An application of the finite element method to curve fitting

An application of the Finite Element Method (FEM) to the solution of a geometric problem is shown. The problem is related to curve fitting i.e. pass a curve trough a set of given points even if they are irregularly spaced. Situations where cur ves with cusps can be encountered in the practice and therefore smooth interpolatting curves may be unsuitable. In this paper the possibilities of the FEM to deal with this type of problems are shown. A particular example of application to road planning is discussed. In this case the funcional to be minimized should express the unpleasent effects of the road traveller. Some comparative numerical examples are also given.

Directional Geodesic Active Contours

We present a non-conformal metric that generalizes the geodesic active contours approach for image segmentation. The new metric is obtained by adding to the Euclidean metric an additional term that penalizes the misalignment of the curve with the image gradient and multiplying the resulting metric by a conformal factor that depends on the edge intensity. In this way, a closer fitting to the edge direction results. The provided experimental results address the computation of the geodesics of the new metric by applying a gradient descent to externally provided curves. The good performance of the proposed techniques is demonstrated in comparison with other active contours methods.

The logarithmic spiral, autoisoptic curve

In the Line of Investigation that in the department of “Technical Drawing” in the School of Agriculture Engineering of Madrid, we carry out on the study of The Technical Curves and his singularities, we demonstrate an interesting property of the Logarithmic Spiral. The demonstrated property consists of which the logarithmic spiral is a autoisoptic curve, that is to say that if from a point P anyone of the spiral tangent straight lines draw up to the previous arc, these form a constant angle α. This demonstration is novel and in addition we get to contribute a method to calculate the angle α given the equation of the spiral.

A fitting algorithm for random modeling the PLC channel

The characteristics of the power-line communication (PLC) channel are difficult to model due to the heterogeneity of the networks and the lack of common wiring practices. To obtain the full variability of the PLC channel, random channel generators are of great importance for the design and testing of communication algorithms. In this respect, we propose a random channel generator that is based on the top-down approach. Basically, we describe the multipath propagation and the coupling effects with an analytical model. We introduce the variability into a restricted set of parameters and, finally, we fit the model to a set of measured channels. The proposed model enables a closed-form description of both the mean path-loss profile and the statistical correlation function of the channel frequency response. As an example of application, we apply the procedure to a set of in-home measured channels in the band 2-100 MHz whose statistics are available in the literature. The measured channels are divided into nine classes according to their channel capacity. We provide the parameters for the random generation of channels for all nine classes, and we show that the results are consistent with the experimental ones. Finally, we merge the classes to capture the entire heterogeneity of in-home PLC channels. In detail, we introduce the class occurrence probability, and we present a random channel generator that targets the ensemble of all nine classes. The statistics of the composite set of channels are also studied, and they are compared to the results of experimental measurement campaigns in the literature.

A 800 kW I-V curve

This paper presents the measurement of the I-V curve of an 800 kW PV generator by means of an own-made capacitive load. Along the lines of some previous works, it is shown that an I-V curve analysis can also be applied to big PV generators and that, when measuring the operating conditions with reference modules and taking some precautions (especially regarding the operating cell temperature), it is still a useful tool for characterizing them and therefore can be incorporated into maintenance procedures. As far as we know, this is the largest I-V curve measured so far.

Gini coefficient, dissimilarity index and Lorenz curve for the spanish port system by type of goods

This paper shows the Gini Coefficient, the dissimilarity Index and the Lorenz Curve for the Spanish Port System by type of goods from 1960 to the year 2010 for business units: Total traffic, Liquid bulk cargo, Solid bulk cargo, General Merchandise and Container (TEUs) with the aim of carcaterizar the Spanish port systems in these periods and propose future strategies.

A 500-kW pv generator I-V curve

This paper presents the measurement of the I-V curve of a 500-kW PV generator by means of an own-made capacitive load. It is shown that I-V curve analysis can also be applied to big PV generators and that when measuring the operation conditions with reference modules and taking some precautions (especially regarding the operation cell temperature), it is still a useful tool for characterizing them and therefore can be incorporated into maintenance procedures. As far as we know, this is the largest I-V curve measured so far.

Parametric Generation of Planing Hulls with NURBS Surfaces

This article presents a mathematical method for producing hard-chine ship hulls based on a set of numerical parameters that are directly related to the geometric features of the hull and uniquely define a hull form for this type of ship. The term planing hull is used generically to describe the majority of hard-chine boats being built today. This article is focused on unstepped, single-chine hulls. B-spline curves and surfaces were combined with constraints on the significant ship curves to produce the final hull design. The hard-chine hull geometry was modeled by decomposing the surface geometry into boundary curves, which were defined by design constraints or parameters. In planing hull design, these control curves are the center, chine, and sheer lines as well as their geometric features including position, slope, and, in the case of the chine, enclosed area and centroid. These geometric parameters have physical, hydrodynamic, and stability implications from the design point of view. The proposed method uses two-dimensional orthogonal projections of the control curves and then produces three-dimensional (3-D) definitions using B-spline fitting of the 3-D data points. The fitting considers maximum deviation from the curve to the data points and is based on an original selection of the parameterization. A net of B-spline curves (stations) is then created to match the previously defined 3-D boundaries. A final set of lofting surfaces of the previous B-spline curves produces the hull surface.

