Rational-spline approximation with automatic tension adjustment

An algorithm for weighted least-squares approximation with rational splines is presented. A rational spline is a cubic function containing a distinct tension parameter for each interval defined by two consecutive knots. For zero tension, the rational spline is identical to a cubic spline; for very large tension, the rational spline is a linear function. The approximation algorithm incorporates an algorithm which automatically adjusts the tension on each interval to fulfill a user-specified criterion. Finally, an example is presented comparing results of the rational spline with those of the cubic spline

An algorithm for surface smoothing with rational splines

Discussed is an algorithm for smoothing surfaces with spline functions containing tension parameters. The bivariate spline functions used are tensor products of univariate rational-spline functions. A distinct tension parameter corresponds to each rectangular strip defined by a pair of consecutive spline knots along either axis. Equations are derived for writing the bivariate rational spline in terms of functions and derivatives at the knots. Estimates of these values are obtained via weighted least squares subject to continuity constraints at the knots. The algorithm is illustrated on a set of terrain elevation data

Testing the Forecasting Performance of Ibex 35 Option-implied Risk-neutral Densities

Published also as: Documento de Trabajo Banco de España 0504/2005.risk-neutral densities, forecasting performance

Structure from Motion with Higher-level Environment Representations

Computer vision is an important area focusing on understanding, extracting and using the information from vision-based sensor. It has many applications such as vision-based 3D reconstruction, simultaneous localization and mapping(SLAM) and data-driven understanding of the real world. Vision is a fundamental sensing modality in many different fields of application. While the traditional structure from motion mostly uses sparse point-based feature, this thesis aims to explore the possibility of using higher order feature representation. It starts with a joint work which uses straight line for feature representation and performs bundle adjustment with straight line parameterization. Then, we further try an even higher order representation where we use Bezier spline for parameterization. We start with a simple case where all contours are lying on the plane and uses Bezier splines to parametrize the curves in the background and optimize on both camera position and Bezier splines. For application, we present a complete end-to-end pipeline which produces meaningful dense 3D models from natural data of a 3D object: the target object is placed on a structured but unknown planar background that is modeled with splines. The data is captured using only a hand-held monocular camera. However, this application is limited to a planar scenario and we manage to push the parameterizations into real 3D. Following the potential of this idea, we introduce a more flexible higher-order extension of points that provide a general model for structural edges in the environment, no matter if straight or curved. Our model relies on linked B´ezier curves, the geometric intuition of which proves great benefits during parameter initialization and regularization. We present the first fully automatic pipeline that is able to generate spline-based representations without any human supervision. Besides a full graphical formulation of the problem, we introduce both geometric and photometric cues as well as higher-level concepts such overall curve visibility and viewing angle restrictions to automatically manage the correspondences in the graph. Results prove that curve-based structure from motion with splines is able to outperform state-of-the-art sparse feature-based methods, as well as to model curved edges in the environment

An isogeometric finite element formulation for phase transitions on deforming surfaces

This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial differential equations (PDEs) that live on an evolving two-dimensional manifold. For the phase transitions, the PDE is the Cahn-Hilliard equation for curved surfaces, which can be derived from surface mass balance in the framework of irreversible thermodynamics. For the surface deformation, the PDE is the (vector-valued) Kirchhoff-Love thin shell equation. Both PDEs can be efficiently discretized using $C^1$-continuous interpolations without derivative degrees-of-freedom (dofs). Structured NURBS and unstructured spline spaces with pointwise $C^1$-continuity are utilized for these interpolations. The resulting finite element formulation is discretized in time by the generalized-$\alpha$ scheme with adaptive time-stepping, and it is fully linearized within a monolithic Newton-Raphson approach. A curvilinear surface parameterization is used throughout the formulation to admit general surface shapes and deformations. The behavior of the coupled system is illustrated by several numerical examples exhibiting phase transitions on deforming spheres, tori and double-tori.Comment: fixed typos, extended literature review, added clarifying notes to the text, added supplementary movie file

Parameter selection in the design of displacement and motion functions by means of B-splines

This work analyses the incidence of the parameter selection of B-spline curves, used in the design of displacement and motion functions, on its degree of freedom and shape. A complete design process based on the use of non-parametric B-spline curves and the convenience of selecting the curve parameters from the point of view of its practical application is shown. In order to make easy the design and use of the displacement function, the algorithms for derivation and integration of the B-splines used are presented. Three case studies validate the proposed design process and the selection of the adequate parameters. The first case presents the design of a displacement function of a roller follower driven by a disk cam; the corresponding cam profile and its prototype are shown. The second case presents the design of the motion function corresponding to the cutting unit of a manufacturing cardboard tube machine. The third case exposes the design of the displacement function of the bar feeding mechanism in a single-spindle automatic lathe, to produce a partial thread screw of hexagonal head.Postprint (author's final draft

08221 Abstracts Collection -- Geometric Modeling

From May 26 to May 30 2008 the Dagstuhl Seminar 08221 ``Geometric Modeling\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Mind the Gap! Consumer Perceptions and Choices of Medicare Part D Prescription Drug Plans

Medicare Part D provides prescription drug coverage through Medicare approved plans offered by private insurance companies and HMOs. In this paper, we study the role of current prescription drug use and health risks, related expectations, and subjective factors in the demand for prescription drug insurance. To characterize rational behavior in the complex Part D environment, we develop an intertemporal optimization model of enrollment decisions. We generally find that seniors' choices respond to the incentives provided by their own health status and the market environment as predicted by the optimization model. The proportion of individuals who do not attain the optimal choice is small, but the margin for error is also small since enrollment is transparently optimal for most eligible seniors. Further, there is also evidence that seniors over-react to some salient features of the choice situation, do not take full account of the future benefit and cost consequences of their decisions, or the expected net benefits and risk properties of alternative plans.