强化“几何”特征 重视“结合”意识——例谈解析几何中强化“几何”特征和综合解题意识培养

解析几何的本质是几何问题,几何问题借以代数计算,更加便捷,代数问题通过几何图形更加形象直观,高考主要借以代数工具解决几何问题,但是也不能忽略对代数问题几何化或者代数几何相结合意识的培养,特别是强化运用“几何”特征以及代数几何结合解决解析几何问题.文章中以高考真题和名校模拟题为例进行了一题多解分析,并利用反馈变式练习以强化解题意识.

High-precision automatic measurement of two-dimensional geometric features based on machine vision

To realize high-precision automatic measurement of two-dimensional geometric features on parts, a cooperative measurement system based on machine vision is constructed. Its hardware structure, functional composition and working principle are introduced. The mapping relationship between the feature image coordinates and the measuring space coordinates is established. The method of measuring path planning of small field of view （FOV） images is proposed. With the cooperation of the panoramic image of the object to be measured, the small FOV images with high object plane resolution are acquired automatically. Then, the auxiliary measuring characteristics are constructed and the parameters of the features to be measured are automatically extracted. Experimental results show that the absolute value of relative error is less than 0. 03% when applying the cooperative measurement system to gauge the hole distance of 100 mm nominal size. When the object plane resolving power of the small FOV images is 16 times that of the large FOV image, the measurement accuracy of small FOV images is improved by 14 times compared with the large FOV image. It is suitable for high-precision automatic measurement of two-dimensional complex geometric features distributed on large scale parts.

Geometrical characteristic investigation of the Baihetan irregular columnar jointed basalt and corresponding numerical reconstruction method

Columnar jointed rock mass with unique geometric and geological properties is one spectacular example of geometrical order in nature.Columnar joints are generally accepted to be formed by spatially uniform volume contraction during cooling.In this paper,substantial field work was performed to study the geological characteristics of irregular columnar jointed basalt on the left bank dam foundation in the Baihetan Hydropower Station,where the columnar jointed rock mass is extensively exposed due to excavation.The quantitative measurements of the sizing of polygonal crack pattern of columnar joints and assessment of their degree of irregularity were summarized.Considering the irregularity of polygonal crack pattern,a modified Voronoi polygon(MVP)method was developed to model the special polygonal crack pattern of columnar joints.The new polygonal pattern obtained by the MVP method consists of a large number of irregular polygons,of which the degree of irregularity is consistent with the field measurement results.This method can reproduce the rapid evolution from an initial ideal regular hexagonal pattern to a final actual irregular polygonal pattern as the degree of irregularity increases.The compression tests of columnar jointed rock mass with different irregularity show that the geometric irregularity has a great influence on its mechanical properties.This numerical construction method provides a reliable way to reconstruct columnar joint structure with specific polygonal crack pattern,which is consistent with onsite columnar jointed basalt.

A Precise Information Extraction Algorithm for Lane Lines

Lane line detection is a fundamental step in applications like autonomous driving and intelligent traffic monitoring. Emerging applications today have higher requirements for accurate lane detection. In this paper, we present a precise information extraction algorithm for lane lines. Specifically, with Gaussian Mixture Model(GMM), we solved the issue of lane line occlusion in multi-lane scenes. Then, Progressive Probabilistic Hough Transform(PPHT) was used for line segments detection. After K-Means clustering for line segments classification, we solved the problem of extracting precise information that includes left and right edges as well as endpoints of each lane line based on geometric characteristics. Finally, we fitted these solid and dashed lane lines respectively. Experimental results indicate that the proposed method performs better than the other methods in both single-lane and multi-lane scenarios.

RESEARCH ON FRACTAL CHARACTERISTICS OF URBAN TRAFFIC NETWORK STRUCTURE BASED ON GIS

Traffic network is an importance asp ect of researching controllable parameters of an urban spatial morpholo-gy.Based on GIS,traffic network str ucture complexity can be understood by using fractal geometry in which th e length-radius dimension describes change of network density,and ramification-radius dimension describes complexity and accessibility of urban network.It i s propitious to analyze urban traffic network and to understand dynamic c hange process of traffic network using expanding f ractal-dimension quantification.Meanwhile the length-radius dimension and ramifica-tion-radius dimension could be rega rd as reference factor of quantitative describing urban traffic network.

