Image-Based Angular Distortion Metric of Map Projections by Using Surface Fitting for Noise Reduction

Measuring, analyzing, reducing, and optimizing distortions in map projections is important in cartography. In this study, we introduced a novel image-based angular distortion metric based on the previous spherical great circle arcs-based metric. Images with predefined patterns were used to generate distorted images using mapping software. The generated distorted images with known patterns were then exploited to calculate the proposed angular distortion metric. The mapping software performed the underlying transformation of map projections. Therefore, there was no direct explicit dependence on the forward equations of the map projections in our proposed metric. However, there were fairly large computation errors in the ordinary image-based approach without special correction. To reduce the error, we introduced surface-fitting-based noise reduction in our approach. We established and solved systems of linear equations based on bivariate polynomial functions in the process of noise reduction. Sufficient experiments were made to validate the proposed image-based metric and the accompanying noise reduction approach. In the experiment, the NASA G.Projector was employed as the mapping software for evaluating more than 200 map projections. Experimental results demonstrated that the proposed image-based approach and surface fitting-based noise reduction are feasible and practical for the evaluation of the angular distortion of map projections.

Conic Projections with Three or More Standard Parallels

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.

Proposed single-zone map projection system for Turkey

The coordinate base of the maps or sheets produced is the Universal Transversal Mercator (UTM) conformal projection, and it is not possible to work in a single coordinate system in Turkey. Therefore, a transition from UTM to other conformal projections is required. For the countries extending in an east–west UTM zone width like Turkey, composite projection (CP), a double standard paralleling Lambert Conformal Conic (LCC) and double map projections (DP) are used widely. However, this process causes increase in working load and processing errors by users. This study aims to determine a common projection system that can be used in the whole country. In this context, a composite projection from UTM and LCC projection has been defined for the first time. According to the results obtained, map projection CP with the least distortion values in both east–west and north–south directions has been chosen. With the CP selection, a single coordinate system has been determined for medium- and large-scale maps. Projection correction formulas, scale factor and false origin have been determined for map coordinates in CP. These distortions are obtained with a difference of less than 1 cm for 1 km long sides and less than 0.003″ for the azimuth value of this side, when the correction formulas are used.

Best cylindrical map projections according to the undesirability of angular and areal distortions

Seeking low distortion maps, it is usual to assume that areal and angular distortions are equally undesirable on the map. However, this might not be the case for certain map thematics. Should angular distortions be a bit less preferred to areal distortions, maps of unbalanced distortions may be developed. In this paper, the known analytic solution for the best cylindrical map projection is extended to such more general requirements by utilizing calculus of variations. The overall distortion of the resulted mappings are calculated and compared to each other to explore the distortion characteristics of these intentionally unbalanced map projections.

Metadata: A pedagogical tool for the teaching of map projections in Elementary School

Digital interactive maps include a set of metadata, which show the purpose the user can use the map. Metadata in digital interactive world maps inform users about important information, such as the map projection. This research examines whether the educational and teaching use of the metadata of digital interactive maps construct a tool in the approach to the issue of map projection in Elementary School. The research was carried out in 17 Elementary Schools of Thessaloniki, Greece, where 6th-grade students (Ν = 655) were engaged in a series of activities related to metadata and map projections. ArcGIS Online was used as a didactic tool. Results showed that metadata of digital interactive maps have a great pedagogical value. The identification of the different information in the metadata, i.e., the map projection, and the students’ decision of what they can and cannot study with each map, is an important finding regarding their educational relevance.

Local Linear Scale Factors in Map Projections of an Ellipsoid

The main problem in cartography is that it is not possible to map/project/transform a spherical or ellipsoidal surface into a plane without distortions. The distortions of areas, angles, and/or distances are immanent to all maps. It is known that scale changes from point to point, and at certain points, the scale usually depends on the direction. The local linear scale factor c is one of the most important indicators of distortion distribution in the theory of map projections. It is not possible to find out the values of the local linear scale factor c in directions of coordinate axes x and y immediately from the definition of c. To solve this problem, in this paper, we derive new formulae for the calculation of c for a rotational ellipsoid. In addition, we derive the formula for computing c in any direction defined by dx and dy. We also considered the position and magnitude of the extreme values of c and derived new formulae for a rotational ellipsoid.

Art and Argument: Indigitization of a Kiowa Historical Map for Teaching and Research

How might we teach undergraduate students about Indigenous geographies using historical maps? This paper describes processes associated with the bridging of a historical Kiowa map with computerized geographic information systems (GIS) and undergraduate geography curriculum. The authors applied an indigital framework as an approach for melding Indigenous and Western knowledge systems into a third kind of construct for teaching undergraduate students about historical/contemporary spatial issues. Indigital is the blending of Indigenous knowledge systems, such as storytelling, language, calendar keeping, dance, and songs, with computerized systems. We present an origin story about the indigitization of a historical Kiowa pictorial map, known as the Chál-ko-gái map, at the University of Missouri, USA. Undergraduate student engagement with the map resulted in new questions about Indigenous geographies, particularly map projections, place names, and the meaning of Kiowa symbols.