True Surfaces Research Articles

An oblate‐spheroid geopotential approximation for global meteorology

AbstractThe spherical geopotential approximation used in most meteorological global models assumes a spherical shape for the Earth and its geopotential field. Consequently, the deviation of the geoid surface from a sphere, and the observed meridional variations of the apparent gravity are not represented. These two errors are small but their effect on medium or long‐term forecasts is debated because they are systematic and might have cumulative effects. Various formulations with spheroidal iso‐geopotential surfaces have been proposed recently, but none of them combines the advantages of an accurate description for the geopotential field and of horizontal/vertical orthogonal coordinate surfaces. This article proposes a spheroidal coordinate system which meets these two requirements. The transformation and metric factors are defined analytically. The coordinate system is defined as an approximation of orthogonal horizontal/vertical coordinates in which the vertical lines are not exactly orthogonal to true horizontal surfaces. The consequences of this deviation from orthogonality are quantified and upper bounds for the resulting errors are obtained mathematically, i.e. independently of any arbitrary numerical process. The precision of the coordinate can be made as large as desired by raising the truncation of the Taylor series used to approach its exact value, and it is shown that, in practice, truncation values in the range 5 to 8 are appropriate for global numerical weather prediction.

New Frontiers for Cartilage Repair and Protection.

Objective:Articular cartilage injury is common after athletic injury and remains a difficult treatment conundrum both for the surgeon and athlete. Although recent treatments for damage to articular cartilage have been successful in alleviating symptoms, more durable and complete, long-term articular surface restoration remains the unattained goal. In this article, we look at both new ways to prevent damage to articular surfaces as well as new techniques to recreate biomechanically sound and biochemically true articular surfaces once an athlete injures this surface. This goal should include reproducing hyaline cartilage with a well-integrated and flexible subchondral base and the normal zonal variability in the articular matrix.Results:A number of nonoperative interventions have shown early promise in mitigating cartilage symptoms and in preclinical studies have shown evidence of chondroprotection. These include the use of glucosamine, chondroitin, and other neutraceuticals, viscosupplementation with hyaluronic acid, platelet-rich plasma, and pulsed electromagnetic fields. Newer surgical techniques, some already in clinical study, and others on the horizon offer opportunities to improve the surgical restoration of the hyaline matrix often disrupted in athletic injury. These include new scaffolds, single-stage cell techniques, the use of mesenchymal stem cells, and gene therapy.Conclusion:Although many of these treatments are in the preclinical and early clinical study phase, they offer the promise of better options to mitigate the sequelae of athletically induced cartilage.

How to Make the Cassie Wetting State Stable?

Wetting of rough hydrophilic and hydrophobic surfaces is discussed. The stability of the Cassie state, with air trapped in relief details under the droplet, is necessary for the design of true superhydrophobic surfaces. The potential barrier separating the Cassie state and the Wenzel state, for which the substrate is completely wetted, is calculated for both hydrophobic and hydrophilic surfaces. When the surface is hydrophobic, the multiscaled roughness of pillars constituting the surface increases the potential barrier separating the Cassie and Wenzel states. When water fills the hydrophilic pore, the energy gain due to the wetting of the pore hydrophilic wall is overcompensated by the energy increase because of the growth of the high-energetic liquid-air interface. The potential barrier separating the Cassie and Wenzel states is calculated for various topographies of surfaces. Structural features of reliefs favoring enhanced hydrophobicity are elucidated.

Challenges in protein-folding simulations

Experimental studies of protein folding processes are frequently hampered by the fact that only low resolution structural data can be obtained with sufficient temporal resolution. Molecular dynamics simulations offer a complementary approach, providing extremely high resolution spatial and temporal data on folding processes. The effectiveness of such simulations is currently hampered by continuing questions regarding the ability of molecular dynamics force fields to reproduce the true potential energy surfaces of proteins, and ongoing difficulties with obtaining sufficient sampling to meaningfully comment on folding mechanisms. We review recent progress in the simulation of three common model systems for protein folding, and discuss how recent advances in technology and theory are allowing protein folding simulations to address their current shortcomings.

Modelling the Spatial Distribution of DEM Error

Assessment of a DEM’s quality is usually undertaken by deriving a measure of DEM accuracy – how close the DEM’s elevation values are to the true elevation. Measures such as Root Mean Squared Error and standard deviation of the error are frequently used. These measures summarise elevation errors in a DEM as a single value. A more detailed description of DEM accuracy would allow better understanding of DEM quality and the consequent uncertainty associated with using DEMs in analytical applications. The research presented addresses the limitations of using a single root mean squared error (RMSE) value to represent the uncertainty associated with a DEM by developing a new technique for creating a spatially distributed model of DEM quality – an accuracy surface. The technique is based on the hypothesis that the distribution and scale of elevation error within a DEM are at least partly related to morphometric characteristics of the terrain. The technique involves generating a set of terrain parameters to characterise terrain morphometry and developing regression models to define the relationship between DEM error and morphometric character. The regression models form the basis for creating standard deviation surfaces to represent DEM accuracy. The hypothesis is shown to be true and reliable accuracy surfaces are successfully created. These accuracy surfaces provide more detailed information about DEM accuracy than a single global estimate of RMSE.

