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We present efficient and robust algorithms for intersecting a rational parametric freeform surface with a general swept surface. A swept surface is given as a one-parameter family of cross-sectional curves. By computing the inters...
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We present efficient and robust algorithms for intersecting a rational parametric freeform surface with a general swept surface. A swept surface is given as a one-parameter family of cross-sectional curves. By computing the intersection between a freeform surface and each cross-sectional curve in the family, we can solve the intersection problem. We propose two approaches, which are closely related to each other. The first approach detects certain critical points on the intersection curve, and then connects them in a correct topology. The second approach converts the intersection problem to that of finding the zero-set of polynomial equations in the parameter space, We first present these algorithms for the special case of intersecting a freeform surface with a ruled surface or a ringed surface. We then consider the intersection with a general swept surface, where each cross-sectional curve may be defined as a rational parametric curve or as an implicit algebraic curve.
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The full wave approach to problems of scattering by rough surfaces has been applied to the problem of depolarization of the scattered radiation fields by objects of finite conductivity and irregular shape. In the analysis, complet...
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The full wave approach to problems of scattering by rough surfaces has been applied to the problem of depolarization of the scattered radiation fields by objects of finite conductivity and irregular shape. In the analysis, complete expansions are employed, exact boundary conditions are imposed, and a variable coordinate system that conforms with the local features of the irregular surface is used. The full wave solutions are expressed in forms that can be readily compared with earlier solutions, and they can be used to reconcile the differences and bridge the wide gap between these solutions. Thus the full wave solutions for the backscatter cross section are shown to reduce to the physical optics solutions when the high-frequency, stationary phase approximations are used. Similarly, for slightly rough surfaces the full wave expressions reduce to the perturbational solutions for the backscatter cross section. The full wave solutions are shown to be consistent with the duality reciprocity and realizability relationships in electromagnetic theory. These solutions are invariant to coordinate transformations. Since upward and downward scattering are considered in the analysis, multiple scattering and shadowing effects are taken into account in a self-consistent manner. Thus the total scattered field varies continuously as the observer moves across a shadow boundary, and there is no need to introduce transition terms derived from other theories. The full wave approach can be applied to deterministic, periodic, and random rough surfaces. It can also be used to determine the scattering by finite scatterers in the presence of rough land or sea.
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The problem of electromagnetic wave propagation over a horizontal, nonconstant immittance plane, whose immittance value is a function of incident grazing angle, is considered. An equivalent specification of the immittance surface ...
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The problem of electromagnetic wave propagation over a horizontal, nonconstant immittance plane, whose immittance value is a function of incident grazing angle, is considered. An equivalent specification of the immittance surface is in terms of its angle-dependent reflection coefficient. Expressions are provided for the field on a vertical line given the field on a previous vertical line. The vertical line field is initialized at the plane containing the source where its aperture current distribution is specified. Both two-dimensional and three-dimensional fields are considered, and the expressions are valid for either polarization. The form of expressions is particularly suited for implementing with the Fourier split-step algorithm of the parabolic wave equation. Extension to inhomogeneous atmosphere to account for mild atmospheric inhomogeneities is presented. Several examples are considered where the immittance arises from small-scale and large-scale surface roughnesses. A numerical procedure is described wherein incomplete or approximate reflection coefficient data are made to conform to the assumptions made in the development of the expressions. This is demonstrated for a surface reflection coefficient which is governed by the Miller-Brown-Vegh roughness reduction factor. Numerical results are presented for propagation under ducting conditions over a rough surface for frequencies from HF through microwave.
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Reflection of a vertically polarized electromagnetic plane wave from a periodic rough surface is considered. The surface is characterized locally by a boundary impedance. By using a perturbation analysis, a general expression is o...
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Reflection of a vertically polarized electromagnetic plane wave from a periodic rough surface is considered. The surface is characterized locally by a boundary impedance. By using a perturbation analysis, a general expression is obtained for the amplitudes of the scattered waves which is valid for all spectral and all perturbation orders. It is shown that the results obtained here are consistent with earlier analyses of Rice, Wait, and Barrick. In addition, the general expression permits one to discern some important properties of the amplitudes for a purely sinusoidal surface. Among other things, we show that all odd perturbation orders are zero for the specular mode.
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This work concentrated on the machined surface properties produced by the multi-axis ball-end milling process in order to enhance the high-performance application of multiaxis ball-end milling technology. The cutting speed of the ...
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This work concentrated on the machined surface properties produced by the multi-axis ball-end milling process in order to enhance the high-performance application of multiaxis ball-end milling technology. The cutting speed of the engaged cutting edges and machining characteristics under various inclination angles were analyzed. The effects of inclination angles on the machined surface hardness, residual stresses, surface textures, topographies, and roughness were investigated under up-milling and down-milling conditions. Under up-milling condition, the machined surface hardness with regard to various tilt angles are larger than the ones under corresponding lead angles, and the variations of surface hardness with increasing lead angles are not apparent. In down-milling condition, double-peaks shape appears in the changing curve of surface hardness with increasing tilt and lead angles. The residual stresses present the overall trend of firstly increasing, then decreasing, and finally increasing with the increasing tilt angle from -45 to 45 degrees. The surface residual stresses in both feed and cross-feed directions firstly decrease, and then increase with the increasing lead angle. Under both up-milling and down-milling, the compressive residual stresses significantly appear at the tool inclination angles near 0 degrees due to extrusion action of the cutting edges close to tool tip and the low effective cutting speed. For down-milling condition, the surface textures are approximately parallel with the feed direction when using tilt angles with large values, and are approximately perpendicular to feed direction under varying lead angles. The apparent machining marks under negative tilt angles with relatively larger absolute values and obvious regular surface patterns corresponding to positive tilt angles could be observed. More surface pits and burrs and circular arc textures probably appear under small tilt angles and lead angles near 0 degrees.