Geometrical feature analysis and disaster assessment of the Xinmo landslide based on remote sensing data

At 5:39 am on June 24, 2017, a landslide occurred in the village of Xinmo in Maoxian County, Aba Tibet and Qiang Autonomous Prefecture(Sichuan Province, Southwest China). On June 25, aerial images were acquired from an unmanned aerial vehicle(UAV), and a digital elevation model(DEM) was processed. Landslide geometrical features were then analyzed. These are the front and rear edge elevation, accumulation area and horizontal sliding distance. Then, the volume and the spatial distribution of the thickness of the deposit were calculated from the difference between the DEM available before the landslide, and the UAV-derived DEM collected after the landslide. Also, the disaster was assessed using high-resolution satellite images acquired before the landslide. These include Quick Bird, Pleiades-1 and GF-2 images with spatial resolutions of 0.65 m, 0.70 m, and 0.80 m, respectively, and the aerial images acquired from the UAV after the landslide with a spatial resolution of 0.1 m. According to the analysis, the area of the landslide was 1.62 km2, and the volume of the landslide was 7.70 ± 1.46 million m3. The average thickness of the landslide accumulation was approximately 8 m. The landslide destroyed a total of 103 buildings. The area of destroyed farmlands was 2.53 ha, and the orchard area was reduced by 28.67 ha. A 2-km section of Songpinggou River was blocked and a 2.1-km section of township road No. 104 was buried. Constrained by the terrain conditions, densely populated and more economically developed areas in the upper reaches of the Minjiang River basin are mainly located in the bottom of the valleys. This is a dangerous area regarding landslide, debris flow and flash flood events Therefore, in mountainous, high-risk disaster areas, it is important to carefully select residential sites to avoid a large number of casualties.

Characteristics of turbulent flow distribution in branch piping system

Flow distribution in branch piping system is affected by flow characteristics and different geometric variations. Most of the flow distribution studies are performed with one-dimensional analysis to yield overall information only. However, detailed analysis is required to find effects of design parameters on the flow distribution. For this aspect, three-dimensional turbulent flow analysis was performed to assess turbulence model performance and effects of upstream pressure and branch pipe geometry. Three different turbulence models of standard k-e model, realizable k-e model and standard k-co yield similar results, indicating small effects of turbulence models on flow characteristics analysis. Geometric variations include area ratio of main and branch pipes, branch pipe diameter, and connection shape of main and branch pipes. Among these parameters, area ratio and branch diameter and shape show strong effect on flow distribution due to high friction and minor loss. Uniform flow distribution is one of common requirements in the branch piping system and this can be achieved with rather high total loss design.

Experimental Study on Roof Structure Characteristics and Its Failure Pattern in Coal Roadway

Based on the investigation and statistics of logs of 211 bole holes and strata data from 79 roadways in 13 coal mines located in Xishan, Jincheng, Lu’an, Fenxi, and Huozhou in China, the roadways’ roof structures were classified as multi-thin-layer, thin-thick combined layer, integrated thick layer, thick-coal layer, and cracked layer according to the geometric features and spatial strength distribution of surrounding rock. Then eight sub-categories were defined as different situations. And seven simulation modeling tests were carried out. The strata structures of these models were different from each other. At last, the relationship between roof structure and its failure pattern was discussed.

A bearing fault feature extraction method based on cepstrum pre-whitening and a quantitative law of symplectic geometry mode decomposition

In order to extract the fault feature of the bearing effectively and prevent the impact components caused by bearing damage being interfered with by discrete frequency components and background noise,a method of fault feature extraction based on cepstrum pre-whitening(CPW)and a quantitative law of symplectic geometry mode decomposition(SGMD)is proposed.First,CPW is performed on the original signal to enhance the impact feature of bearing fault and remove the periodic frequency components from complex vibration signals.The pre-whitening signal contains only background noise and non-stationary shock caused by damage.Secondly,a quantitative law that the number of effective eigenvalues of the Hamilton matrix is twice the number of frequency components in the signal during SGMD is found,and the quantitative law is verified by simulation and theoretical derivation.Finally,the trajectory matrix of the pre-whitening signal is constructed and SGMD is performed.According to the quantitative law,the corresponding feature vector is selected to reconstruct the signal.The Hilbert envelope spectrum analysis is performed to extract fault features.Simulation analysis and application examples prove that the proposed method can clearly extract the fault feature of bearings.

