Imaging and Doppler parameter estimation for maneuvering target using axis mapping based coherently integrated cubic phase function

In this paper, we propose a novel imaging and Doppler parameter estimation algorithm for ground maneuvering targets. Since the cross-track acceleration will induce the quadratic chirp rate (third-order phase) in the phase history, it may cause the maneuvering target severely smeared in the Doppler domain. To obtain a well-focused target imaging result, the quadratic chirp rate must be estimated accurately. Though cubic phase function (CPF) is efficient in estimating the parameters of a single maneuvering target, it may suffer from the identifiability problem when dealing with multiple maneuvering targets. To address these issues, an axis mapping (AM) based coherently integrated cubic phase function (CICPF) algorithm is proposed. This algorithm consists of two stages. Firstly, the linear chirp rate migration (i.e. quadratic chirp rate) of target in the time and chirp-rate domain is corrected by AM. After that, a dechirping technique is utilized to coherently integrate the auto-terms, and suppress the cross-terms and spurious peaks. Compared with several existing quadratic chirp rate estimation approaches, AM based CICPF (AMCICPF) algorithm can acquire lower signal-to-noise ratio threshold and estimate the centroid frequency, chirp rate and quadratic chirp rate of maneuvering target simultaneously. By compensating the chirp rate and quadratic chirp rate, a finely focused maneuvering target imaging can be obtained. Both simulated and real data processing results show that the AMCICPF algorithm serves as a good candidate for maneuvering target Doppler parameter estimation and imaging.     

Boolean operations on general planar polygons

Computing boolean operations between general planar polygons is one of the fundamental problems in geometric and solid modeling. In this work we present a new algorithm to calculate intersection, union and difference, valid for general planar polygons (manifold and non-manifold, with and without holes), based on a formal representation system. This formal model is based on the concept of simplicial chain, developed by Feito and Rivero (Computers & Graphics 22(5) (1998)). Using algebraic operations between simplicial chains we can obtain any general polygon and the Boolean operations between them. The fact of that our algorithm is based on simplicial chains and their operations, reduces the study of special cases, and allows us to develop a robust and efficient algorithm to calculate the intersection between general polygons.     

基于线段与线段求交的矩形窗口裁剪算法

我们首先对线段是否完全可见进行判定 ,然后对被裁剪线段与矩形窗口四边所在的线段是否相交进行判定并求交。若交点存在则用替换法替换相应的点 ,最后连接被替换后的点得到被裁剪后的线段 ;若交点不存在则线段完全不可见 ,线段将被完全裁剪掉。     

Unconditionally stable C1-cubic spline collocation method for solving parabolic equations

This article aims to present a new approach based on C¹-cubic splines introduced by Sallam and Naim Anwar [Sallam, S. and Naim Anwar, M. (2000). Stabilized cubic C¹-spline collocation method for solving first-order ordinary initial value problems, Int. J. Comput. Math., 74, 87–96.], which is A-stable, for the time integration of parabolic equations (diffusion or heat equation). The introduced method is an example of the so-called method of lines (the solution is thought to consist of space discretization and time integration), which is an extension of the 1/3-Simpson's finite-difference scheme. Our main objective is to prove the unconditional stability of the proposed method as well as to show that the method is convergent and is of order O (h ²)?+?O (k ⁴) i.e. it is a fourth-order in time and second-order in space. Computational results also show that the method is relevant for long time interval problems.     

Numerical integration of partial differential equations using cubic splines

This paper presents techniques for the numerical solution of partial differential equations using cubic spline collocation.

The main spline relations are presented and incorporated into solution procedures for partial differential equations. The computational algorithm in every case is a tridiagonal matrix system amenable to efficient inversion methods. Truncation errors and stability are briefly discussed. Finally, some examples of their application to parabolic and hyperbolic systems with mixed boundary conditions are presented.

The results obtained are encouraging and justify further research in this field.     

