Updating conventional soil maps by mining soil–environment relationships from individual soil polygons

Conventional soil maps contain valuable knowledge on soil–environment relationships.Such knowledge can be extracted for use when updating conventional soil maps with improved environmental data.Existing methods take all polygons of the same map unit on a map as a whole to extract the soil–environment relationship.Such approach ignores the difference in the environmental conditions represented by individual soil polygons of the same map unit.This paper proposes a method of mining soil–environment relationships from individual soil polygons to update conventional soil maps.The proposed method consists of three major steps.Firstly,the soil–environment relationships represented by each individual polygon on a conventional soil map are extracted in the form of frequency distribution curves for the involved environmental covariates.Secondly,for each environmental covariate,these frequency distribution curves from individual polygons of the same soil map unit are synthesized to form the overall soil–environment relationship for that soil map unit across the mapped area.And lastly,the extracted soil–environment relationships are applied to updating the conventional soil map with new,improved environmental data by adopting a soil land inference model(SoLIM)framework.This study applied the proposed method to updating a conventional soil map of the Raffelson watershed in La Crosse County,Wisconsin,United States.The result from the proposed method was compared with that from the previous method of taking all polygons within the same soil map unit on a map as a whole.Evaluation results with independent soil samples showed that the proposed method exhibited better performance and produced higher accuracy.

An Algorithm for Partitioning Polygons into Convex Parts

An algorithm for partitioning arbitrary simple polygons into a number of convex parts was presented. The concave vertices were determined first, and then they were moved by using the method connecting the concave vertices with the vertices of falling into its region B,so that the primary polygon could be partitioned into two subpolygons. Finally, this method was applied recursively to the subpolygons until all the concave vertices were removed. This algorithm partitions the polygon into O(l) convex parts, its time complexity is max(O(n),O(l 2)) multiplications, where n is the number of vertices of the polygon and l is the number of the concave vertices.

基于Polygons的写实人物建模

对于三维动画的人来说,创造出一个属于自己的写实角色是每个人的梦想。即能够把角色制作的十分真实,就像真的生活在现实生活中一样,这类角色的结构一般都极为准确,准确到每一块肌肉、每一条血管、甚至每一条衣服上的褶皱。本文以实现一个真实的人物建模为项目,完整的讲解了人物建模的整个流程。整个流程分为五个步骤:搭建基本几何人体,细化几何人体,基本四肢的制作,头部的制作,手脚的制作,最终完成了整个人体的建模。本文重点研究了在进行多边形建模的过程中怎么根据人体骨骼,肌肉的走向来进行合理的布线。

On a Fixed Value Theorem for Directed Areas in Conic Circumscribed Polygons and Applications

Using polar equations for conic sections, we research conic circumscribed n-sided polygons（n ≥ 4） deeply on the basis of papers[1-3]. We obtain a general fixed value theorem for directed areas of some triangles in conic circumscribed n-sided polygons and derive as many as n（n - 3） concurrent points of three lines and some other collinear, equiareal results in conic circumscribed n-sided polygons（n ≥ 4）. So the results of papers[1-3] are unified.

A New Method of Recognizing Polygons under Perspective Transformation

Existing methods for recognizing polygons can be improved. A new concept ＂homograph＂ and then a new method for recognizing polygons based on the principle of homograph are proposed. First, five topological characteristics and geometrical characteristics are introduced that are invariant to describe polygon under perspective transformation. Then, the new concept of homograph is defined in terms of five topological characteristics and geometrical characteristics. Based on this definition, a new algorithm is proposed for recognizing that two polygons are homograph. The topological structure is introduced to analyze homograph qualitatively and the algorithm is insensitive to noises; and the geometrical structure is introduced to analyze homograph quantitatively, thus the algorithms can show tiny differences between polygons. It can not only recognize the objects with different shapes but also distinguish between objects with same shape but with different sizes and scales. Comparing with other recognition algorithms, the algorithm presented showed apparent improvement. The effectiveness of the algorithm is demonstrated by experiments.