A Testing of SOTER Project in China

A SOTER (soil and terrain digital database) project at the scale of 1:500000 has been tested using the CIS (geographical information system) methodology in Hainan Province of tropical China. Soil and terrain map units were delineated by SOTER manual. An ARC/ INFO GIS software has been used for geometric data storing and map editing, with attribute data stored in a relational database management system, dBASEIII PLUS.

Two-order Hermite vector-interpolating subdivision schemes

A family of two-order Hermite vector-interpolating subdivision schemes is proposed and its convergence and con- tinuity are analyzed. The iterative level can be estimated for given error. The sufficient conditions of C2 continuity are proved. Geometric features of subdivision curves, such as line segments, cusps and inflection points, are obtained by appending some conditions to initial vectorial Hermite sequence. An algorithm is presented for generating geometric features. For an initial se- quence of two-order Hermite elements from unit circle, the numerical error of the 4th subdivided level is O(10?4).

Dependence of Conductance of Corrugated Graphene Quantum Dot on Geometrical Features

Dependence of conductance of corrugated graphene quantum dot(CGQD)on geometrical features includinglength,width,connection and edge is investigated by the first principles calculations.The results demonstrate that theconductance of CGQD with different geometrical features is different from each other.The positions and amplitudesof discrete levels in densities of states and transmission coefficients are sensitive to geometrical features.The I-Vcharacteristics of graphene are modified by size and edge,it is surprise the current does not change monotonously butoscillatory with length.And they are slight change for different connections.

A feature extraction and correspondence algorithm for laser range finder with sensor uncertainty

This paper presents a feature extraction and correspondence algorithm which employs a novel feature transform. Unlike conventional approaches such as Hough Transform, we employ a robust but simple approach to extract the geometrical feature under real dynamic world conditions. Multi-threshold segmentation and the split-and-merge method are employed to interpret geometrical features such as edge, concave corners, convex corners, and segments in a unified framework. The features are represented by feature tree (F-Tree) so as to compactly represent the environments and some important properties of the F-Tree are discussed in this paper. To demonstrate the validity of the approach, we show the actual experiment results which are based on real Laser Range Finder data and real time analysis. The comparative study with Hough Transform shows the advantages and the high performance of the proposed algorithm.

Comparison Between Two Solutions Based on the Relationship of Load-deflection Character of a Large Deflection Rubber Circular Plate

The rubber circular plate is considered as a kind of membrane. Based on the character that there exists no bending moment inside a membrane, the geometric behavior of the rubber circular plate in expanding state was described with the aid of a group of mathematic method. The relationship between deflection and load was attained by means of calculating stress and strain inside the curved surface of rubber plate. Meantime, based on Hencky method, the relationship between deflection and load was attained and considered as the Hencky solution. The different results given rise by the two different resolving methods were compared. The deviation results from the Hencky method was discussed, and a kind of correcting method was put forward.

Experimental Study on 3D Geometrical and Fractal Characteristics of Fracture Surface of Rock-Like Materials Based on GIS Technique

In order to research the characteristic and mechanism of fracture of rock-like materials,the morphology of rock fracture surface under the breakages of uniaxial compression and triaxial compression was observed and measured by means of a new-type 3D laser scanning system.Based on geographic information system(GIS)technique,the fracture surfaces were 3D visualized and reestablished.According to GIS 3D statistics,the geometrical characteristics of fracture surfaces under different breakage conditions were analyzed,and then based on fractal theory,the change laws of fractal dimension of fracture surfaces were discussed under the conditions of different cell pressures and initial water contents of rock.Furthermore,the relationships between characteristics of fracture surface and mechanical properties of rock were discussed.The results indicate that cell pressure,initial water content,and mechanical parameters of rock are the important factors to influence on the geometrical characteristics of fracture surface.The research provides a new experimental method for quantitative study on the fracture characteristics of various materials under different breakage conditions.