Uncertainty in ellipse fitting using a flatbed scanner: development and experimental verification

In the field of dimensional metrology, the use of optical measuring machines requires the handling of a large number of measurement points, or scanning points, taken from the image of the measurand. The presence of correlation between these measurement points has a significant influence on the uncertainty of the result. The aim of this work is the development of an estimation procedure for the uncertainty of measurement in a geometrically elliptical shape, taking into account the correlation between the scanning points. These points are obtained from an image produced using a commercial flat bed scanner. The characteristic parameters of the ellipse (coordinates of the center, semi-axes and the angle of the semi-major axis with regard to the horizontal) are determined using a least squares fit and orthogonal distance regression. The uncertainty is estimated using the information from the auto-correlation function of the residuals and is propagated through the fitting algorithm according to the rules described in Evaluation of Measurement Data—Supplement 2 to the ‘Guide to the Expression of Uncertainty in Measurement’—Extension to any number of output quantities. By introducing the concept of cut-off length, it can be observed how it is possible to take into account the presence of the correlation in the estimation of uncertainty in a very simple way while avoiding underestimation.

Canonical Correlation Analysis for Interpreting Airborne Laser Scanning Metrics along the Lorenz Curve of Tree Size Inequality

Canonical Correlation Analysis for Interpreting Airborne Laser Scanning Metrics along the Lorenz Curve of Tree Size Inequality

Surface fitting in geomorphology - examples for regular-shaped volcanic landforms

In nature, several types of landforms have simple shapes: as they evolve they tend to take on an ideal, simple geometric form such as a cone, an ellipsoid or a paraboloid. Volcanic landforms are possibly the best examples of this ?ideal? geometry, since they develop as regular surface features due to the point-like (circular) or fissure-like (linear) manifestation of volcanic activity. In this paper, we present a geomorphometric method of fitting the ?ideal? surface onto the real surface of regular-shaped volcanoes through a number of case studies (Mt. Mayon, Mt. Somma, Mt. Semeru, and Mt. Cameroon). Volcanoes with circular, as well as elliptical, symmetry are addressed. For the best surface fit, we use the minimization library MINUIT which is made freely available by the CERN (European Organization for Nuclear Research). This library enables us to handle all the available surface data (every point of the digital elevation model) in a one-step, half-automated way regardless of the size of the dataset, and to consider simultaneously all the relevant parameters of the selected problem, such as the position of the center of the edifice, apex height, and cone slope, thanks to the highly performing adopted procedure. Fitting the geometric surface, along with calculating the related error, demonstrates the twofold advantage of the method. Firstly, we can determine quantitatively to what extent a given volcanic landform is regular, i.e. how much it follows an expected regular shape. Deviations from the ideal shape due to degradation (e.g. sector collapse and normal erosion) can be used in erosion rate calculations. Secondly, if we have a degraded volcanic landform, whose geometry is not clear, this method of surface fitting reconstructs the original shape with the maximum precision. Obviously, in addition to volcanic landforms, this method is also capable of constraining the shapes of other regular surface features such as aeolian, glacial or periglacial landforms.

Assessment of diastolic chamber properties of the right ventricle by global fitting of pressure-volume data and conformational analysis of 3D + T echocardiographic sequences

Assessment of diastolic chamber properties of the right ventricle by global fitting of pressure-volume data and conformational analysis of 3D + T echocardiographic sequences

3-D modeling of perimeter recombination in GaAs diodes and its influence on concentrator solar cells

This paper describes a complete modelling of the perimeter recombination of GaAs diodes which solves most unknowns and suppresses the limitations of previous models. Because of the three dimensional nature of the implemented model, it is able to simulate real devices. GaAs diodes on two epiwafers with different base doping levels, sizes and geometries, namely square and circular are manufactured. The validation of the model is achieved by fitting the experimental measurements of the dark IV curve of the manufactured GaAs diodes. A comprehensive 3-D description of the occurring phenomena affecting the perimeter recombination is supplied with the help of the model. Finally, the model is applied to concentrator GaAs solar cells to assess the impact of their doping level, size and geometry on the perimeter recombination.

Deciduous tree reconstruction algorithm based on cylinder fitting from mobile terrestrial laser scanned point clouds

Vector reconstruction of objects from an unstructured point cloud obtained with a LiDAR-based system (light detection and ranging) is one of the most promising methods to build three dimensional models of orchards. The cylinder fitting method for woody structure reconstruction of leafless trees from point clouds obtained with a mobile terrestrial laser scanner (MTLS) has been analysed. The advantage of this method is that it performs reconstruction in a single step. The most time consuming part of the algorithm is generation of the cylinder direction, which must be recalculated at the inclusion of each point in the cylinder. The tree skeleton is obtained at the same time as the cluster of cylinders is formed. The method does not guarantee a unique convergence and the reconstruction parameter values must be carefully chosen. A balanced processing of clusters has also been defined which has proven to be very efficient in terms of processing time by following the hierarchy of branches, predecessors and successors. The algorithm was applied to simulated MTLS of virtual orchard models and to MTLS data of real orchards. The constraints applied in the method have been reviewed to ensure better convergence and simpler use of parameters. The results obtained show a correct reconstruction of the woody structure of the trees and the algorithm runs in linear logarithmic time

Optimization of energy extraction in transverse galloping

A numerical method to analyse the stability of transverse galloping based on experimental measurements, as an alternative method to polynomial fitting of the transverse force coefficient Cz, is proposed in this paper. The Glauert–Den Hartog criterion is used to determine the region of angles of attack (pitch angles) prone to present galloping. An analytic solution (based on a polynomial curve of Cz) is used to validate the method and to evaluate the discretization errors. Several bodies (of biconvex, D-shape and rhomboidal cross sections) have been tested in a wind tunnel and the stability of the galloping region has been analysed with the new method. An algorithm to determine the pitch angle of the body that allows the maximum value of the kinetic energy of the flow to be extracted is presented.