A new fast algorithm for computing the distance between two disjoint convex polygons based on Voronoi diagram

Computing the distance between two convex polygons is often a basic step to the algorithms of collision detection and path planning. Now, the lowest time complexity algorithm takes O(logm+logn) time to compute the minimum distance between two disjoint convex polygons P and Q, where n and m are the number of the polygons’ edges respectively. This paper discusses the location relations of outer Voronoi diagrams of two disjoint convex polygons P and Q, and presents a new O(logm+logn) algo- rithm to compute the minimum distance between P and Q. The algorithm is simple and easy to implement, and does not need any preprocessing and extra data structures.

TWO NEW RECOGNITION METHODS FOR SPATIAL PLANAR POLYGONS

Two new recognition methods for the spatial planar POlygon using perspective invariants are presented. The corss-ratio (R c) of a vetex and the co-base area rotio (RA) of a edge in a spatial planar polygon are proposed and used as the invariant primitive of the recognition eigenvector. The second distance error decision rule (SD EDR) estimating the relative error of RA is introduced also too. The mthods could recognize a spatial planar polygon with an arbitrary orientation through only a single perspective view. Experimental examples are gievn.

Simulated Annealing Algorithm and Its Application in Irregular Polygons Packing

Two dimensional irregular polygons packing problem is very difficult to be solved in traditional optimal way.Simulated annealing(SA)algorithm is a stochastic optimization technique that can be used to solve packing problems.The whole process of SA is introduced firstly in this paper. An extended neighborhood searching method in SA is mainly analyzed. A general module of SA algorithm is given and used to lay out the irregular polygons. The judgment of intersection and other constrains of irregular polygons are analyzed. Then an example that was used in the paper of Stefan Jakobs is listed.Results show that this SA algorithm shortens the computation time and improves the solution.

Rational Equiangular Polygons

The main purpose of this note is to investigate equiangular polygons with rational edges. When the number of edges is the power of a prime, we determine simple, necessary and sufficient conditions for the existence of such polygons. As special cases of our investigations, we settle two conjectures involving arithmetic polygons.

Polygons and Tessellations

When am I ever going to use this?GEOGRAPHY The size and shape of each state in the United States is different.Analyze the shapes of the states in both groups at the right.1.Find the difference between the shapes of the states in Group 1and the shapes of the states in Group 2.2.Why do most states have boundaries that are not straight line segments?The states listed in Group 1 above are examples of polygons.A polygon is a simple,closed figure formed by three or more straight lines.A simple figure does not have lines that cross each other.You have drawn a closed figure when your pencil ends up where it started.

Central configurations consist of two layer twisted regular polygons

In this paper, we study the existence of a special twisted regular polygonal central configuration in R3.

Flow past polygons with an odd number of edges

In Tian and Wu (2009),the present authors studied the inviscid and viscous flow past polygons with an arbitrary but even number of edges and with one apex pointing to the free stream.Here we extend the results to the flow past polygons with an odd number of edges,and an arbitrary direction.Flow features such as the shape of stationary lines,stabilities of vortex pairs,1st critical Reynolds numbers,and flow patterns with separations,similar to or different from the results for even-sided polygons,are identified.

An Optimal Algorithm for Solving Collision Distance Between Convex Polygons in Plane

In this paper,we study the problem,of calculating the minimum collision distance between two planar convex polygons when one of them moves to another along a given direction.First,several novel concepts and properties are explored,then an optimal algorithm OPFIV with time complexity O(log(n+m))is developed and its correctness and optimization are proved rigorously.

A High Frequency Boundary Element Method for Scattering by Convex Polygons with Impedance Boundary Conditions

We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions.Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy.Extending earlier work by Chandler-Wilde and Langdon for the sound soft problem,we propose a novel Galerkin boundary element method,with the approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh with smaller elements closer to the corners of the polygon.Theoretical analysis and numerical results suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency of the incident wave.

Boolean Operations on Conic Polygons

An algorithm for Boolean operations on conic polygons is proposed. Conic polygons are polygons consisting of conic segments or bounded conics with directions. Preliminaries of Boolean operations on general polygons are presented. In our algorithm, the intersection points and the topological relationships between two conic polygons are computed. Boundaries are obtained by tracking path and selecting uncrossed boundaries following rule tables to build resulting conic polygons. We define a set of rules for the intersection, union, and subtraction operations on conic polygons. The algorithm considers degeneration cases such as homology, complement, interior, and exterior. The algorithm is also evaluated and implemented.

