通用地图投影选择研究

在分析现有的地图投影选择、评价标准和地图投影形变量之间关系的基础上,尝试引入形状比、长度比和面积比的概念,作为通用地图投影的选择、评价的基本度量指标,并通过层次分析法确定其权重,为通用地图投影的选择提供了思路,并通过实验验证了该方法的可行性与合理性。     

关于微分圆投影变成变形椭圆的分析与研究

针对各种地图学教材中关于变形椭圆的证明提出了三个问题,通过对地图投影中的微分圆垂直投影或 斜投影分析,不仅证明了微分圆投影变成了变形椭圆,而且利用几何分析解决了各种地图学教材中关于变形椭圆 证明出现的三个问题,对进一步了解地图投影的变形分布规律有着重要的意义。     

论述探求地图投影的理论与方法

本文在指明地图投影所要研究的问题之后,提出按投影的变形性质,按投影的经纬线形状,按投影的变形分布,按投影的其它条件四种类型探求地图投影的理论与方法,基本上概括了探求地图投影问题的全部,为学习这门学科提供了研究的思路和基础。     

利用三维点云数据的地铁隧道断面连续截取方法研究

提出了一种可应用于变形监测的基于三维激光点云的隧道断面连续截取方法.该方法分为点云拼接、中轴线提取和断面截取.隧道中轴线的提取通过随机采样一致性算法和最小二乘平差算法完成;断面截取过程先基于隧道轴线信息调整隧道姿态,再对隧道数据采取局部曲面拟合进行,其中引用了限制最小二乘算法和随机采样一致性算法.采用RIEGL VE-400获取的地铁隧道点云数据进行了验证.实验证明了本文方法在三维激光扫描技术的应用方面具有一定的实践意义.     

变形最小的等面积伪圆柱投影

为使高纬地区变形有所改善,可采用把伪圆柱地图投影的极点扩展成极线的方法。确定了极线长度与赤道长度的比率,即可给出一个一种变形最小的伪圆柱地图投影,最小误差技术的变分法是由爱瑞爵士(Sir George Airy)提出的,本文用正弦投影来说明这种方法。     

Web墨卡托投影及其性质分析

Web墨卡托投影是目前网络地图服务广泛采用的地图投影方法,但是该投影在使用之初便引起广泛争议,而且关于该投影目前仍缺乏统一的理解与认识。本文以Web墨卡托投影的定义为基本依据,推导了其变形公式,深入分析了该投影的变形特点,并从变形差异、坐标值、等角航线投影后形状等3个方面与墨卡托投影进行比较分析,在此基础之上归纳出关于Web墨卡托投影性质的3点结论。     

几何刚性和法向量采样一致性的点云配准算法

针对三维激光点云配准中随机采样一致性(RANSAC)算法存在采样次数多、准确度低的缺点,该文提出了一种结合几何刚性和法向量一致性的点云配准算法。该算法通过改进采样策略降低采样次数并提升匹配精度,首先将点云的法向量信息加入采样集,使得每次的采样点从三对减少为两对;接着以两对采样点的刚性和法向量一致性计算置信度来确定当前采样是否置信;最后以迭代运算选取采样内点数最高的样本来估算变换矩阵实现点云精确配准。对激光三维点云进行配准试验,结果表明,本文方法在匹配效率及匹配性能上均优于传统RANSAC算法,且配准精度更高。     

基于Monte Carlo采样策略的UKF算法应用

UKF算法中,Sigma采样点体现对均值和方差的传递精度.文中利用一种新的采样策略——蒙特卡洛模拟法采样策略,生成Sigma点集,再对每个Sigma点进行非线性变换,变换后仍通过非线性卡尔曼滤波公式计算,利用一个仿真算例验证采样策略的适用性.     

利用算子微分理论和反演方法探求地图投影正解变换

探求地图投影模型是一个很复杂的数学问题,涉及诸多数学理论和方法,解算步骤和过程一般都很繁琐。此处根据现代数学中的算子微分理论和微分几何理论,采用反演的方法对地图投影的正解变换进行了研究,简化了地图投影正解求解的过程和步骤。基本思路是先通过求解地图投影的反解变换,再根据反解变换求其相应的正解变换。并利用微分算子理论中的等角和等面积投影定理,分别验证了所探求的正反解是等角投影还是等面积投影。最后经过算例证明该方法的快捷性和有效性。     

小比例尺地图投影设计方法研究

针对地图投影的设计通常只能由具有数学与制图专业知识的专家完成的不足,该文对Robinson完全视觉化的地图投影方法进行扩展,提出一种基于软件方法的小比例尺世界地图投影设计方法,使普通用户能够快速创建新的地图投影或是修改一个已存在的投影:利用纬线长、纬线与赤道的距离、纬线弯曲度、经线弯曲度四个参数描述一种投影,并通过对比例变形、面积变形、角度变形、可接受的变形度等变形指标的视觉化展示向用户直观反映新投影的变形程度;同时通过可结构化的指数从整体上评估区域和角度变形。最后以Aitoff投影为例验证了方法的正确性。     

An adaptable equal-area pseudoconic map projection

Equivalence (the equal-area property of a map projection) is important to some categories of maps. However, unlike conformal projections, completely general techniques do not exist for creating new, computationally reasonable equal-area projections. The literature describes many specific equal-area projections and a few equal-area projections that are more or less configurable, but flexibility is still sparse. This work describes a new, highly configurable equal-area projection system consisting of arcs of concentric circles, placing it in the pseudoconic class. The system uses a novel technique to hybridize the Bonne pseudoconic projection and the Albers conic projection, subsuming many existing projections as degenerate cases. With the resulting system and the technique used to develop it, map projection designers will have greater choice in tailoring the projection to the need. The system may be particularly suited to maps that dynamically adapt to changing scale and region of interest, such as required for online maps.     

