基于极点到坐标原点的距离函数的常规地图投影分类体系

In our previous works, we described the projections that make it possible to construct maps of the celestial bodies in planetary scale – the azimuthal and cylindrical projections of different distortion classes. However, for regions in the middle latitudes, it is advisable to use a conic projection, which has not been developed previously. In this investigation, we describe the development of three conic projections of a triaxial ellipsoid: a conic projection with true scale along meridians, an equal-area conic projection, and a quasi-conformal conic projection. The quasi-conformal conic projection is a projection close to the conformal projection in the neighbourhood of each meridian corresponding to a meridian section. We treat conic projections as projections in which the meridians are a bundle of straight lines emanating from a single point, and parallels are curves constructed in accordance with the selected character of distortion. This definition of conic projections of the triaxial ellipsoid allows us to connect various classes of projections in a system. Thus, cylindrical projections can be considered as a limiting case of conic projections, and azimuthal projections as a special case. For the triaxial ellipsoid as a surface that can be projected on a plane without distortions, we use a direct elliptic cone tangent to the ellipsoid. The projections are calculated, and maps in these projections are created for the first time.

This paper presents a 3D model descriptor based on the linear prediction coding (LPC) coefficients to retrieve 3D objects. In this method, the 3D object is projected on the lateral surface of a cylinder parallel to one of its principal axes and centered at the centroid of the object. To improve efficiency, cylindrical projection is performed on three cylinders parallel to principal axes. Besides, the object is projected on a sphere centered at the centroid of the 3D object. The surface of object is converted to two-dimensional shapes as a result of performing the projections which preserves the geometric features of the object. Then, LPC coefficients are extracted from the two-dimensional projected shapes. These coefficients estimate the parameters of correlated signal, efficiently. Since the cylindrical and spherical projections of the 3D model are correlated surfaces, LPC coefficients describe the surfaces as well. The rotation normalization is performed employing the principal component analysis. Furthermore, the retrieval performance is enhanced employing SVM-OSS similarity measure which efficiently compares two model feature vectors. We implement an experimental comparison on PSB database of 3D models in order to demonstrate the performance of the proposed descriptor. Experimental results show the effectiveness of the proposed descriptor compared to current methods.

Map projections are usually interpreted by mapping a sphere onto an auxiliary surface, and then the surface is developed into a plane. It is taken as a fact without proof that the parallels in which the auxiliary surface intersects the sphere are mapped without distortions. In a previous paper, based on a theoretical consideration and illustrated with several examples, the author concluded that explaining cylindrical projections as mapping onto a cylindrical surface is not a good approach, because it leads to misunderstanding important properties of projection. In this paper I prove that there are no equal-area, equidistant, or conformal cylindrical projections for which the standard parallel will coincide with secant parallel after folding the map into a cylinder.

Novel map projections can be derived by solving one of the two primary problems in mathematical cartography: direct and inverse. The combination of the equations of existing projections is a method that belongs to the direct problem category in mathematical cartography. As projections of different types, different classes, and different aspects can be combined, a considerable number of projections can be obtained by using this method. This paper aims to develop a novel projection by combining two conformal cylindrical projections with different aspects, namely normal and transverse, to reduce the distortions in map projection. It is observed that the resulting projection exhibits less distortion than those in normal and transverse cylindrical projections. Furthermore, the developed projection preserves conformality.

Abstract. The basic property of all map projections is the distribution of inevitable distortions. Conic projections with one or two standard parallels are mentioned in the literature. These are parallels with the property that the distortion of length, area and angles equals zero at each of their points. It turns out that there are conic projections with no standard parallels, as well as those with more than two standard parallels. Such projections exist not only in theory, but examples of such projections can also be constructed.

