Investigating the Eulerian numbers and uniform B-spline recurrence relations, a connection between Eulerian numbers and B-spline values at knot points is proved, and a relation to inner products of uniform B-splines is shown. This connection allows, with few operations, to evaluate the B-spline curve at domain knots and could be utilized to obtain an easy approximation and representation of B-s...

We extend Schoenberg’s family of polynomial splines with uniform knots to all fractional degrees α > −1. These splines, which involve linear combinations of the one-sided power functions x+ = max(0, x) α, are α-Hölder continuous for α > 0. We construct the corresponding B-splines by taking fractional finite differences and provide an explicit characterization in both time and frequency domains....

Diffusion Tensor MRI (DT-MRI) measurements are a discrete noisy sample of an underlying macroscopic effective diffusion tensor field, D(x), of water. This field is presumed to be piecewise continuous/smooth at a gross anatomical length scale. Here we describe a mathematical framework for obtaining an estimate of this tensor field from the measured DT-MRI data using a spline-based continuous app...

The objective of the paper is to continue the study of an interesting class of rational splines in polar coordinates, introduced by SS anchez-Reyes 17] and independently by de Casteljau 6]. We refer to these curves as p-splines. They are a generalization of certain analogous of B ezier curves in polar coordinates which we call p-B ezier. We present an alternative way to have an exact representa...

The layout of the survey is as follows. After a short discussion of cardinal B-splines, i.e., of B-splines on a uniform knot sequence, in Section 2, B-splines for an arbitrary knot sequence are introduced in Section 3 and shown to be a basis for certain spaces of piecewise polynomial functions. Various simple properties of B-splines are listed in Section 4, and the relationship between a spline...

s of MMA2015, May 26–29, 2015, Sigulda, Latvia c © 2015 ON HIGHER DEGREE F-TRANSFORMS BASED ON B-SPLINES MARTINS KOKAINIS and SVETLANA ASMUSS 1 Department of Mathematics, University of Latvia Zeļļu iela 8, R̄ıga, LV-1002, Latvia 2 Institute of Mathematics and Computer Science, University of Latvia Raiņa bulvāris 29, R̄ıga, LV-1459, Latvia E-mail: [email protected], [email protected] The ...

Ultrasonic scanning is the most commonly used method for detecting breast cancer. Traditional ultrasound mainly relies on manual examination, which requires doctors with rich clinical experience. The path planning of robot examination based binocular vision and non-uniform rational B-Splines (NURBS) proposed in this paper to solve limitations traditional methods. First, images are acquired by c...

Limit analysis can be used to directly calculate the ultimate load of structures without considering cumbersome elastic–plastic analysis. We present an adaptive mesh refinement strategy by mean extended isogeometric (XIGA) in association with second-order cone programming (SOCP) for kinematic limit hole and inclusion problems. The location captured level set function regard its interfaces. loca...