New measures for analysis and comparison of shape distortion in world map projections

ABSTRACT

World maps can have quite different depictions of reality depending on the projection adopted, and this can influence our perception of the world. In this respect, shape is a significant property that needs to be considered, especially when representing large regions in general-purpose world maps. A map projection distorts most geometric properties (area, distance, direction/angle, shape, and specific curves) and usually preserves a single property or provides a compromise between different properties when transforming terrestrial features from globe to plane. The distortions are mainly classified based on area, distance and direction/angle and analyzed with Tissot’s theorem. However, this theorem offers a local (pointwise) solution, so the distortion assessment is valid at infinitesimal scale (i.e. for very small regions). For this reason, different approaches are required to analyze the distortions at finite scale (i.e. for larger regions). However, there are very few attempts at analyzing and comparing shape distortion of landmasses in world map projections owing to the fact that shape measurement is difficult and usually involves measuring different characteristics. Seeking to fill this gap, in this study, compactness and elongation distortion measures are introduced. In this regard, 16 world map projections are analyzed and compared with these distortion measures in a GIS environment, based on map datasets of continents and countries. An analysis of the effect of the levels of detail of the datasets is also presented.     

Symbolization of Map Projection Distortion: A Review

One of the most fundamental steps in map creation is the transformation of information from the surface of a globe onto a flat map. Mapmakers have developed and used hundreds of different map projections over the past 2,000 years, yet there is no perfect choice because every map projection uniquely alters some aspect of space during the transformation process. Detailed information about the type, amount, and distribution of distortion is essential for choosing the best projection for a particular map or data set. The distortion inherent in projections can be measured and symbolized much like any other map variable. Methods for symbolizing map projection distortion are reviewed, with each method described and illustrated in graphical form. The symbolization methods are collected under ten separate headings organized from simple to more complex in terms of interpretation. Most of these methods are highly effective at communicating distortion, yet they are rarely used beyond textbooks and technical documentation. Map projections and the distortions they carry need to be better understood by spatial data developers, distributors, and users. Map distortion should be carried along with map data as confidence layers, and the easily accessible distortion displays should be available to help in the selection of map projections. There is a suitably wide array of symbolization methods to match any need from basic education to research.     

地图投影反解变换的一种新方法

通常地图投影反解变换有2种方法,即多项式拟合法和投影方程解析法.多项式法利用已知控制点的坐标对应关系,通过最小二乘法拟合求解地图投影反解变换的多项式函数,其优点是反解模型与地图投影无关,算法具有通用性,缺点是反算精度较低.解析法根据地图投影正算公式,在一定条件下通过解方程求得地图投影反解变换解析式,其优点是反解变换精度高,缺点是解法复杂.本文利用计算数学方法,根据地图投影变换的基本数学原理,提出了一种新的地图投影反解变换方法,双向迭代逼近法(BDIRA).具有反解变换精度高、收敛速度快、算法通用和GIS软件编程实现方便等特点.     

等分分层组合投影研究

针对中国地理格网(1°、10°等多级格网系统)的分割方法,设计了一种适合该格网系统的新型地图投影——分层组合投影。从微分几何的观点出发,把地球椭球按等纬度分割成若干层圆台,分别建立每个圆台的投影模型,即可得到一种地图投影。这种投影还可根据格网间隔的不同进行细分,从而发展成为一种适合多分辨率格网模型的动态地图投影。通过对该投影进行变形计算表明,该投影可以保持等角,而且面积和长度变形都很小,特别是在高纬度地区,与Mercator投影相比变形明显减小。     

等角投影变换的常系数公式及其在高斯—克吕格投影换带中的应用

讨论了等角投影变换的常系数一般公式及应用模型,墨卡托投影和高斯－克吕格投影问题的正解变换及其在高斯－克吕格投影换带中的应用,常系数计算公式优于传统的变系数计算公式,是基于计算机的等角投影变换的最佳模型,它在计算机制图,地理数据库,ＧＩＳ等领域中有着广泛的应用。     

海岸带数据集成中的空间坐标转换方法研究

就海岸带空间数据集成中所涉及的多种坐标系统一、多种地图投影转换等问题作了详细分析。并提出了有效的解决方案。     

Mixed cylindric map projections of the ellipsoid of revolution

The mixed spherical map projections of equiareal, cylindric type are based upon the Lambert projection and the sinusoidal Sanson–Flamsteed projection. These cylindric and pseudo-cylindric map projections of the sphere are generalized to the ellipsoid of revolution (biaxial ellipsoid). They are used in consequence by two lemmas to generate a horizontal and a vertical weighted mean of equiareal cylindric map projections of the ellipsoid of revolution. Its left–right deformation analysis via further results leads to the left–right principal stretches/eigenvalues and left–right eigenvectors/eigenspace, as well as the maximal left–right angular distortion for these new mixed cylindric map projections of ellipsoidal type. Detailed illustrations document the cartographic synergy of mixed cylindric map projections. Received: 23 April 1996 / Accepted: 19 April 1997     

Map-Projection Graphics from a Personal Computer

Some inexpensive personal computers may be programmed to produce, at a nominal incremental cost, map projection graphics useful as educational tools. Programs have been developed to produce outline maps based on anyone of dozens of projections, in almost any aspect, at a size of up to 13.5 by 27.1 cm or 20.3 by 20.3 cm [5?by 10? in. or 8 by 8 in.]. They are printed in a dot-matrix format normally containing up to 320 by 768 dots, with alternatives of 640 by 768 or 960 by 576 dots. Available options include features such as interrupted projection, miscellaneous great or small circles, and Tissot indicatrices. The maps often require many hours to prepare, but the programs can run unattended after initial parameters have been entered.