The hyperelliptical and other new pseudo cylindrical equal area map projections

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.

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.

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.

ABSTRACTEquivalence (the equal-area property of a map projection) is important to some categories of maps. However, unlike for conformal projections, completely general techniques have not been developed 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 develops a tractable technique for generating a continuum of equal-area projections between two chosen equal-area projections. The technique gives map projection designers unlimited choice in tailoring the projection to the need. The technique is particularly suited to maps that dynamically adapt optimally to changing scale and region of interest, such as required for online maps.

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.

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.

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.

地球椭球面上的经线交于极点而纬线则相互平行。地图上的经纬网是地球椭球面上的经纬网的拓扑映射。投影网中极点到坐标原点的距离函数关联着7类常规地图投影的分类。距离等于零时对应着方位投影；距离为有限值时对应着圆锥投影和多圆锥投影;距离为无穷大时对应着圆柱投影。方位和伪方位投影的纬线为同心圆；圆锥和伪圆锥投影的纬线为同心圆弧；多圆锥投影的纬线为同轴圆弧；圆柱和伪圆柱投影的纬线为赤道的平行线。所有正常投影的经线均为直线，而伪型投影只有作为投影网对称轴的中央经线是直线，其余经线为中央经线的轴对称曲线。多圆锥投影的经线与伪型投影相同。极点到坐标原点的距离函数，与常规地图投影的分类具有等价关系，从而可以推出常规地图投影的一般定义。 The longitudes of earth ellipsoid intersect at the poles and the latitudes are parallel to each other. The grid of longitudes and latitudes on the map is the topological map of the grid of longitudes and latitudes on earth ellipsoid. The distance function of the poles to the coordinate origin in the pro-jection grid is related to the classification of seven types of routine map projection. When the dis-tance is equal to zero, it is azimuthal projection; when the distance is finite, it is conic projection or polyconic projection; when the distance is infinite, it is cylindrical projection. The latitude of azi-muthal projection and pseudo-azimuthal projection are homocentric circles. The latitude of conic projection and pseudo-conic projection are homocentric circular arc. The latitude of polyconic projection is coaxial arc. The latitude of cylindrical projection and pseudo-cylindrical projection are parallel lines of the equator. All the longitudes of normal projection are straight, while for the pseudo-projection, only the central meridian of symmetry axis of a projection grid is a straight line and the remaining longitudes is the axisymmetric curve of the central longitudes. Meridian of polyconic projection is identical with the pseudo type projection. The distance function of the pole to the coordinate origin is equivalent to the classification of the routine map projection, so that the general definition of routine map projection can be deduced.

A major source of risk in project management is inaccurate forecasts of project costs, demand, and other impacts. The paper presents a promising new approach to mitigating such risk based on theories of decision-making under uncertainty, which won the 2002 Nobel Prize in economics. First, the paper documents inaccuracy and risk in project management. Second, it explains inaccuracy in terms of optimism bias and strategic misrepresentation. Third, the theoretical basis is presented for a promising new method called “reference class forecasting,” which achieves accuracy by basing forecasts on actual performance in a reference class of comparable projects and thereby bypassing both optimism bias and strategic misrepresentation. Fourth, the paper presents the first instance of practical reference class forecasting, which concerns cost forecasts for large transportation infrastructure projects. Finally, potentials for and barriers to reference class forecasting are assessed.

High-resolution regional and global raster databases are currently being generated for a variety of environmental and scientific modeling applications. The projection of these data from geographic coordinates to a plane coordinate system is subject to significant areal error. Sources of error include users selecting an inappropriate projection or incorrect parameters for a given projection, algorithmic errors in commercial geographic information system (GIS) software, and errors resulting from the projection of data in the raster format. To assess the latter type of errors, the accuracy of raster projection was analyzed by two methods. First, a set of 12 one-degree by one-degree quadrilaterals placed at various latitudes was projected at several raster resolutions and compared to the projection of a vector representation of the same quadrilaterals. Second, several different raster resolutions of land cover data for Asia were projected and the total areas of 21 land cover categories were tabulated and compared. While equal-area projections are designed to specifically preserve area, the comparison of the results of the one-degree by one-degree quadrilaterals with the common equal area projections (e.g., the Mollweide) indicates a considerable variance in the one-degree area after projection. Similarly, the empirical comparison of land cover areas for Asia among various projections shows that total areas of land cover vary with projection type, raster resolution, and latitude. No single projection is best for all resolutions and all latitudes. While any of the equal-area projections tested are reasonably accurate for most applications with resolutions of eight-kilometer pixels or smaller, significant variances in accuracies appear at larger pixel sizes.