Assessment of brain surface extraction from PET images using Monte Carlo Simulations

In this paper, we evaluate quantitatively the performance of the fully automatic deformable model with dual surface minimization (DM-DSM) method for brain surface extraction from positron emission tomography (PET) images with Monte Carlo simulated data. In addition, we cross validate the DM-DSM method with a method based on MRI-PET registration for PET brain delineation. For this, the automated image registration (AIR) algorithm is combined with the anatomical brain surface extractor (BSE) algorithm. Two radiopharmaceuticals were considered: C-11-Raclopride and F-18-FDG. The success of the two methods was quantified by measuring the similarity between the extracted and the true brain volume. Also local differences between the extracted and the true brain surfaces were measured. With FDG, the DM-DSM method yielded brain surfaces of high accuracy and they were more accurate than with the image registration based method. With Raclopride, the accuracy of the DM-DSM method was slightly lower than with FDG and, on the average, similar to the accuracy of the image registration based method. However with Raclopride, maximal local differences between true and extracted surfaces were found to be greater with DM-DSM. In addition, preliminary experiments with images containing simulated pathology were done and the performance of DM-DSM was excellent in these experiments. To summarize, we found that the DM-DSM method can reliably extract brain surfaces of high accuracy from PET images.

Quantitative fractography by digital image processing: NIH Image macro tools for stereo pair analysis and 3-D reconstruction.

A set of NIH Image macro programs was developed to make qualitative and quantitative analyses from digital stereo pictures produced by scanning electron microscopes. These tools were designed for image alignment, anaglyph representation, animation, reconstruction of true elevation surfaces, reconstruction of elevation profiles, true-scale elevation mapping and, for the quantitative approach, surface area and roughness calculations. Limitations on time processing, scanning techniques and programming concepts are also discussed.

Effects of thermal roughness on X-ray studies of liquid surfaces

The effects of thermal roughness on X-ray studies of liquid surfaces will be discussed. In contrast to solid surfaces, for which the surface height–height correlation function remains finite at large distances, for liquid surfaces thermal fluctuations induce a logarithmic dependence for distances smaller than a gravitationally induced cutoff that is of the order of mm. As a result of this there is no true specular X-ray reflectivity liquid surfaces. Theory and measurements explaining this phenomena will be presented.

Left ventricular shape analysis from three-dimensional echocardiograms

The objective of this study was to develop and validate a three-dimensional technique of left ventricular shape analysis. Geometric phantoms and left ventricles of excised calf hearts, normal human subjects, and one subject each with aortic stenosis and dilated cardiomyopathy were reconstructed from three-dimensional echocardiograms. The fit between the reconstructions and true surfaces of the geometric phantoms and excised ventricles was determined. To evaluate in vivo left ventricular shape, a center axis was constructed from the centroid of the mitral annulus to the furthest endocardial point. Regional shape was evaluated as the relative distances of 16 separate myocardial segments from the center axis compared with a population-derived mean value. Global shape was evaluated as the average standard deviation from the normal value over the 16 segments. The system precisely reproduced the shapes of the phantoms and excised left ventricles (root-mean-square error between true and reconstructed surface 1.0 0.2 mm and 1.2 0.8 mm, respectively). The in vivo shape analysis differentiated the pathological from normal left ventricles. (J Am Soc Echocardiogr 1998;11:761-9.)

ISS Assessment of the Influence of Nonpore Surface in the XPS Analysis of Oil-Producing Reservoir Rocks

The application of X-ray photoelectron spectroscopy (XPS) to oil-producing reservoir rocks is new and has shown that pore surface concentrations can be related to rock wettability. In the preparation of fresh fractures of rocks, however, some nonpore surface corresponding to the connection regions in the rocks is created and exposed to XPS. To assess the potential influence of this nonpore surface in the XPS analysis of rocks here we use ion scattering spectroscopy (ISS), which has a resolution comparable to the size of the pores, higher than that of XPS, with an ion gun of He+at maximum focus. Sample charging effects are partially eliminated with a flood gun of low energy electrons. All the ISS signals are identified by means of a formula which corrects any residual charging on the samples. Three rock samples are analyzed by XPS and ISS. The almost unchanged ISS spectra obtained at different points of a given sample suggest that the nonpore surface created in the fracture process is negligibly small, indicating that XPS data, from a larger surface spot, represents the composition of true pore surfaces. The significant changes observed in ISS spectra from different samples indicate that ISS is sample specific.

