Even though isogeometric analysis has a clear advantage regarding the number of degrees of freedom needed to achieve a certain level of accuracy, the time needed for matrix assembly (by means of numerical integration of stiffness or mass matrix entries) constitutes a severe bottleneck in the process. In order to overcome this difficulty, we propose the new approach of Integration by Interpolati...

The interpolation algorithm plays an essential role in the digital image correlation (DIC) technique for shape, deformation, and motion measurements with subpixel accuracies. At the present, little effort has been made to improve the interpolation methods used in DIC. In this Letter, a family of recursive interpolation schemes based on B-spline representation and its inverse gradient weighting ...

Smoothness is a desirable characteristic of interpolated zero curves; not only is it intuitively appealing, but there is some evidence that it provides more accurate pricing of securities. This paper outlines the mathematics necessary to understand the smooth interpolation of zero curves, and describes two useful methods: cubic-spline interpolation—which guarantees the smoothest interpolation o...

A method is presented to interpolate real affine plane curves with second degree NURBS (Non Uniform Rational Bezier Splines). The curve into object is initially partitioned into an arbitrary number of arcs. Then each arc is approximated with a conic section passing thru its extremes, thru a third intermediate point and being tangent to the arc at the extremes. Each arc is then parameterized by ...

As usual, denote by KW [a, b] the Sobolev class consisting of every function whose (r − 1)st derivative is absolutely continuous on the interval [a, b] and its rth derivative is bounded by K a.e. in [a, b]. For a function f ∈ KW [a, b], its values and derivatives up to r−1 order at a set of nodes x are known. These values are said to be given Hermite information. This work reports results on be...

In this paper we consider discrete splines S(j), j ∈ Z, with equidistant nodes which may grow as O(|j|s) as |j| → ∞. Such splines are relevant for the purposes of digital signal processing. We give the definition of discrete B-splines and describe their properties. Discrete splines are defined as linear combinations of shifts of the B-splines. We present a solution to the problem of discrete sp...

In this paper, we will apply cubic B-splines on a uniform mesh to explore the numerical solutions and numerical derivatives of a class of nonlinear second-order boundary value problems with two dependent variables. Our new method is based on the cubic spline interpolation. The analytical solutions and any-order derivatives can be well approximated with 4th order accuracy. Furthermore, our new m...

This paper presents an algorithm for solving forward kinematics problem of the Stewart Platform and an application for modeling of the Stewart Platform's motions. The developed application is able to solve forward kinematics problem in given accuracy; to calculate curve of the tool positioned on the mobile platform; to calculate possible deviation of the tool from a nominal position if lengths ...

Trivariate splines solve a special case of scattered data interpolation problem in the volume bounded by two concentric spheres. A triangulation ∆ of the unit sphere S is constructed based on the vertex set V. Given a partition P of the interval [1, R], let Sτ×ρ σ×δ be the space of the spherical splines of degree σ and smoothness τ over ∆ tensored with the univariate radial splines of degree δ ...

Achieving accurate interpolation is an important requirement for many signal-processing applications. While nearest-neighbor and linear interpolation methods are popular due to their native GPU support, they unfortunately result in severe undesirable artifacts. Better interpolation methods are known but lack a native GPU support. Yet, a particularly attractive one is prefiltered cubicspline int...