The research goal is to determine the level of accuracy of Adriatic Sea renderings on selected portolan charts by using the quantitatively–analytical approach and to determine the level of portolan charts usability for navigational purposes. The manuscript is divided into two main subject matters, each divided on three and four core chapters respectively. In the first subject matter, map projection that is geometrically most similar to the renderings of Adriatic Sea on portolan charts has been determined catrometrcally. Afterwards, chronological variations of mapping accuracy, along with geometrical deviations of particular charts from their average geometry, were determined compared to that projection. Also, in this part of the research, the Adriatic Sea basin was divided regionally and functionally, which resulted in detection of mapping accuracy variations for each particular segment of those divisions. In the second subject matter, the first aspect of charts’ usability are physical dimensions of Adriatic Sea renderings on charts themselves. The second aspect is the relation between portolan charts’ counterclockwise rendering tilt and direction and value of contemporary magnetic variation. The third aspect is the relation between terrestrial navigation across the Adriatic Sea and the portolan chart accuracy, whilst the fourth aspect represents geometrical interrelation between the accuracy of portolan charts and the accuracy of textual data on navigational routes contained in selected portolans. One of the fundamental conclusions is that the renderings of Adriatic Sea basin on portolan charts show immense accuracy levels, especially if bearing-mapping accuracy of cross-basin lines is considered, and that portolan charts, at least on their segments on which Adriatic Sea is being displayed, are intentionally made with the appliance of map projection which shows the characteristics of conformal cylindrical (Mercator) map projection in its normal aspect. Also, the research results implicitly suggest that it is highly unlikely that portolan charts are genuine medieval products, but rather that they represent the copies of older charts made in certain earlier period. Fundamental arguments that support such assumption are: calculated inexistence of charts’ accuracy increase during three-century period, higher accuracy of cross-basin bearings than that of coastal bearings, and higher accuracy of cross-basin routes in portolans (in general) than that of their coastal routes.

For regional groundwater flow models (areas greater than 100,000 km2 ), improper choice of map projection parameters can result in model error for boundary conditions dependent on area (recharge or evapotranspiration simulated by application of a rate using cell area from model discretization) and length (rivers simulated with head-dependent flux boundary). Smaller model areas can use local map coordinates, such as State Plane (United States) or Universal Transverse Mercator (correct zone) without introducing large errors. Map projections vary in order to preserve one or more of the following properties: area, shape, distance (length), or direction. Numerous map projections are developed for different purposes as all four properties cannot be preserved simultaneously. Preservation of area and length are most critical for groundwater models. The Albers equal-area conic projection with custom standard parallels, selected by dividing the length north to south by 6 and selecting standard parallels 1/6th above or below the southern and northern extent, preserves both area and length for continental areas in mid latitudes oriented east-west. Custom map projection parameters can also minimize area and length error in non-ideal projections. Additionally, one must also use consistent vertical and horizontal datums for all geographic data. The generalized polygon for the Floridan aquifer system study area (306,247.59 km2 ) is used to provide quantitative examples of the effect of map projections on length and area with different projections and parameter choices. Use of improper map projection is one model construction problem easily avoided.

This paper summarizes the early geological maps about Hungary with special respect to their color codes, surface symbol systems and map projections. The process from the ad hoc color usage of the earliest maps, through the influence of the color system proposed by the Bologna Geological Congress of 1881 to the symbol system of the modern maps is shown. Analysing the coordinate grids of these map products, the older ones can be rectified in equidistant conic or Cassini projections while the ones of Bockh and Koch and Loczy et al. can be interpreted as both conic and Budapest-centered Stereographic projected. The ambiguity is because of the relatively low scale of the maps, enabling projection errors of several hundred meters without practical consequences.

Abstract. Although cartographic products have been produced for thousands of years, cartography as a science has only been established in the early 20th century. Great works of cartography include, for instance, the conic map projections by Ptolemy, the Tabula Rogeriana by Idrisi, the Waldseemüller map, and the Mercator map. Numerous cartographers, predominantly mathematicians, have shaped the theory of map projections throughout the centuries.With the advent of geographic information systems (GIS) in the 1960s and the rapid developments of digital technologies, cartography found itself in the middle of an identity crisis. For some time, it was not clear whether cartography would become obsolete and be replaced by GIS mapping technologies or whether GIS is a novel manifestation of cartography. During this period various misconceptions about the role of maps and mapping as well as uncertainty about the future developments of mapping in general added to this confusion.This contribution elaborates the major characteristics of cartography versus other disciplines, in particular geography and GIS, and takes a look at possible future directions and developments with regard to the theory of cartography as well as novel and future display technologies. Personal observations of the author during his professional life since the early 1980s illustrate these developments.

Small-scale maps currently used are made by scanning and editing printed maps and its shortcoming is accumulated errors at the time of editing and low accuracy. TM projection method is used but its accuracy varies. In addition, small-scale maps are made without consideration of usability and compatibility with other scale maps. Therefore, it is necessary to suggest projection and coordinates system improvement methods in consideration of usability and compatibility between data. The results of this study reveal that in order to make the optimum small-scale map, projection that fits the purpose of map usage in each scale, coordinate system and neat line composition should be selected in consideration of interrelation and compatibility with other maps. Conic projection should be used to accurately illustrate the entire country, but considering usability and compatibility with other maps, traversing cylindrical projection should be used instead of conic projection. For coordinates system of the small-scale map, Universal Transverse Mercator (UTM-K) based on the World Geodetic System should be used instead of conventional longitude and latitude coordinate system or Transverse Mercator.