Fast image matching algorithm based on affine invariants

Feature-based image matching algorithms play an indispensable role in automatic target recognition （ATR）. In this work, a fast image matching algorithm （FIMA） is proposed which utilizes the geometry feature of extended centroid （EC） to build affine invariants. Based on at-fine invariants of the length ratio of two parallel line segments, FIMA overcomes the invalidation problem of the state-of-the-art algorithms based on affine geometry features, and increases the feature diversity of different targets, thus reducing misjudgment rate during recognizing targets. However, it is found that FIMA suffers from the parallelogram contour problem and the coincidence invalidation. An advanced FIMA is designed to cope with these problems. Experiments prove that the proposed algorithms have better robustness for Gaussian noise, gray-scale change, contrast change, illumination and small three-dimensional rotation. Compared with the latest fast image matching algorithms based on geometry features, FIMA reaches the speedup of approximate 1.75 times. Thus, FIMA would be more suitable for actual ATR applications.

A New Approach on Quantum Gravity in Lyra Geometry

This article investigates quantum gravity through a new approach based on quantization of spacetime and Lyra geometry. Singularity functions are applied to the study, whose main focus is to investigate the physics in the surroundings of supermassive bodies. Present work is a continuation of the research program on quantum gravity and time machines established by the author in a previous publication. The physical and geometrical features of the model are discussed.

Thermodynamic Curvature and Phase Transitions from Black Hole with a Coulomb-Like Field

In this paper, we first investigate the thermodynamic features of the black hole with a coulomb-like field. Moreover, we obtain the geometric description of the black hole thermodynamics. We find that for the black hole with a coulomb-like field the Weinhold geometry is fiat, whereas its Ruppeiner geometry is curved. For the heat capacity and curvature calculation shows the Ruppeiner geometry has a transition point.

Deposition Morphology of Non-homogeneous Debris Flow and Its Energy Characteristics

Non-homogeneous two-phase debris flows are widely found in the western mountainous regions of China. To investigate the characteristics of the debris flow deposition process related to the morphology and extent of the debris fan, a series of physical experiments were carried out using an experimental flume. Some useful relationships were obtained to link the flow velocity with the geometric characteristics of deposition morphology and the corresponding area or volume. Based on these, some expressions about energy dissipation process in both the transport-deposition zone and deposition zone are presented, and improved equations describing solidliquid two-phase energy transformations in the specific deposition zone are also established. These results provide a basis for further investigating the underlying mechanisms of non-homogeneous debris flows, based upon which effective disaster control measures can be undertaken.

Fractal desulfurization kinetics of high-sulfur coal

The pore structure characteristics of high-sulfur coal from Wansheng in Chongqing have been studied by a nitrogen adsorption method （BET）. The effects of grinding and pre-treating with nitric acid on the inorganic sulfur content of coal have been investigated. Organic sulfur in coal pretreated with nitric acid was desulfurized by using propylene-glycol-KOH （PG-KOH）. Fractal kinetic properties of these two desulfurization procedures were investigated by using fractal geometric theory. The results show that both the specific surface area and pore volume increased with the decrease in particle diameter. The microspore surface of coal had fractal characteristics; the fractal dimension was 2.48. The sulfur content decreased with the decrease in particle diameter by grinding. After pretreatment with nitric acid, the desulfurization ratio （DFR） of inorganic sulfur increased to over 99% and the DFR of total sulfur to over 70%. The desulfurization procedure of inorganic sulfur had fractal kinetic characteristics; its reactive frac- tal dimension was 2.94. The organic sulfur desulfurization procedure by PG-KOH was also tallied with fractal kinetic properties; the reactive fracta! dimension was 2.57. The effect of temperature on the desul- furization ratio of organic sulfur can be described with an Arrhenius empirical equation. The rate constant, pre-exponential factor and the activation energy of the reaction increased with the decrease in particle diameter.