The evaluation of points and the computations of in¯ection points or cusps on a curve are often necessary in CAGD applications. When a curve is represented in a B-spline form, such computations can be made easier once it is transformed into a set of piecewise polynomial curves in power form. The usual practice of the transformation of a B-spline curve into a set of piecewise polynomial curves i...

The Finite Cell Method (FCM), which combines the fictitious domain concept with high-order p-FEM, permits the effective solution of problems with very complex geometry, since it circumvents the computationally expensive mesh generation and guarantees exponential convergence rates for smooth problems. The present contribution deals with the coupling of the FCM approach, which has been applied so...

The objective of this study was to assess the efficiency of three mathematical models (power, exponential and logarithmic functions) for the calculation of the horizontal mass transport (HMT), as compared to the linear spline interpolation for the Cyclone Dust Sampler (CDS) and one with a Cone (CDSC), modified Wilson and Cooke trap (MWAC) and big spring number eight (BSNE). For the purposes of t...

Univariate subdivision schemes are efficient iterative methods to generate smooth limit curves starting from a sequence of arbitrary points. Aim of this paper is to present and investigate a new family of 6-point interpolatory non-stationary subdivision schemes capable of reproducing important curves of great interest in geometric modeling and engineering applications, if starting from uniforml...

In this paper we present a novel approach to construct B-spline wavelets under constraints, taking advantage of the lifting scheme. Constrained B-spline wavelets allow multiresolution analysis of B-splines which fixes positions, tangents and/or high order derivatives at some user specified parameter values, thus extend the ability of B-spline wavelets: smoothing a curve while preserving user sp...

This paper addresses the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. The basic idea of the approach is to find the conditions for precise merging of two B-spline curves, and perturb the control points of the curves by constrained optimization subject to satisfying these conditions. To obtain a merged curve without superfluous knots, we present a new k...

New approaches of particle swarm optimisation algorithm based on Gaussian and Cauchy distributions to adjust the control points of B-spline neural networks are proposed. B-spline networks are trained by gradient-based methods, which may fall into local minimum during the learning procedure. To overcome the problems encountered by the conventional learning methods, particle swarm optimisation  ...

We present a data reduction scheme for efficient surface storage, by introducing a coefficient–based least squares spline operator that does not require any pointwise evaluation to approximate (in a lower dimension spline space) a given bivariate B–spline function. In order to define an accurate approximation of the target spline with a significant reduction of the space dimension, this operato...

The main goal of this paper is to present some generalizations of polynomial B-splines, which include exponential B-splines and the larger family of exponential pseudo-splines. We especially focus on their connections to subdivision schemes. In addition, we generalize a well-known result on the approximation order of exponential pseudo-splines, providing conditions to establish the approximatio...