A note on the polynomial surface fitting method for estimation of winds at different isobaric levels using the observed wind at 850 hPa level

A third degree polynomial surface fitting technique is adopted to compute the winds at different isobaric levels for the limited area domain from 35°E to 140°E and 30° S to 40oN for the month of June. The polynomial surfaces are fitted to the ratios of the monthly mean winds at different isobaric levels with the 850 hPa winds. The surfaces are fitted to the II and v components of the winds separately. The winds for the level are then reconstructed using the computed coefficients and observed wind at 850 hPa. The results of the technique are presented and discussed in the paper.

Pressure modes for hyperbolic paraboloid roofs

This paper presents a study on Singular Value Decomposition (SVD) of pressure coefficients hyperbolic parabolic roofs. The main goal of this study is to obtain pressure coefficient maps taking into account spatial non-uniform distribution and time-depending fluctuations of the pressure field. To this aim, pressure fields are described through pressure modes estimated by using the SVD technique. Wind tunnel experimental results on eight different geometries of buildings with hyperbolic paraboloid roofs are used to derive these pressure modes. The truncated SVD approach was applied to select a sufficient number of pressure modes necessary to reconstruct the measured signal given an acceptable difference. The truncated pressure modes are fitted through a polynomial surface to obtain a parametric form expressed as a function of the hyperbolic paraboloid roof geometry. The superpositions of pressure (envelopes) for all eight geometry were provided and used to modify mean pressure coefficients, to define design load combinations. Both symmetrical and asymmetrical pressure coefficient modes are used to estimate the wind action and to calculate the vertical displacements of a cable net by FEM analyses. Results clearly indicate that these load combinations allow for capturing large downward and upward displacements not properly predicted using mean experimental pressure coefficients.

Computing Birational Polynomial Surface Parametrizations without Base Points

In this paper, we present an algorithm for reparametrizing birational surface parametrizations into birational polynomial surface parametrizations without base points, if they exist. For this purpose, we impose a transversality condition to the base points of the input parametrization.

Compensated Evaluation of Tensor Product Surfaces in CAGD

In computer-aided geometric design, a polynomial surface is usually represented in Bézier form. The usual form of evaluating such a surface is by using an extension of the de Casteljau algorithm. Using error-free transformations, a compensated version of this algorithm is presented, which improves the usual algorithm in terms of accuracy. A forward error analysis illustrating this fact is developed.

IMPROVING THE LOCAL GEOMETRIC GEOID MODEL OF FCT ABUJA ACCURACY BY FITTING A HIGHER ORDER/DEGREE POLYNOMIAL SURFACE

The improvement of the accuracy of a local geometric geoid model using the same data set (geoid heights) requires the fitting of a higher degree polynomial surface to the data set. Consequently, this paper presents improving the local geometric geoid model of FCT, Abuja accuracy by fitting a higher order polynomial surface. A fifth degree polynomial surface was fit to the existing geoid heights of 24 points used previously for the determination of the geometric geoid model of the study area to improve its accuracy. The least squares adjustment technique was applied to compute the model parameters, as well as the fit. The RMSE index was applied to compute the accuracy of the model. The computed accuracy (0.081m) of the model was compared with those of the previously determined geoid models (Multiquadratic, 0.110m and Bicubic, 0.136m models) of the study area to determine which of the models best fit the study area, as well as has the highest resolution. The comparison result shows that the fifth degree polynomial surface best fit the study area.

A New Adaptive Image Interpolation Method to Define the Shoreline at Sub-Pixel Level

This paper presents a new methodological process for detecting the instantaneous land-water border at sub-pixel level from mid-resolution satellite images (30 m/pixel) that are freely available worldwide. The new method is based on using an iterative procedure to compute Laplacian roots of a polynomial surface that represents the radiometric response of a set of pixels. The method uses a first approximation of the shoreline at pixel level (initial pixels) and selects a set of neighbouring pixels to be part of the analysis window. This adaptive window collects those stencils in which the maximum radiometric variations are found by using the information given by divided differences. Therefore, the land-water surface is computed by a piecewise interpolating polynomial that models the strong radiometric changes between both interfaces. The assessment is tested on two coastal areas to analyse how their inherent differences may affect the method. A total of 17 Landsat 7 and 8 images (L7 and L8) were used to extract the shorelines and compare them against other highly accurate lines that act as references. Accurate quantitative coastal data from the satellite images is obtained with a mean horizontal error of 4.38 ± 5.66 m and 1.79 ± 2.78 m, respectively, for L7 and L8. Prior methodologies to reach the sub-pixel shoreline are analysed and the results verify the solvency of the one proposed.