基于双轴极坐标的插补算法研究

本文以双转轴绘图仪为例介绍了两种基于双轴极坐标的新型插补算法,这两种算法也可广泛用于数控加工系统中。其算法简单,易于实现,插补误差小,且没有累计误差。

圆锥曲线运动中的力

本文给出在任何初始条件下 ,沿圆锥曲线运动的质点所受的作用力 .

ANTI-ROTATION AND ANTI-SCALE IMAGE MATCHING ALGORITHM FOR NAVIGATION SYSTEM

Based on the inertial navigation system, the influences of the excursion of the inertial navigation system and the measurement error of the wireless pressure altimeter on the rotation and scale of the real image are quantitatively analyzed in scene matching. The log-polar transform （LPT） is utilized and an anti-rotation and anti- scale image matching algorithm is proposed based on the image edge feature point extraction. In the algorithm, the center point is combined with its four-neighbor points, and the corresponding computing process is put forward. Simulation results show that in the image rotation and scale variation range resulted from the navigation system error and the measurement error of the wireless pressure altimeter, the proposed image matching algo- rithm can satisfy the accuracy demands of the scene aided navigation system and provide the location error-correcting information of the system.

Passive ranging algorithm in terms of polar coordinates

For the missile with passive seeker,the improvement of passive ranger's precision is one of the key issues in development of the defense penetrate strategy. On the offensive warheads,the infrared imaging device was used to measure the line-of-sight angle information of the blocker,and then using the algorithm of Kalman Filter under polar coordinates,the distance from the blocker to the warheads was obtained. The simulation result under polar coordinates was compared with that of Cartesian coordinate. The validity of the method was analyzed,and the schemes of improvement were brought out.

Adaptive preprocessing algorithms of corneal topography in polar coordinate system

New adaptive preprocessing algorithms based on the polar coordinate system were put forward to get high-precision corneal topography calculation results. Adaptive locating algorithms of concentric circle center were created to accurately capture the circle center of original Placido-based image, expand the image into matrix centered around the circle center, and convert the matrix into the polar coordinate system with the circle center as pole. Adaptive image smoothing treatment was followed and the characteristics of useful circles were extracted via horizontal edge detection, based on useful circles presenting approximate horizontal lines while noise signals presenting vertical lines or different angles. Effective combination of different operators of morphology were designed to remedy data loss caused by noise disturbances, get complete image about circle edge detection to satisfy the requests of precise calculation on follow-up parameters. The experimental data show that the algorithms meet the requirements of practical detection with characteristics of less data loss, higher data accuracy and easier availability.

Elastic simulation method in an irregular polar coordinate system

When simulating the propagation of seismic waves in some special structures,such as tunnels and boreholes,finite difference forward modeling in the polar system has higher accuracy than the traditional Cartesian system.In actual situations,the polar space is the most irregular.To solve this problem,a forward modeling method for an irregular polar coordinate system is proposed to improve the simulation accuracy.First,an irregular surface of the polar space was meshed into an irregular polar system.After the transformation,the undulating surface was mapped into a plane one,and the wavefield was then computed in an irregular polar system.The Lebedev staggered grid was used to solve the wave equations in the irregular polar system.In addition,the artificial absorption boundary,cylindrical free boundary,and circumferential boundary conditions were used to absorb the boundary reflection.We selected three polar space models to demonstrate the new method in this study.The results show that the proposed elastic simulation method in an irregular polar coordinate system can produce more accurate and stable simulation results when modeling seismic wave propagation in an irregular polar space.Elastic full waveform inversion further shows that the irregular polar system elastic simulation method can accurately simulate the wavefield in an undulating polar space.

Elastic reverse-time migration in irregular tunnel environment based on polar coordinates

When seismic exploration is conducted in a special geological environment such as a tunnel space,the traditional imaging method in the Cartesian coordinate system cannot accurately discretize the air column in that environment.Thus,obtaining Thus,obtaining highquality imaging results is diffi cult.Therefore,an elastic-wave reverse-time migration method based on the polar coordinate system is proposed.In this method,three boundary conditions exist:outer,inner,and corner boundaries.In the outer boundary,the polar-coordinated absorbing boundary in the radial direction is used to suppress the artifi cial-boundary refl ection.The free-surface boundary condition is adopted in the tunnel space at the inner boundary.In the angular boundaries,we use two diff erent boundary conditions for two cases.The air column in the tunnel space is usually not an irregular circle.Therefore,the irregular tunnelspace geological body in the polar coordinate system is meshed into curvilinear grids and transformed into a regular one in an auxiliary polar coordinate system using the mapping method.Finally,elastic reverse-time migration technology is applied into the auxiliary polar coordinate system.In the numerical examples,two typical models are used to test the proposed method,which verify that the proposed method can obtain accurate images from the datasets in the tunnel space.

High Efficiency Stereo Audio Compression Method Using Polar Coordinate Principle Component Analysis for Wireless Communications

High efficiency audio compression is the basic technology in audio involved multimedia communications. Downmixing and parametric coding is efficient coding scheme with wide applications in some up-to-date audio codecs such as Parametric Stereo (PS) in EAAC+ and MPEG-Surround. Principle Component Analysis (PCA) stereo coding followed this idea to map two channels to one channel with maximum energy and parameterize the secondary channel. This paper investigates the conventional PCA method performance under general stereo model with multiple sound sources and different directions, and then proposes a Polar Coordinate based PCA (PC-PCA) stereo coding method. It has been proved that when multiple sound sources exist with different directions, PC-PCA is better than the conventional PCA method when Mean to Standard deviation Ratio (MSR) is large. A stereo codec based on PC-PCA is proposed to validate the performance improvement of proposed method. Objective and subjective tests show the proposed method achieves a comparative quality and saves 50% parameter bit rate comparing with conventional PCA method, and obtains a 4-8 MUSHRA scores improvement comparing with state-of-the-art stereo codec at the same parameter bit rate.

