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.

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.

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.

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。

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.

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.

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.

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.

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.

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.

Entanglement polygon inequalities for a class of mixed states

The study on the entanglement polygon inequality of multipartite systems has attracted much attention.However,most of the results are on pure states.Here we consider the property for a class of mixed states,which are the reduced density matrices of generalizedW-class states in multipartite higher dimensional systems.First we show the class of mixed states satisfies the entanglement polygon inequalities in terms of Tsallis-q entanglement,then we propose a class of tighter inequalities for mixed states in terms of Tsallis-q entanglement.At last,we get an inequality for the mixed states,which can be regarded as a relation for bipartite entanglement.

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.

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.

基于Polygon-Nurbs混合建模的汽车造型数字化设计

文章阐述了汽车造型数字化设计中Polygon建模与Nurbs建模的特点与适用情境。提出了一种基于Polygon-Nurbs混合建模的汽车造型数字化设计方法。该建模方法的核心流程是先采用多边形确定形体,再使用Nurbs建模构建稳定的曲面。基于该混合建模思路,进行了汽车造型设计实践,证明了该建模方法能够发挥两种建模方式的优点,快速准确构建形体,并能生成高质量的曲面模型。

基于Polygon的雕塑法计算机辅助造型设计方法

计算机辅助设计技术已成为设计表现的必备手段,对于概念造型设计而言,接近传统手工方式的设计方法更易于被艺术设计师理解和接受。在对比目前主要计算机辅助造型方法的基础上,从分析传统手工雕塑造型的方式出发,针对概念设计和艺术造型设计的实际特征,提出了基于Polygon建模的雕塑法建模思路,给出了具体的建模步骤和合理布线的评价方法,并通过民间工艺品-泥塑马的造型实现过程进行了实例验证。实际运用证明,计算机雕塑建模方法对于艺术设计的三维软件建模理念具有较强的实用性,能够充分按照设计师的构思理念进行造型设计,对于创意设计而言更易于被造型设计师理解和运用。

基于Polygon之间相互切割的算法描述与实现

在地理信息系统(GIS)或一些图形处理中,经常会碰到地理图形切割,以及对切割后的数据进行处理。文章主要讨论了由Polygon切割Polygon生成Polygon算法的现实意义,以及如何实现切割后的Polygon自动生成算法的问题。

基于内多边形一阶共振效应的压电俘能风力发电

现有压电振子采用瞬态冲击振动方式能获得较大的初始动能,但其结构复杂,且在连续瞬态冲击下难以实现一阶共振,无法获得最佳振幅和输出功率。提出一种基于内多边形结构的风力瞬态冲击压电俘能方法及实现装置,该装置在一定风速下能连续发生一阶共振获得高输出性能,有利于改变无线网络节点传感器的供电方式以及提升传感器使用便捷性。理论分析和数值仿真模拟结果表明,在风速为17.0 m·s^(-1)时,该装置能在连续瞬态冲击下产生频率为131.40 Hz的一阶振动并发生共振。实验结果表明压电俘能风力发电装置的最佳匹配负载为20 kΩ,负载最大功率可达4.73 mW。在最佳匹配负载下,该装置压电陶瓷片的功率密度达到833.68μW·cm^(-3)。与非一阶共振状态相比,负载功率至少提升了1倍,能有效满足大部分无线网络节点传感器的供能需求。

考虑车轮多边形磨损的机车轮轨动力特性研究

针对车轮的多边形磨损,建立了重载列车轨道三维耦合动力学模型,研究了机车车轮多边形磨损引起的轮轨动力相互作用。在动力学模型中嵌入了低粘着区(LAZ)和防滑控制算法,以分析在正常和低粘着条件下车轮多边形磨损对轮轨纵向和横向相互作用的影响。在两台不同磨损模式的机车上进行了对比试验,包括车轮周向磨损测量和机车振动试验,验证了模型的合理性。在此基础上分析了多边形磨损的动态响应,结果表明车轮多边形磨损不仅会加剧车轮/轨道的垂直力,还会加剧车轮与轨道之间的纵向相互作用。多边形磨损对机车前两轮对与后两轮对的纵向相互作用影响较大。

长度尺寸的图像测量算法设计

在工业生产中,常常需要测量图像的尺寸。为避免传统测量方法耗时耗力且准确性不高的弊端,本文探索通过多边形拟合方法来得到被测图像的长度尺寸。通过拟合图像中的边缘点形成一个多边形,用于近似目标形状。实验的结果验证了本文算法的有效性。

基于禁忌搜索的含异形板件的板式家具码垛优化算法

为了减少含异形板件的板式家具打包的包裹个数,提出基于禁忌搜索的该类板式家具码垛优化算法;分析该类板式家具码垛问题的约束条件,并建立目标函数;采用可以有效确定订单中所有该类板式家具码垛顺序与旋转方向的编码方式,并利用启发式算法生成实时监测包裹质量的较优初始解,以便利用禁忌搜索求解该类板式家具码垛问题;结合临界多边形和最低水平线法,设计将编码转换为对应码垛方案的解码方式,并给出所提出算法的适配值函数及邻域结构;利用禁忌搜索计算该类板式家具订单,确定并优化每个板件的码垛顺序、旋转方向与码垛位置,得到包裹个数较少的码垛方案;选取欧洲排样问题兴趣小组(ESICUP)提供的算例测试所提出的算法,并与已有研究中可复现的板件智能分包方法对比。结果表明,相对于对比方法,所提出算法所得该类板式家具打包的包裹个数减少38.46%,验证了所提出算法的可行性与有效性。