Parallels plane projection and its geometric features

A new equivalent map projection called the parallels plane projection is proposed in this paper. The transverse axis of the parallels plane projection is the expansion of the equator and its vertical axis equals half the length of the central meridian. On the parallels plane projection, meridians are projected as sine curves and parallels are a series of straight, parallel lines. No distortion of length occurs along the central meridian or on any parallels of this projection. Angular distortion and the proportion of length along meridians (except the central meridian) introduced by the projection transformation increase with increasing longitude and latitude. A potential application of the parallels plane projection is that it can provide an efficient projection transformation for global discrete grid systems.

A discrete square global grid system based on the parallels plane projection

We developed a direct partitioning method to construct a seamless discrete global grid system (DGGS) with any resolution based on a two-dimensional projected plane and the earth ellipsoid. This DGGS is composed of congruent square grids over the projected plane and irregular ellipsoidal quadrilaterals on the ellipsoidal surface. A new equal area projection named the parallels plane (PP) projection derived from the expansion of the central meridian and parallels has been employed to perform the transformation between the planar squares and the corresponding ellipsoidal grids. The horizontal sides of the grids are parts of the parallel circles and the vertical sides are complex ellipsoidal curves, which can be obtained by the inverse expression of the PP projection. The partition strategies, transformation equations, geometric characteristics and distortions for this DGGS have been discussed. Our analysis proves that the DGGS is area-preserving while length distortions only occur on the vertical sides off the central meridian. Angular and length distortions positively correlate to the increase in latitudes and the spanning of longitudes away from a chosen central meridian. This direct partition only generates a small number of broken grids that can be treated individually.

A study on the antibacterial activity of one-dimensional ZnO nanowire arrays: effects of the orientation and plane surface

In this study, ZnO nanowire arrays with different orientations were prepared. Confocal laser scanning microscopy (CLSM) and field- emission scanning electron microscope (FE- SEM) technique were employed for understanding the disparities in antibacterial activity between different orientations of ZnO nanoarrays. The effects of the different planes of ZnO nanowire were also discussed for the first time.

Spontaneous emission properties of organic film in plane optical microcavity

The spontaneous emission properties of a single layer organic film in plane optical microcavities were studied. Optical microcavity was formed by a Tris(8-quinolinolato) aluminium (Alq) film sandwiched between a distributed Bragg reflector (DBR) and a Ag metallic reflector. Two kinds of microcavities were devised by using a different DBR structure. Compared with a Alq film, significantly spectral narrowing and intensity enhancement was observed in the two microcavities, which is attributed to the microcavity effect. The spectra characteristics of the two microcavities showed that the structure of DBR has much influence on the emission properties of a microcavity. (C) 2000 Elsevier Science S.A. All rights reserved.

Preparation of SnO2 thin films with extremely preferred orientation along (101) plane by LB deposition technique

SnO2 thin films with extremely preferred orientation along (101) plane were made by LB technique and characterized by FTIR,, UV-visible, X-ray diffraction, X-ray photoelectron spectroscopy and SEM.

Epitaxial crystallization of sPP on the (100) lattice plane of HDPE crystals

Crystallization behavior of syndiotactic polypropylene(sPP) on the (100) lattice plane of high-density polyethylene(HDPE) crystals was studied by means of transmission electron microscopy and electron diffraction. The results indicate that sPP crystals can grow epitaxially on the (100) PE lattice plane with their chain directions +/-37 degrees apart from the chain direction of the HDPE substrate. The contact planes are (100) lattice planes for both polymers. This kind of epitaxy is explained in terms of parallel alignment of HDPE chains along the rows formed by the {CH3, CH2,CH3} groups in the (100) lattice plane of the sPP crystals. This implies that in the epitaxial crystallization of sPP with fiber oriented HDPE substrate, not only the (110) but also the (100) HDPE lattice planes can act as the oriented nucleation sites. Furthermore, according to the poor matching between HDPE chains in the (100) lattice plane and the {CH3, CH2, CH3} group rows in the (100) lattice plane of the sPP crystals, it is concluded that the geometric matching is not the only controlling factor for the occurrence of polymer epitaxy.