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The interaction of a plane wave and a slightly rough surface tilted away from a reference plane is investigated. Expressions for the scattered fields are obtained to second order for a perfectly conducting and a dielectric surface...
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The interaction of a plane wave and a slightly rough surface tilted away from a reference plane is investigated. Expressions for the scattered fields are obtained to second order for a perfectly conducting and a dielectric surface. In the limiting case of no tilt the fields agree with those of Rice. When the normal to the surface is rotated about the intersection between the incidence plane and the reference plane, the treatment yields important polarization effects and gives explicitly as a function of the tilt which irregularities on the surface contribute to the scattered power. Numerical results are obtained to investigate the relative magnitudes of the terms contributing to the cross sections.
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Milder's operator expansion formalism for scattering from surfaces of moderate slope is extended to the case of electromagnetic scattering from an interface between media of arbitrary isotropic electromagnetic properties, i.e., di...
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Milder's operator expansion formalism for scattering from surfaces of moderate slope is extended to the case of electromagnetic scattering from an interface between media of arbitrary isotropic electromagnetic properties, i.e., dielectric, magnetic, or imperfectly conducting materials. A numerical implementation of the second-order formulas is described. It computes scattering amplitudes for complicated two-dimensional surfaces in a few minutes on a workstation. Computations of oblique scattering from sinusoidal gratings demonstrate that the scheme is very accurate for moderate values of Fresnel number, surface curvature, and grazing angle. Practical applications include radar scattering from the ocean and optical scattering from rough metals and insulators.
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One method of analyzing radiation and propagation above a surface is to employ an effective surface impedance to describe the effect of the boundary. In this paper an expression is derived for the effective impedance at grazing in...
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One method of analyzing radiation and propagation above a surface is to employ an effective surface impedance to describe the effect of the boundary. In this paper an expression is derived for the effective impedance at grazing incidence of a slightly rough interface between air and a finitely conducting medium for which the Leontovich boundary condition is applicable. The perturbation technique of Rayleigh and Rice is employed, and attention is restricted to vertical polarization. The resulting effective surface impedance consists of two terms, the impedance of the lower medium when the surface is perfectly smooth and a term accounting for roughness. The latter term can be complex in general and depends on the strengths of the roughness spectral components present. The result is applicable to either deterministic periodic surfaces or random rough surfaces. Various alternate definitions of the effective surface impedance are examined and are seen to be equivalent. The analysis of power flow at the surface permits the interpretation of the interaction process in terms of scattered fields.
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We investigated whether sulfur-bearing species are present on the icy Galilean moon Callisto by analyzing eight near-infrared reflectance spectra collected over a wide range of sub-observer longitudes. We measured the band areas a...
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We investigated whether sulfur-bearing species are present on the icy Galilean moon Callisto by analyzing eight near-infrared reflectance spectra collected over a wide range of sub-observer longitudes. We measured the band areas and depths of a 4 mu m feature in these spectra, which has been attributed to sulfur dioxide (SO2), as well as carbonates, in previously collected data sets of this moon. All eight spectra we collected display the 4 mu m band. The four spectra collected over Callisto's leading hemisphere display significantly stronger 4 mu m bands compared to the four trailing hemisphere spectra (>3 sigma difference). We compared the central wavelength position and shape of Callisto's 4 mu m band to laboratory spectra of various sulfur-bearing species and carbonates. Our comparison demonstrates that Callisto's 4 mu m band has a spectral signature similar to thermally altered sulfur, as well as a 4.025 mu m feature attributed to disulfanide (HS2). Our analysis therefore supports the presence of S-bearing species on Callisto but is not consistent with the presence of SO2. The significantly stronger 4 mu m band detected on Callisto's leading hemisphere could result from collisions with H2S-rich dust grains that originate on Jupiter's retrograde irregular satellites or implantation of magnetospheric S ions that originate from volcanic activity on Io. Alternatively, S-bearing species could be native to Callisto and are exposed by dust collisions and larger impacts that drive regolith overturn, primarily on its leading side.
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The tactile perception of a surface texture is mediated by factors such as material, topography, and vibrations induced by the sliding contact. In this paper, sensory characterizations are developed together with topographical and...
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The tactile perception of a surface texture is mediated by factors such as material, topography, and vibrations induced by the sliding contact. In this paper, sensory characterizations are developed together with topographical and tribo-tactile characterizations to relate perceived features with objective measurements of tribological and dynamic signals. Two sets of surface samples are used in this study: the first set is made of a commercial floor covering tiles that aim at counter-typing natural wood flooring, with both a visual and a tactile texture mimicking wood. A second set is custom-made by replicating the first set using a plain purple polyurethane resin. The comparison between tribo-tactile signals and sensory analysis allowed the identification of objective indices for textures with slight topographical differences. Even though the topography of the replicated samples is the same as their corresponding commercial products, the fact that the material is different, induces differences in the contact and vibrational parameters. This in turn modifies the discrimination performances during the sensory experiment. Tactile characteristics collected during sensory procedures are found to be in agreement with objective indices such as friction coefficients and induced vibrations.
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