广义三次DP曲线

给出一组带有两个形状参数的三次多项式基函数,它是三次DP基函数的扩展;分析该基函数的性质;基于该组函数定义了广义三次DP曲线,它不仅具有与DP曲线类似的性质,还可通过改变参数几或产使其具有形状可调性。当这两段曲线相拼接时,在满足一定的条件下,曲线可达到G^2或C^2连续,从而为自由曲线设计提供了一种有效的方法。     

An investigation into design of fair surfaces over irregular domains using data-dependent triangulation

Design of fair surfaces over irregular domains is a fundamental problem in computer-aided geometric design (CAGD), and has applications in engineering sciences (in aircraft, automobile, ship science etc.). In the design of fair surfaces over irregular domains defined over scattered data, it was widely accepted till recently that the classical Delaunay triangulation be used because of its global optimum property. However, in recent times it has been shown that for continuous piecewise linear surfaces, improvements in the quality of fit can be achieved if the triangulation pattern is made dependent upon some topological or geometric property of the data set or is simply data dependent. The fair surface is desired because it ensures smooth and continuous surface planar cuts, and these in turn ensure smooth and easy production of the surface in CAD/CAM, and favourable resistance properties. In this paper, we discuss a method for construction of C¹ piecewise polynomial parametric fair surfaces which interpolate prescribed ℜ³ scattered data using spaces of parametric splines defined on H³ triangulation. We show that our method is more specific to the cases when the projection on a 2-D plane may consist of triangles of zero area, numerically stable and robust, and computationally inexpensive and fast. Numerical examples dealing with surfaces approximated on plates, and on ships have been presented.     

New approach in depositing thick, layered cubic boron nitride coatings by oxygen addition—structural and compositional analysis

Cubic boron nitride (c-BN) can be produced by PVD and PA-CVD techniques by intensive ion bombardment leading to highly stressed films limiting its use in industrial applications. Various attempts have been undertaken to reduce the compressive stress of c-BN thin films. A significant reduction in compressive stress and a substantially improved adhesion was achieved by a new coating concept consisting of a two-step adhesion-promoting base layer, a compositional-graded nucleation layer obtained by a stepwise decrease of the oxygen content in the Ar/N₂/O₂ atmosphere and a low-stressed c-BN:O top layer with controlled oxygen addition. The four-layer c-BN:O film with a thickness of 3 μm was deposited by unbalanced radio frequency magnetron sputtering of a hot-pressed hexagonal boron nitride target on silicon substrates. The adhesion layer was deposited in a mixed Ar/O₂ atmosphere of 0.26 Pa with a stepwise increased nitrogen gas flow and a subsequent increase of the ion energy by increasing the substrate bias from 0 to − 250 V. The c-BN nucleation was gradually initiated by decreasing the O₂ gas flow. The present study was focused on the investigation of the morphology, the microstructure on the nanoscale, and the bonding structure using scanning electron microscopy (SEM), Fourier-Transmission infra-red spectroscopy (FTIR), high-resolution transmission electron microscopy (HRTEM) and electron energy loss spectroscopy (EELS) employing analytical scanning transmission electron microscopy (ASTEM). The HRTEM images revealed a four-layer coating consisting of a gradual nucleation of t-BN, on which a gradual nucleation of c-BN was achieved by decreasing the oxygen gas flow.     

Solid-state interfacial reactions and compound morphology of cBN grain and surface Ti coating

In order to research thoroughly the mechanism of the solid-state interfacial reactions and the induced compound morphology of cubic boron nitride (cBN) abrasive grains and the surface Ti-coating layer, annealing experiments of Ti-coated cBN grains were conducted at different temperatures of 550-950 °C for dwell times of 60 min under high-vacuum conditions. The corresponding interfacial characteristics were investigated by differential thermal analysis, X-ray diffraction and scanning electron microscopy. The results show that the relevant interfacial reactions and compound morphology between cBN and Ti are significantly influenced by the heat-treatment temperature. No reaction occurs below 550 °C, and TiN is the sole reaction product during heating from 650-750 °C. Three kinds of compounds, TiN, TiB₂ and TiB, can exist in the interfacial region at 950 °C. Here, the favorable interfacial structures, cBN/TiB₂/TiB/(TiB+TiN)/TiN/Ti, are developed for the excellent mechanical and chemical transition effects between cBN grains and Ti coating. The thermodynamic analysis finally predicts that there is a reasonable probability for the formation of such a special interfacial transition layer.