FROM DIMER TO POLYMER .2. EXTENDED TO SYSTEMS POSSESSING 2-FOLD SCREW AXIS OR GLIDE PLANE

The approach for constructing the qualitative band structure of a polymer from corresponding dimer has been extended to the system possessing two-fold screw axis or. glide plane. The classification of energy levels of the dimer in the present case depends on pseudo-symmetry/antisymmetry instead of psendo-in-phase/out-of-phase property of the orbitals. Several typical conductive polymers are then discussed follow this approach. Among them are cis-polyacetylene, polyparaphenylene with a twist ang...

The Synthesis of Stable Grasps in the Plane

This paper addresses the problem of synthesizing stable grasps on arbitrary planar polygons. Each finger is a virtual spring whose stiffnes and compression can be programmed. The contacts between the finger tips and the object are point contacts without friction. We prove that all force-closure grasps can be made stable, and it costs 0(n) time to synthesize a set of n virtual springs such that a given force closure grasp is stable. We can also choose the compliance center and the stiffness matrix of the grasp, and so choose the compliant behavior of the grasped object about its equilibrium. The planning and execution of grasps and assembly operations become easier and less sensitive to errors.

Eliminating False Matches for the Projective Registration of Free-Form Surfaces with Small Translational Motions

Liu, Yonghuai. Eliminating False Matches for the Projective Registration of Free-Form Surfaces with Small Translational Motions. IEEE Transactions on Systems, Man and Cybernetics, Part B: Cybernetics, vol. 35, no. 3, pp. 607-624, 2005.

Problems of maximal mean resistance on the plane

Plakhov, A.Y.; Gouveia, P.D.F., (2007) 'Problems of maximal mean resistance on the plane', Nonlinearity 20(9) pp.2271-2287 RAE2008

An Invariant Representation for Matching Trajectories across Uncalibrated Video Streams

We introduce a view-point invariant representation of moving object trajectories that can be used in video database applications. It is assumed that trajectories lie on a surface that can be locally approximated with a plane. Raw trajectory data is first locally approximated with a cubic spline via least squares fitting. For each sampled point of the obtained curve, a projective invariant feature is computed using a small number of points in its neighborhood. The resulting sequence of invariant features computed along the entire trajectory forms the view invariant descriptor of the trajectory itself. Time parametrization has been exploited to compute cross ratios without ambiguity due to point ordering. Similarity between descriptors of different trajectories is measured with a distance that takes into account the statistical properties of the cross ratio, and its symmetry with respect to the point at infinity. In experiments, an overall correct classification rate of about 95% has been obtained on a dataset of 58 trajectories of players in soccer video, and an overall correct classification rate of about 80% has been obtained on matching partial segments of trajectories collected from two overlapping views of outdoor scenes with moving people and cars.

View Registration Using Interesting Segments of Planar Trajectories

We introduce a method for recovering the spatial and temporal alignment between two or more views of objects moving over a ground plane. Existing approaches either assume that the streams are globally synchronized, so that only solving the spatial alignment is needed, or that the temporal misalignment is small enough so that exhaustive search can be performed. In contrast, our approach can recover both the spatial and temporal alignment. We compute for each trajectory a number of interesting segments, and we use their description to form putative matches between trajectories. Each pair of corresponding interesting segments induces a temporal alignment, and defines an interval of common support across two views of an object that is used to recover the spatial alignment. Interesting segments and their descriptors are defined using algebraic projective invariants measured along the trajectories. Similarity between interesting segments is computed taking into account the statistics of such invariants. Candidate alignment parameters are verified checking the consistency, in terms of the symmetric transfer error, of all the putative pairs of corresponding interesting segments. Experiments are conducted with two different sets of data, one with two views of an outdoor scene featuring moving people and cars, and one with four views of a laboratory sequence featuring moving radio-controlled cars.

Projective injections of geometries and their affine extensions

We present a general method allowing the construction geometries whose diagram is an extension of the diagram of a given geometry. Some applications of this construction process are described. © 1995 Birkhäuser Verlag.