Bi-cylindrical conformal map projection

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.

A review of the last 50 years finds that the traditional breakdown of Soviet cartography into its specialized research disciplines no longer conforms to current needs. Soviet cartography has been divided historically into mathematical cartography, map science (the study of maps and their uses), map compilation and editing, map design and production. A growing specialization in cartography by thematic disciplines (geomorphic mapping, agricultural mapping, etc.) with widely differing requirements and principles of compilation and editing suggests the need for a restructuring of the research disciplines. In addition to mathematical cartography, concerned with map projections and map measurements, the new structure would include: technical cartography (the study of source materials, map design and production); natural-historic cartography (principles of compilation and editing of maps of the physical environment), and socioeconomic cartography (concerned with the mapping of human phenomena).

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.

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.

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.

In order to be able to read the information a map conveys, we must be familiar with the distribution and size of the inevitable distorsions. Otherwise, our knowledge will be deficient or even wrong. The paper first defines the terms standard point and standard line. The standard point is the point where the inevitable distortions caused by mapping are equal to zero. This definition can be visually interpreted as a Tissot distortion ellipse that becomes a unit circle. After that, it is natural to say that the standard line is composed of standard points. A large number of examples show that the map projection does not have to have standard points at all, but that it can have one such point, two such points or a whole line of standard points. In the latter case, it can be parallels, meridians or lines parallel to the image of the middle meridian, as is the case with the Gauss-Krüger or transverse Mercator projection.

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.

In map projections theory, various criteria have been proposed to evaluate the mean distortion of a map projection over a given area. Reports of studies are not comparable because researchers use different methods for estimating the deviation from the undistorted state. In this paper, statistical methods are extended to be used for averaging map projection distortions over an area. It turns out that the measure known as the Airy–Kavrayskiy criterion stands out as a simple statistical quantity making it a good candidate for standardization. The theoretical arguments are strengthened by a practical map projection optimization exercise.

rT HE numerous forms of map projections, so confusing to the layman, have been classified by various authorities according to their different properties. Some are equal-area, for example; others are conformal. In most cases there is no standard basis of comparison. Many are difficult to compute, and their existing tables are seldom comparable. In this paper groups of projections are discussed which have as their common characteristic the representation of lines of equal latitude as concentric circles or as straight parallel lines, the latter being, of course, only a special case of the former. Simple relationships are disclosed, which permit easy classification and tabulation. A general equation for the spacing of the parallels of latitude in these groups is given, from which may be derived, as special cases, a number of projections that are already familiar and unlimited series of others. The projections within each series are, in general, easy to compute.

ABSTRACTThe traditional way to calculate the global distortion of a given area in a map projection is to create what we call a local distortion criterion that is a function of the infinitesimal semi-axes of the Tissot's indicatrix. Some contemporary scholars criticize this method, saying that the map readers face distortion of the finite type. These researchers suggest taking plenty of simple random spherical elements (line sections, triangles) and average the distortion on them. Although the aforementioned researchers all state that their approach is something fundamentally different from the traditional method, the major disadvantage is that this method is irreproducible. Therefore, it has to be investigated whether the difference is really significant between these methods and if it is, what its nature is. At first, different distortion values are evaluated on a huge number of various projections showing the whole Earth. Correlation analysis shows that there exists a strong linear dependence between the corresponding infinitesimal and finite measures. A considerable difference can be observed if the examined area is not the whole globe rather a part of it. After optimizing a projection for different distortion measures, the isolines of equal distortion follow the boundary lines significantly closer using the traditional approach.

Does strategic planning enhance or impede innovation and firm performance? The current literature provides contradictory views. This study extends the resource-advantage theory to examine the conditions in which strategic planning increases or decreases the number of new product development projects and firm performance. The authors test the theoretical model by collecting data from 227 firms. The empirical evidence suggests that more strategic planning and more new product development (NPD) projects lead to better firm performance. Firms with organizational redundancy benefit more from strategic planning than firms with less organizational redundancy. Increasing R&D intensity boosts both the number of NPD projects and firm performance. Strategic planning is more effective in larger firms with higher R&D intensity for increasing the number of NPD projects. The results reported in this study also consist of several findings that challenge the traditional views of strategic planning. The evidence suggests that strategic planning impedes, not enhances, the number of NPD projects. Larger firms benefit less, not more, from strategic planning for improving firm performance. Larger firms do not necessarily create more NPD projects. Increasing organizational redundancy has no effect on the number of NPD projects. These empirical results provide important strategic implications. First, managers should be aware that, in general, formal strategic planning decreases the number of NPD projects for innovation management. Improvised rather than planned activities are more conducive to creating NPD project ideas. Moreover, innovations tend to emerge from improvisational processes, during which the impromptu execution of NPD activities without planning spurs “thinking outside the box,” which enhances the process of creating NPD project ideas. Therefore, more flexible strategic plans that accommodate potential improvisation may be needed in NPD management since innovation-related activities cannot be planned precisely due to the unexpected jolts and contingencies of the NPD process. Second, large firms with high levels of R&D intensity can overcome the negative effect of strategic planning on the number of NPD projects. Specifically, a firm's abundant resources, when allocated and deployed for NPD activities, signal the high priority and importance of the NPD activities and thus motivate employees to acquire, collect, and gather customer and technical knowledge, which leads to creating more NPD projects. Finally, managers must understand that managing strategic planning and generating NPD project ideas are beneficial to the ultimate outcome of firm performance despite the adverse relationship between strategic planning and the number of NPD projects.