Strong/weak limits and strong/weak differentials of multi-variable indeterminate forms. III: Transformations

Various transforms of the indeterminate forms are presented in this part, which include simplification in spherical coordinates, origin translation, axis alteration, transformation of limit conservation and application of Xh?K0. Fundamental factors for numerical simplification are provided respectively for bi-variable indeterminate forms, tri-variable indeterminate forms and the universal extending multiplier.

圆锥曲线中一类垂直问题的探究

圆锥曲线的定义、方程和性质,无不体现着代数形式与几何性质的和谐统一,即数形结合思想的应用.其中存在的诸多与垂直有关的定值问题也绝非偶然,这是由圆锥曲线的定义及特性所决定的.近几年高考中,就出现了一些圆锥曲线的垂直问题.先看如下一道椭圆中的垂直问题.

选修4系列教学难点及解决策略

苏教版新课标教材选修4包括《几何证明选讲》、《矩阵与变换》、《坐标系与参数方程》、《不等式选讲》4个专题江苏高考是以附加题中4小题选2小题作答为考试内容,每题10分,共20分,占附加题总分的50%,考查的多为容易题;而在高二第二学期期末考试是以附加题中4组选2组作答为考试内容,每组2题,共40分,考查的也多为容易题。根据高考的需要以及教研室的建议和要求,我们跟大家一样,选择《矩阵与变换》、《坐标系与参数方程》

Biological object recognition approach using space variant resolution and pigeon-inspired optimization for UAV

Recognizing the target from a rotated and scaled image is an important and difficult task for computer vision. Visual system of humans has a unique space variant resolution mechanism(SVR) and log-polar transformations(LPT) is a mapping method that is invariant to rotation and scale. Motivated by biological vision, we propose a novel global LPT based template-matching algorithm(GLPT-TM) which is invariant to rotational and scale changes; and with pigeon-inspired optimization(PIO) used to optimize search strategy, a hybrid model of SVR and pigeon-inspired optimization(SVRPIO) is proposed to accomplish object recognition for unmanned aerial vehicles(UAV) with rotational and scale changes of the target. To demonstrate the efficiency, effectiveness and reliability of the proposed method, a series of experiments are carried out. By rotating and scaling the sample image randomly and recognizing the target with the method, the experimental results demonstrate that our proposed method is not only efficient due to the optimization, but effective and accurate in recognizing the target for UAV.

Finite Element Method Formulation in Polar Coordinates for Transient Heat Conduction Problems

The aim of this paper is the formulation of the finite element method in polar coordinates to solve transient heat conduction problems. It is hard to find in the literature a formulation of the finite element method(FEM) in polar or cylindrical coordinates for the solution of heat transfer problems. This document shows how to apply the most often used boundary conditions. The global equation system is solved by the Crank-Nicolson method. The proposed algorithm is verified in three numerical tests. In the first example, the obtained transient temperature distribution is compared with the temperature obtained from the presented analytical solution. In the second numerical example, the variable boundary condition is assumed. In the last numerical example the component with the shape different than cylindrical is used. All examples show that the introduction of the polar coordinate system gives better results than in the Cartesian coordinate system. The finite element method formulation in polar coordinates is valuable since it provides a higher accuracy of the calculations without compacting the mesh in cylindrical or similar to tubular components. The proposed method can be applied for circular elements such as boiler drums, outlet headers, flux tubes. This algorithm can be useful during the solution of inverse problems, which do not allow for high density grid. This method can calculate the temperature distribution in the bodies of different properties in the circumferential and the radial direction. The presented algorithm can be developed for other coordinate systems. The examples demonstrate a good accuracy and stability of the proposed method.

THE EFFECT OF BOUNDARY SHAPE ON BOUNDARY LAYER OF P-MODEL PLATE PROBLEMS WITH HARD SIMPLY SUPPORT

The paper shows that, for a unit circular plate, Reissner-Mindlin plate model with hard simply support does not capture the boundary layer behaviour for the bending moment when the load is independent of θ, where (r,θ) is the polar coordinates in plane. In contrast p-model shows this boundary layer, which is proved theoretically and numerically. But for the case when the boundary is a straight line, the boundary layer for p-model is weak and disappears as the plate thickness tends to zero.

Mathematical modeling and numerical simulation of telephone cord buckles of elastic films

An annular sector model for the telephone cord buckles of elastic thin films on rigid substrates is established, in which the von Krman plate equations in polar coordinates are used for the elastic thin film and a discrete version of the Griffith criterion is applied to determine the shape and scale of the parameters. A numerical algorithm combining the Newmark-β scheme and the Chebyshev collocation method is designed to numerically solve the problem in a quasi-dynamic process. Numerical results are presented to show that the numerical method works well and the model agrees well with physical observations, especially successfully simulated for the first time the telephone cord buckles with two humps along the ridge of each section of a buckle.