Laser scanning and quasi-helical tool path definition of arbitrary curved surface models

In rapid prototyping it is frequently necessary to define and CNC machine the complete surface form of complex three-dimensional shapes. In this work arbitrary curved surfaces are digitized by rotating them in angular increments and acquiring lines of surface data points at each angular position, with a triangulation-based laser range finder. The laser scanner data is filtered, and reconstructed, so that cutter offsets and quasi-helical toolpaths for CNC machining can be directly formed. The approach may be used for machining basically any type of object and is not limited to true surfaces of revolution. A scanned and CNC machine perfume bottle is used as an example to illustrate the capabilities of this approach.

Scanning electron microscopic observations of the basal surface of the human oral mucosa and squamous cell carcinoma

The basal surface of epithelial cells in the normal oral mucosa and cancer lesions were investigated by scanning electron microscopy. The basal lamina and collagen fibers having been completely removed by strong alkali digestion, the true basal surfaces of the epithelium and cancer lesions were demonstrated in three dimensions. Visible on the outer surface of the nest of cancer cells was a flowerlike structure, presumably the connecting portion of the neighboring cancer nest.

Representation of three-dimensional surface topography in CAD-systems and image-processing software

Adequate graphical representation of a measured machined surface for evaluation of its functional properties, is a well-known industrial problem. The use of profile curves has been the dominating technique in displaying the roughness and topography of a machined surface. The representation of topography is often made by assembling multiple-sampled 2-D profile curves (raster scan) to create the visual effect of a surface from a pre-selected viewing angle. During recent years, a number of 3-D surface measurement systems have been presented and commercial systems are now available on the market. This paper describes the possibilities with a system recently developed for representation of measured 3-D surface topography as wire frame or true surfaces. The system consists of a PC-computer for surface topography measuring and collecting of surface point coordinates connected to widespread CAD-systems and image processing software, CATIA, AutoCAD and Image, which are running on different computer platforms such as IBM-mainframe, Unix and VMS workstations as well as Apple Macintosh and IBM personal computers. Some of the advantages and limitations of the system and areas of application are demonstrated in a representation of bearing area and oil retaining volume of a cylinder liner.

An introduction to polar forms

Polar forms, which simplify the construction of polynomial and piecewise-polynomial curves and surfaces and lead to new surface representations and algorithms, are reviewed. The polar forms of polynomial curves, Bezier curves, and B-spline are discussed. Tensor product surfaces, the most popular surfaces in computer-aided geometric design, true surfaces, Bezier triangles, B-patches, and a triangular B-spline scheme that combines B-patches and simplex splines are also discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Topography of opsin within disk and plasma membranes revealed by a rapid-freeze deep-etch technique.

Rod outer segments in fresh rat retinas were examined by a rapid-freeze, deep-etch technique to explore how membrane proteins are organized at the macromolecular level. Cross-fractures revealed that intradiscal membranes are adherent to each other except at the rim. When an isolated fresh retina was incubated in a hypotonic solution for a few minutes, the interdiscal space was expanded and the cytoplasmic surface of the disk membrane was found to be covered with protrusions except at the rim. A few particles were scattered among the protrusions and were attached to the cytoplasmic surface. Since the distribution density of the cytoplasmic surface protrusions was similar to that of the P-face particles, which are known to reflect opsins, the protrusions were considered to be portions of opsins extending into the cytoplasm. The intradiscal surfaces in chemically-fixed retinas were rather smooth and were labelled with anti-opsin antibodies and wheat germ agglutinin. The true surfaces of the plasma membrane were found to be similar in fine structure to those of the disk. A model of the macromolecular organization of rod outer segments is proposed on the basis of these observations. The model shows apposed opsins within a disk membrane adhering to one another except at the rim. These opsins, as well as those in the plasma membrane, are minimally exposed to the extracellular surface, but protrude deeply into the cytoplasm.

