Control vectors for splines

Traditionally, modelling using spline curves and surfaces is facilitated by control points. We propose to enhance the modelling process by the use of control vectors. This improves upon existing spline representations by providing such facilities as modelling with local (semi-sharp) creases, vanishing and diagonal features, and hierarchical editing. While our prime interest is in surfaces, most of the ideas are more simply described in the curve context. We demonstrate the advantages provided by control vectors on several curve and surface examples and explore avenues for future research on control vectors in the contexts of geometric modelling and finite element analysis based on splines, and B-splines and subdivision in particular.This is the final published manuscript. It is available from Elsevier in Computer-Aided Design here: http://www.sciencedirect.com/science/article/pii/S0010448514001973

A new local basis for designing with tensioned splines

Journal ArticleRecently there has been a great deal of interest in the use of "tension" parameters to augment control mesh vertices as design handles for piecewise polynomials. A particular local cubic basis called p-splines, which has been termed a "generalization of B-splines", has been proposed as an appropriate basis. These functions are defined only for floating knot sequences. This paper uses the known property of B-splines that with appropriate knot vectors they span what are called here spaces of tensioned splines, and that particular combinations of them, called LT-splines, form bases for the spaces of tensioned splines. In addition, this paper shows that these new proposed bases have the variation diminishing property, the convex hull property, and straightforward knot insertion algorithms, and that both curves and individual basis functions can be easily computed. Sometimes it is desirable to interpolate points and also use these tension parameters so interpolation methods using the LT-spline bases are presented. Finally, the above properties are established for uniform and nonuniform knot vectors, open and floating end conditions, and homogeneous and nonhomogeneous tension parameter pairs

On Using a Support Vector Machine in Learning Feed-Forward Control

For mechatronic motion systems, the performance increases significantly if, besides feedback control, also feed-forward control is used. This feed-forward part should contain the (stable part of the) inverse of the plant. This inverse is difficult to obtain if non-linear dynamics are present. To overcome this problem, learning feed-forward control can be applied. The properties of the learning mechanism are of importance in this setting. In the paper, a support vector machine is proposed as the learning mechanism. It is shown that this mechanism has several advantages over other learning techniques when applied to learning feed-forward control. The method is tested with simulation

Estimation of constant and time-varying dynamic parameters of HIV infection in a nonlinear differential equation model

Modeling viral dynamics in HIV/AIDS studies has resulted in a deep understanding of pathogenesis of HIV infection from which novel antiviral treatment guidance and strategies have been derived. Viral dynamics models based on nonlinear differential equations have been proposed and well developed over the past few decades. However, it is quite challenging to use experimental or clinical data to estimate the unknown parameters (both constant and time-varying parameters) in complex nonlinear differential equation models. Therefore, investigators usually fix some parameter values, from the literature or by experience, to obtain only parameter estimates of interest from clinical or experimental data. However, when such prior information is not available, it is desirable to determine all the parameter estimates from data. In this paper we intend to combine the newly developed approaches, a multi-stage smoothing-based (MSSB) method and the spline-enhanced nonlinear least squares (SNLS) approach, to estimate all HIV viral dynamic parameters in a nonlinear differential equation model. In particular, to the best of our knowledge, this is the first attempt to propose a comparatively thorough procedure, accounting for both efficiency and accuracy, to rigorously estimate all key kinetic parameters in a nonlinear differential equation model of HIV dynamics from clinical data. These parameters include the proliferation rate and death rate of uninfected HIV-targeted cells, the average number of virions produced by an infected cell, and the infection rate which is related to the antiviral treatment effect and is time-varying. To validate the estimation methods, we verified the identifiability of the HIV viral dynamic model and performed simulation studies.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS290 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Formulation of an isogeometric shell element for crash simulation

In this paper, we propose, for the isogeometric analysis, a shell model based on a degenerated three dimensional approach. It uses a first order kinematic description in the thickness with transverse shear (Reissner-Mindlin theory). We examine various approaches to describe the geometry and compare them on various linear and non-linear benchmark problems. Both geometric and material non-linearities are treated. The obtained results are compared with the solutions of isogeometric solid model and with other numerical solutions found in the literature