Approximation Algorithms for Solving Packing Problems of Convex Polygons in Plane

The problem of initial collision between convex polygons is studied in detail, and a fast algorithm for finding the embedded depth is obtained, by which the fast approximate algorithm for solving packing problems of convex polygons in plane is constructed.

On the Polygonal Wear Evolution of Heavy-Haul Locomotive Wheels due to Wheel/Rail Flexibility and Its Mitigation Measures

Wheel polygonal wear can immensely worsen wheel/rail interactions and vibration performances of the train and track,and ultimately,lead to the shortening of service life of railway components.At present,wheel/rail medium-or high-frequency frictional interactions are perceived as an essential reason of the high-order polygonal wear of railway wheels,which are potentially resulted by the flexible deformations of the train/track system or other external excitations.In this work,the effect of wheel/rail flexibility on polygonal wear evolution of heavy-haul locomotive wheels is explored with aid of the long-term wheel polygonal wear evolution simulations,in which different flexible modeling of the heavy-haul wheel/rail coupled system is implemented.Further,the mitigation measures for the polygonal wear of heavy-haul locomotive wheels are discussed.The results point out that the evolution of polygonal wear of heavy-haul locomotive wheels can be veritably simulated with consideration of the flexible effect of both wheelset and rails.Execution of mixed-line operation of heavy-haul trains and application of multicut wheel re-profiling can effectively reduce the development of wheel polygonal wear.This research can provide a deep-going understanding of polygonal wear evolution mechanism of heavy-haul locomotive wheels and its mitigation measures.

Measured dynamic load distribution within the in situ axlebox bearing of high-speed trains under polygonal wheel–rail excitation

The dynamic load distribution within in-service axlebox bearings of high-speed trains is crucial for the fatigue reliability assessment and forward design of axlebox bearings. This paper presents an in situ measurement of the dynamic load distribution in the four rows of two axlebox bearings on a bogie wheelset of a high-speed train under polygonal wheel–rail excitation. The measurement employed an improved strain-based method to measure the dynamic radial load distribution of roller bearings. The four rows of two axlebox bearings on a wheelset exhibited different ranges of loaded zones and different means of distributed loads. Besides, the mean value and standard deviation of measured roller–raceway contact loads showed non-monotonic variations with the frequency of wheel–rail excitation. The fatigue life of the four bearing rows under polygonal wheel–rail excitation was quantitatively predicted by compiling the measured roller–raceway contact load spectra of the most loaded position and considering the load spectra as input.

凸F-多边形内部的F-点数

An F-polygon is a simple polygon whose vertices are F-points, which are points of the set of vertices of a tiling of R~2 by regular triangles and regular hexagons of unit edge. Let f(v) denote the least possible number of F-points in the interior of a convex F-polygon K with v vertices. In this paper we prove that f(10) = 10, f(11) = 12,f(12) = 12.

Investigation on influencing factors of wheel polygonization of a plateau high-speed EMU train

Purpose–This study aims to investigate the cause of high-order wheel polygonization in a plateau high-speed electric multiple unit(EMU)train.Design/methodology/approach–A series of field tests were conducted to measure the vibration accelerations of the axle box and bogie when the wheels of the EMU train passed through tracks with normal rail roughness after re-profiling.Additionally,the dynamic characteristics of the track,wheelset and bogie were also measured.These measurements provided insights into the mechanisms that lead to wheel polygonization.Findings–The results of the field tests indicate that wheel polygonal wear in theEMUtrain primarily exhibits 14–16 and 25–27 harmonic orders.The passing frequencies of wheel polygonization were approximately 283–323 Hz and 505–545 Hz,which closely match the dominated frequencies of axle box and bogie vibrations.These findings suggest that the fixed-frequency vibrations originate from the natural modes of the wheelset and bogie,which can be excited by wheel/rail irregularities.Originality/value–The study provides novel insights into the mechanisms of high-order wheel polygonization in plateau high-speed EMU trains.Futher,the results indicate that operating the EMU train on mixed lines at variable speeds could potentially mitigate high-order polygonal wear,providing practical value for improving the safety,performance and maintenance efficiency of high-speed EMU trains.