448 research outputs found
On multi-degree splines
Multi-degree splines are piecewise polynomial functions having sections of
different degrees. For these splines, we discuss the construction of a B-spline
basis by means of integral recurrence relations, extending the class of
multi-degree splines that can be derived by existing approaches. We then
propose a new alternative method for constructing and evaluating the B-spline
basis, based on the use of so-called transition functions. Using the transition
functions we develop general algorithms for knot-insertion, degree elevation
and conversion to B\'ezier form, essential tools for applications in geometric
modeling. We present numerical examples and briefly discuss how the same idea
can be used in order to construct geometrically continuous multi-degree
splines
Constructing an overall dynamical model for a system with changing design parameter properties
This study considers the identification problem for a class of non-linear parameter-varying systems associated with the following scenario: the system behaviour depends on some specifically prescribed parameter properties, which are adjustable. To understand the effect of the varying parameters, several different experiments, corresponding to different parameter properties, are carried out and different data sets are collected. The objective is to find, from the available data sets, a common parameter-dependent model structure that best fits the adjustable parameter properties for the underlying system. An efficient Common Model Structure Selection (CMSS) algorithm, called the Extended Forward Orthogonal Regression (EFOR) algorithm, is proposed to select such a common model structure. Two examples are presented to illustrate the application and the effectiveness of the new identification approach
Matrix representations for multi-degree B-splines
The paper is concerned with computing the B-spline basis of a multi-degree spline space, namely a space of piecewise functions comprised of polynomial segments of different degrees. To this aim, we provide a general method to work out a matrix representation relating the sought basis with another one easier to compute. This will allow us, for example, to calculate a multi degree B-spline basis starting from local Bernstein bases of different degrees or from the B-spline basis of a spline space where all sections have the same degree. This change of basis can be translated into a conceptually simple and computationally efficient algorithm for the evaluation of multi-degree B-splines
Identification of Nonlinear Parameter-Dependent Common-Structured models to accommodate varying experimental conditions and design parameter properties
This study considers the identification problem for a class of nonlinear parameter-varying systems associated with the following scenario: the system behaviour depends on some specifically prescribed parameter properties, which are adjustable. To understand the effect of the varying parameters, several different experiments, corresponding to different parameter properties, are carried out and different data sets are collected. The objective is to find, from the available data sets, a common parameter-dependent model structure that best fits the adjustable parameter properties for the underlying system. An efficient common model structure selection (CMSS) algorithm, called the extended forward orthogonal regression (EFOR) algorithm, is proposed to select such a common model structure. Several examples are presented to illustrate the application and the effectiveness of the new identification approach
Interactive display of isosurfaces with global illumination
Journal ArticleAbstract-In many applications, volumetric data sets are examined by displaying isosurfaces, surfaces where the data, or some function of the data, takes on a given value. Interactive applications typically use local lighting models to render such surfaces. This work introduces a method to precompute or lazily compute global illumination to improve interactive isosurface renderings. The precomputed illumination resides in a separate volume and includes direct light, shadows, and interreflections. Using this volume, interactive globally illuminated renderings of isosurfaces become feasible while still allowing dynamic manipulation of lighting, viewpoint and isovalue
Evolutionary structural pptimisation based on boundary element representation of b-spline geometry
Evolutionary Structural Optimisation (ESO) has become a well-established technique for determining the optimum shape and topology of a structure given a set of loads and constraints. The basic ESO concept that the optimum topology design evolves by slow removal and addition of material has matured over the last ten years. Nevertheless, the development of the method has almost exclusively considered finite elements (FE) as the approach for providing stress solutions. This thesis presents an ESO approach based on the boundary element method. Non-uniform rational B-splines (NURBS) are used to define the geometry of the component and, since the shape of these splines is governed by a set of control points, use can be made of the locations of these control points as design variables. The developed algorithm creates internal cavities to accomplish topology changes. Cavities are also described by NURBS and so they have similar behaviour to the outside boundary. Therefore, both outside and inside are optimised at the same time. The optimum topologies evolve allowing cavities to merge between each other and to their closest outer boundary. Two-dimensional structural optimisation is investigated in detail exploring multi-load case and multi-criteria optimisation. The algorithm is also extended to three-dimensional optimisation, in which promising preliminary results are obtained. It is shown that this approach overcomes some of the drawbacks inherent in traditional FE-based approaches, and naturally provides accurate stress solutions on smooth boundary representations at each iteration
Progettazione e Sviluppo di una Web App per curve MD-spline
La tesi si occupa della progettazione e sviluppo di una Web App scritta in HTML5 e canvas e JavaScript che ha l'obiettivo di permettere di sperimentare le potenzialità di una nuova classe di curve 2D utili per il disegno denominata C1 MD-spline
Exchangeability and sets of desirable gambles
Sets of desirable gambles constitute a quite general type of uncertainty
model with an interesting geometrical interpretation. We give a general
discussion of such models and their rationality criteria. We study
exchangeability assessments for them, and prove counterparts of de Finetti's
finite and infinite representation theorems. We show that the finite
representation in terms of count vectors has a very nice geometrical
interpretation, and that the representation in terms of frequency vectors is
tied up with multivariate Bernstein (basis) polynomials. We also lay bare the
relationships between the representations of updated exchangeable models, and
discuss conservative inference (natural extension) under exchangeability and
the extension of exchangeable sequences.Comment: 40 page
Statistically optimal continuous free energy surfaces from biased simulations and multistate reweighting
Free energies as a function of a selected set of collective variables are
commonly computed in molecular simulation and of significant value in
understanding and engineering molecular behavior. These free energy surfaces
are most commonly estimated using variants of histogramming techniques, but
such approaches obscure two important facets of these functions. First, the
empirical observations along the collective variable are defined by an ensemble
of discrete observations and the coarsening of these observations into a
histogram bins incurs unnecessary loss of information. Second, the free energy
surface is itself almost always a continuous function, and its representation
by a histogram introduces inherent approximations due to the discretization. In
this study, we relate the observed discrete observations from biased
simulations to the inferred underlying continuous probability distribution over
the collective variables and derive histogram-free techniques for estimating
this free energy surface. We reformulate free energy surface estimation as
minimization of a Kullback-Leibler divergence between a continuous trial
function and the discrete empirical distribution and show that this is
equivalent to likelihood maximization of a trial function given a set of
sampled data. We then present a fully Bayesian treatment of this formalism,
which enables the incorporation of powerful Bayesian tools such as the
inclusion of regularizing priors, uncertainty quantification, and model
selection techniques. We demonstrate this new formalism in the analysis of
umbrella sampling simulations for the torsion of a valine sidechain in
the L99A mutant of T4 lysozyme with benzene bound in the cavity.Comment: 24 pages, 5 figure
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