A methodology for the manufacture of forming tools incorporating complex surface geometry with minimum computer resources

This paper presents a methodology for the manufacture of tools embodying true three-dimensional free-form surfaces using PC-based two-and-a-half axis CADCAM systems. The numerical control machining of free-form surfaces is usually accomplished utilizing minicomputer or mainframe computer aided design and manufacturing (CADCAM) systems. The resulting NC data are suitable for either three axis or five axis machining, dependent upon machine tool type/capability and CAM package complexity. However, the cost of such packages and systems precludes their use in smaller companies with only an occasional requirement for components embodying free-form surfaces. The increasing availability of powerful yet reasonably priced personal computers (PCs) coupled with improving software provides such companies with a far cheaper alternative approach. However, a common feature of PC-based CADCAM systems is that they are limited to two-and-a-half axis machining for all but special applications such as three axis canted Z-plane milling or four axis wire electro discharge machining. All the main functions performed on mainframe systems can be performed on personal computers, such as toolpath generation for free-form surfaces, cusp height determination and change in shape and volume which may be used for component springback compensation.

Primary Depth Cues and Background Pattern in the Portrayal of Slant

A rectangularity postulate has been used in algorithms for the purpose of interpreting two-dimensional representations of rectilinear objects. This rectangularity postulate may affect the perception of true surfaces. In this study, rectangular surfaces and trapezoidal surfaces--the latter simulating the horizontal slant-in-depth of the rectangular surfaces--were viewed under static-monocular, moving-monocular, and static-binocular conditions, both with and without a background pattern. The static-binocular condition elicited the greatest number of accurate responses. The moving-monocular condition did not elicit significantly more accurate responses than the static-monocular viewing condition did. The effect of background pattern was insignificant. These results were unexpected in terms of ecological validity and (regarding moving-monocular viewing) because of the importance of the role of relative visual motion in the detection of object motion. However, the results are consistent with the perception of depth separation of two discrete objects.

Magnetic field mapping using an image-intensifying fluorescent probe

A simple, cost-effective image-intensifying fluorescent probe designed for mapping the magnetic surfaces in the heliac sheila is described. It consists of a phosphor-coated metal plate which is enclosed in a grounded U-channel that provides electrostatic shielding. An adjustable accelerating voltage is applied to the metal plate to greatly increase the cathodoluminescence produced by the directed electron beam from an electron gun, and the visible electron-beam image is recorded by a CCD camera. The gain in the image brightness allows significant reduction of the electron-beam energy to minimize the deviation of the measured drift surfaces from the true magnetic surfaces, and to improve resolution for detailed studies of surfaces in the newer stellarator experiments. This technique is particularly suited to electron energies below the phosphor activation threshold, when external image intensifying systems are likely to be very inefficient. Up to 36 toroidal rotations have been observed, limited mainly by the effective cross sections of the fluorescent probe and the electron gun. Mapping at low magnetic field strengths allows detection of small fixed amplitude field errors. Measurements of the gain characteristics and resolution are presented, with an example of the electrically variable resolution achievable with this design. The effect of electron energy on drift surfaces of a heliac is demonstrated.

A diatomics-in-molecules study of the reaction N + + H 2→NH + + H

The diatomics-in-molecules method is used to design a model for the two lowest 3 Apotential-energy surfaces, with the intention of providing a framework in which to study the dynamics of the reaction N +( 3 P g) + H 2→NH + + H. This systematic approach to model construction comprises a search for a physically reasonable DIM basis, and an empirical adjustment that brings the model surfaces closer in line with accurate data. The final DIM model reflects qualitatively the complicated pattern of the true surfaces, but fails to yield quantitative agreement in all parts of the configuration space. Therefore, measures which should be taken to improve the model are discussed.

An Approach to the Low-Cost Computer Aided Manufacture of Components Embodying Free-Form Surfaces

The numerical control (NC) machining of free-form surfaces is usually accomplished utilizing minicomputer or mainframe computer aided design and manufacturing (C ADC AM) systems. The resulting NC data are suitable for either three-axis or five-axis machining dependent upon machine tool type/capability and CAM package complexity. However, the cost of such packages and systems precludes the use of these in smaller companies with an occasional requirement for components embodying free-form surfaces. The increasing availability of powerful yet reasonably priced personal computers (PC) coupled with improving software provides such companies with a far cheaper alternative approach. However, a common feature of PC-based CADCAM systems is that they are limited to 2 1/2-axis machining for all but special applications such as three-axis canted Z-plane milling of four-axis wire electro discharge machining (EDM). This paper presents a method for manufacturing true three-dimensional free-form surfaces using PC-based 2 1/2-axis CADCAM systems. All the main functions performed on mainframe systems can be performed on personal computers, such as toolpath generation for free-form surfaces, cusp height determination and change in shape and volume which may be used for the compensation of shrinkage or to suit market requirements. This is significant for manufacturers who make use of moulds, such as are found in the plastic processing industries. The manufacture of a blown plastic bottle mould is presented as a typical example. The inclusion into the PC environment of features to be found in mainframe systems is also discussed, such as machining the surface patch by patch in any direction or machining a number of patches at one time, shape and volume change in any direction, cusp height determination, etc.