The gnomonic (central) projection for a sphere is well known ([2] page 596). It has the characteristic that great circles project into straight lines, so that the shortest distance on the sphere projects into the shortest distance on the projection plane between the projections of the ends. Given a map obtained from the central projection, a pilot might plan a great circle route by drawing a straight line on it from starting point to destination. The positions of towns and geographical features on the map may then become apparent with regard to the line. The present paper studies the central projection for the spheroid, for which the corresponding characteristic is that great elliptic lines project into straight lines. Comparison may be made with [3] which shows the geodesic on various projections (e.g. UM and Lambert) as curved lines.

Several, mostly new, finite parameter instances of a special class of map projections are derived, illustrated, and evaluated. It is demonstrated that most of the usual evaluation measures are ordinally equivalent and thus that any one of them suffices. The new projections are shown to be at least as good as existing projections and appear otherwise advantageous.

A new methodology and web calculator, known as the emissions quantification tool (EQT), are designed to estimate the emissions impacts of a growing range of specific smart grid technologies and project types. Significant CO2, NOx, and SO2 reductions are possible with these technologies, but results are highly context dependent. This transparent, modular, reproducible, and publically accessible screening tool draws on well-vetted methodologies from trusted sources and allows comparison of possible and completed smart grid project impacts by diverse stakeholders. The live web calculator and full documentation are available at http://eqt.pnnl.gov.

The SPE-Petroleum Resource Management System (SPE-Petroleum Resources Management System, 2007) is a project based system, where the project definition and its treatment play a key role in the estimation and categorization of reserves and resources and their range of uncertainty. This is key to capture the potential downside and upside of the project and the commercial opportunities that may exist. Wrongly defining the project may result in an improper ring-fencing of the elements that must be considered in reserves and resource estimation and in improper risk assessment, with potential for missed opportunities or failure as an outcome. The SPE-PRMS is clear on the type of aggregation that can be used within a field, a property or a project, with probabilistic addition allowed within each of these entities. However, despite this clarity, most companies in the oil and gas industry have not yet adapted their methods to reflect these best practices. The technical literature has devoted significant effort to address technical and commercial issues in probabilistic reserves and resource estimation of a field or incremental activity (e.g., drilling wells). However, very little effort has been devoted to the proper definition of a "project", its attributes, ring-fencing, uncertainty assessment approaches for the fields within the project and in the categorization and aggregation of reserves or resources within the project. Furthermore, downside project economics should capture the true project's downside (or the true P90 of the project) rather than an overly-pessimistic estimate of its proved reserves calculated using arithmetic additions within the project. In order to describe a simple approach to project reserves estimates, this paper uses a Liquefied Natural Gas (LNG) project and its reserves estimate as an example. The selected example shows different interpretations among joint venture (project) partners of the existing standards, recommendations and regulations. The approach described can also be used in other types of projects or resources estimates (e.g. contingent resources), to properly capture the downside and upside risks, uncertainty ranges and project business opportunities, truly reflecting the project's reasonable certainty at the P90 level. Gas projects are preferred to illustrate this approach. For gas commitment purposes, many buyers require the LNG project's proved (P90) reserves to be independently certified before contractual commitments can be finalized. Underestimation of the project's true proved reserves may result in loss of opportunities and/or in an overly-pessimistic assessment of the Proved reserves not reflecting reasonable certainty. Requirements from regulatory bodies (e.g., NARA (SEC), 2009; ESMA, 2011) and their linkages to reserves aggregation within a project are also addressed in this paper.

Fisheye camera is finding increasing number of applications in robotic vision, visual surveillance, and other fields. But the use of super-wide angle fish-eye lenses causes strong distortions in the resulting images. A method for the correction of fisheye distortion using only single images and linearity of imaged objects is presented. Spherical projection is a simple and effective method to transform a fisheye image to a perspective projection image. To use this method, the optic center of the fisheye image and the radius of the projecting sphere must be known in advance. The proposed algorithm is based on ellipse fitting. It requires only the possibility of the extraction of distorted image points from straight lines in the 3D scene. The mathematical model is introduced for the transformation. The method for finding out the optic center and the radius of the projection sphere is discussed. Contrary to most former algorithms, the algorithm discussed here does not depend on information about the real world coordinates of matching points. The correctness and effectiveness of the proposed method are demonstrated with real image.