spline is studied. A wide class of sufficient conditions that admit a G cubic spline interpolant is determined. In particular, convex data as well as data with inflection points are included. The existence requirements are based upon geometric properties of data entirely, and can be easily verified in advance. The algorithm that carries out the ...

In this paper, a simple adaptive interpolation approach is proposed for image interpolation. It depends on modifying the warped distance technique for image interpolation considering the local activity levels in each region of the image. This is performed by weighting the pixels used in the interpolation process with different adaptive weights. The adaptation can be extended to different tradit...

UNLABELLED In myocardial SPECT perfusion imaging, reorientation algorithms from transaxial image planes are used to generate short- and long-axis views of myocardial tracer uptake. We performed phantom experiments with 201Tl to delineate how image reorientation affects the results of quantitative image analysis. METHODS Thirty consecutive patient studies were analyzed to characterize the dist...

Important emerging sources of big data are large-scale predictive simulation models used in e-science and, increasingly, in guiding policy and investment decisions around highly complex issues such as population health and safety. The Splash project provides a platform for combining existing heterogeneous simulation models and datasets across a broad range of disciplines to capture the behavior...

This report presents several approaches aimed at reducing the bias and uncertainty of the free energy difference estimates obtained using the thermodynamic integration simulation strategy. The central idea is to utilize interpolation schemes, rather than the often-used trapezoidal rule quadrature, to fit the thermodynamic integration data, and obtain a more accurate and precise estimate of the ...

We study the use of cubic spline interpolation to represent the centerline of a road, for curves in both R2 and R3 . We look at algorithms to create a representation based on arc length and evenly spaced nodes along the centerline. We also consider methods for moving between rectangular coordinates and coordinates based on distance along the centerline and the offset from that centerline (in R2...

This paper presents a fast and accurate method to determine the available transfer capability. Ralston’smethod is used to predict the two trajectory points of voltagemagnitude, power flow, and maximum generator rotor angle difference. Then, the cubic spline interpolation technique is used to accurately trace the P-V, P-S, or P-Δδ curves between two points of trajectory. The P-V, P-S and PΔδ cur...

In this paper, G continuous cubic spline interpolation of data points in R, based on a discrete approximation of the strain energy, is studied. Simple geometric conditions on data are presented that guarantee the existence of the interpolant. The interpolating spline is regular, loop-, cuspand fold-free.