In this paper we investigate a new class of soft projects, the main feature of which is a significant presence of personality in the design product and its defining role in the use of this product. Today, basic knowledge of soft projects is not enough to effectively manage, although the number of such projects is constantly increasing. The aim of research is to extend the existing knowledge about the nature of the soft projects and further their use as a basis for identifying features of planning their content. To achieve this aim we used methods of analysis, synthesis, graphical modeling.According to the results, the conditions for a successful consumption of product of soft project formed at the time of its creation by changing (formation, development) the necessary worldview competencies of future consumer. On this basis it is formulated the definition of soft project. By means of the proposed model it is shown that a key feature of the classification of such projects depends on two parameters simultaneously - the degree of novelty of variable competence and presence of personality in the product of design. It is shown that the category "competence" for soft projects is considered as a management. Its application for planning the content of soft project involves determining the set of work packages, as well as their rational interconnectedness and duration. In this regard, further development is existed for the traditional model of presentation of hierarchy structure of the project works. The features of its use for educational projects with high degree of softness are considered. It is formulated a hypothesis about the dependence of the duration of work packages, rational correlation types of work, as well as rational forms of realization of the types of works from the heterogeneity of the importance of generated competencies for multiple users.The proposed model, findings and the postulates allow use the traditional tools of content planning for particular class of soft projects. However, this requires additional experimental verification and refinement.

The history of the development of military aeronautical charts began immediately before the First World War. The first charts created at that time did not differ much from topographic maps. Air planes were fairly slow back then and had a small range of action, which meant that the charts were developed at the scale of 1:200,000. When speed of aircraft increased, it soon turned out that this scale was too large. Therefore, many countries began to create charts with smaller scales: 1:300,000 and 1:500,000. The International Map of the World 1:1,000,000 (IMW) was frequently used for continental flights prior to the outbreak of the Second World War, while 1:3,500,000 and 1:5,000,000 maps were commonly used for intercontinental flights. The Second World War brought a breakthrough in the field of aeronautical chart development, especially after 7 December 1941, when the USA entered into the war. The Americans created more than 6000 map sheets and published more than 100 million copies, which covered all continents. In their cartographic endeavours, they were aided foremost by the Brits. On the other hand, the Third Reich had more than 1,500 officers and about 15,000 soldiers and civil servants involved in the development of maps and other geographic publications during the Second World War. What is more, the Reich employed local cartographers and made use of local source materials in all the countries it occupied. The Germans introduced one new element to the aeronautical charts – the printed reference grid which made it easier to command its air force. The experience gained during the Second World War and local conflicts was for the United States an impulse to undertake work on the standardization of the development of aeronautical charts. Initially, standardization work concerned only aeronautical charts issued by the US, but after the establishment of NATO, standardization began to be applied to all countries entering the Alliance. The currently binding NATO STANAGs (Standardization Agreements) distinguish between operational charts and special low-flight charts. The charts are developed in the WGS-84 coordinate system, where the WGS-84 ellipsoid of rotation is the reference surface. The cylindrical transverse Mercator projection was used for the scale of 1:250,000, while the conformal conic projection was used for other scales. The first aeronautical charts issued at the beginning of the 20th century contained only a dozen or so special symbols concerning charts’ navigational content, whereas currently the number of symbols and abbreviations found on such charts exceeds one hundred. The updating documents are published every 28 days in order to ensure that aeronautical charts remain up-to-date between releases of their subsequent editions. It concerns foremost aerial obstacles and air traffic zones. The aeronautical charts published by NATO have scales between 1:50,000 and 1:500,000 and the printed Military Grid Reference System (MGRS), while the aeronautical charts at scales between 1:250,000 and 1:2,000,000 contain the World Geographic Reference System (GEOREF). Nowadays, modern military air planes are characterised by their exceptional combat capabilities in terms of speed, range and manoeuvrability. Aside from aircraft, contemporary armed forces make increasingly frequent use of aerial robots, drones and unmanned cruise missiles. This is why, there has been a noticeable increase, especially in NATO, in the amount of work devoted to the standardization and development of aeronautical charts, as well as deepening of knowledge of navigation and aeronautical information.

After the revolution of 1917, cartographers of the Soviet Union were faced with a severe shortage of qualified personnel for the provision of the necessary cartographic information for their development programme. To overcome this lack they opened a number of new schools for cartographic training and reorganized some that already existed, and as a result of this programme they have been able to make spectacular progress in the mapping of their country. The Soviet Union has completed the series of State Topographical Maps at the scale of 1:100,000, which comprises more than 26,000 sheets, is near completion of a new series at 1:25,000, which will have about 300,000 sheets, and is well advanced with a 1:10,000 series. All topographical maps are made on the Gauss-Kruger cylindrical transverse conformal projection or on the Co-ordinate System of 1942. In the latter system the reference ellipsoid is the Krasovsky, the origin of co-ordinates is the centre of the Round Hall of the Pulkovo Observatory, and the reference for elevations is the Baltic System of Heights. The 1:100,000 State Topographical Map has been used as the basis for general-purpose maps on smaller scales, including a map at 1:1,000,000 appropriate to the standards of the International Map of the World. In addition to its topographic maps the U.S.S.R. has produced many special-purpose maps, among which may be mentioned the various geological maps at scales of 1:200,000, 1:1,000,000, 1:2,500,000, and 1:5,000,000.