<p>The data from the Rosetta mission enabled the reconstruction of the shape of comet 67P/Churyumov-Gerasimenko (hereafter 67P) and the identification of the terrains and features forming its surface. The highly irregular  shape of the comet poses a challenge for the depiction of these geological features on two-dimensional maps. Standard global map projections cannot display the complete surface of 67P because different points on the surface can have the same longitude and latitude.  As a consequence, the geological maps published to date are  created on top of comet images, making them dependent on the viewing angle and image coverage and resolution.</p><p>Here, we make use of the recently published Quincuncial Adaptive Closed Kohonen (QuACK) map. It projects the complete surface of 67P unambiguously onto a square. The QuACK map is topologically equivalent to the Peirce quincuncial projection of the world, which makes it  possible to define generalized longitudes and latitudes. These can be used within any global map projection in order to obtain an  unambiguous QuACK version.</p><p>The mapping of geological features is carried out in three dimensions employing the Small Body Mapping Tool (SBMT). We use images from  the OSIRIS Narrow Angle Camera aboard Rosetta which have been projected onto the shape model of the SBMT. The three-dimensional coordinates are then projected onto two-dimensional maps, either in the QuACK map projection or in the QuACK version of  the equidistant cylindrical projection. We present individual maps for 17 of the 26 regions of 67P, mostly located in the northern  hemisphere. The new maps combine features published in previous studies with newly identified features.</p><p>We discuss the distribution of geological features and the characteristics of the regions. In order to align region boundaries with geological features, we propose two modifications of region definitions.</p>

In cartographic literature, map projections are usually interpreted as mapping to auxiliary development surfaces, and then these surfaces are developed into a plane. The so-called secant projections, i.e. projections in which the auxiliary surface intersects the Earth's sphere or ellipsoid are especially emphasized. It is stated and taken as a fact without proof that the parallels in which the auxiliary surface intersects the sphere are mapped without distortions. An example of such an approach is the publication Basic Cartography, published several years ago by the International Cartographic Association. This paper proves that standard parallels and secant parallels generally do not match. It turns out that the widely accepted facts about secant and standard parallels, which can also be found even in the most recent literature, are wrong and need to be revised. The paper concludes that explaining cylindrical projections as mapping on a cylindrical surface is not a good approach, because it leads to misunderstanding important properties of projection.

Οικονομική της χαρτογράφησης των φυσικών πόρων - η περίπτωση του δασολογίου

The article focuses on the need to evaluate the distribution of coordinates of the object nodes and their filtering (discharge) in order to implement algorithms for calculating the optimal parameters of projection coordinate systems. To solve this task, it is proposed to use the uniform distribution function, the value of which characterizes the concentration degree of the nodes that form the contour of linear objects. At the same time, the Chi-square criterion, as an estimation indicator, allows implementing iterative procedures for combining nodes and generalizing parts of objects to approximate the initial data to the uniform distribution. Studies have shown that it leads to the reduction in the excess concentration of nodes of linear terrain objects, which negatively affects the calculation of optimal parameters for coordinate reference systems. The paper also considers the examples of coordinate systems parameters, which are, moreover, implemented on the basis of oblique map projections, the use of which is possible for solving a wide range of engineering tasks for transport facilities, agriculture and environment studies of the Republic of Chile. The article also provides a graphical comparison of the suggested single 6-degree zone for the specified class of projections with the SIRGAS-Chile coordinate system using the Universal Transverse Mercator coordinate system (UTM Zone 18 and Zone 19). In conclusion the author presents the data that prove the necessity for the mandatory evaluation of the uniformity of initial geodata distribution in order to find the best projection parameters.

Remotely-sensed datasuffers froma varietyof geometrical distortionswhichmustbe accounted for before the data is considered for applications such as mapping and temporal analysis of natural resources. The removal of these distortions on manual basis is a time consuming and tedious job, particularly when large areas are required to be georeferenced. Proceduresare therefore required forthe removal of such distortionsand for bringing the data recorded in a satellite projection to the planimetric accord of the Earth or of any standard map projection. In this paper an automatic rectification system forthe geometrical correction of the High Resolution Picture Transmission( HRPT ) data from the Advanced Very High Resolution Radiometer (AVHRR) on-board the Television and Infra-Red Observation Satellites (TIROS ) is presented. The system comprises four modules.The modules which remove the geometrical errors inherited in the satellite images and bring them to the planimetric accord of a standard map of the area of concerned are particularly analyzed in order to achieve sub-pixel accuracy over a large area. The system has been successfully implemented for the navigation of Great Britain on near real-time basis in the parallel environment of the Alliant Computing System at the Satellite Receiving Station,University of Dundee, U.K.The registrationaccuracy of the results obtained from the automatic procedure has been numerically and visually compared with the results obtained from a standard manual rectification system.