A Square Equal-Area Map Projection with Low Angular Distortion, Minimal Cusps, and Closed-Form Solutions

A novel square equal-area map projection is proposed. The projection combines closed-form forward and inverse solutions with relatively low angular distortion and minimal cusps, a combination of properties not manifested by any previously published square equal-area projection. Thus, the new projection has lower angular distortion than any previously published square equal-area projection with a closed-form solution. Utilizing a quincuncial arrangement, the new projection places the north pole at the center of the square and divides the south pole between its four corners; the projection can be seamlessly tiled. The existence of closed-form solutions makes the projection suitable for real-time visualization applications, both in cartography and in other areas, such as for the display of panoramic images.

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.

Automated Bale Mapping Using Machine Learning and Photogrammetry

An automatic method of obtaining geographic coordinates of bales using monovision un-crewed aerial vehicle imagery was developed utilizing a data set of 300 images with a 20-megapixel resolution containing a total of 783 labeled bales of corn stover and soybean stubble. The relative performance of image processing with Otsu’s segmentation, you only look once version three (YOLOv3), and region-based convolutional neural networks was assessed. As a result, the best option in terms of accuracy and speed was determined to be YOLOv3, with 80% precision, 99% recall, 89% F1 score, 97% mean average precision, and a 0.38 s inference time. Next, the impact of using lower-cost cameras was evaluated by reducing image quality to one megapixel. The lower-resolution images resulted in decreased performance, with 79% precision, 97% recall, 88% F1 score, 96% mean average precision, and 0.40 s inference time. Finally, the output of the YOLOv3 trained model, density-based spatial clustering, photogrammetry, and map projection were utilized to predict the geocoordinates of the bales with a root mean squared error of 2.41 m.

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.

Portolankarten – Aufnahme und Abbildung

Maps are flat images of the earth‘s surface. The basis and prerequisite for their production is the relative spatial definition of the map content on the earth‘s surface, and this is usually done in the context of surveying recording processes. The particular accuracy of the portolan charts, which have passed on since the thirteenth century, suggests that these were also created on the basis of specific measurements, although details of their creation have not yet been clarified. Questions about the data base and especially about the projection of the maps have been the subject of scientific research for over 100 years (Kretschmer 1909; Campbell 2021). Here, for the first time, a method is presented that makes it possible to construct maps of the Mediterranean with simple aids (compasses and ruler) in such a way that they correspond to the accuracy and other properties of the portolan charts. A map projection is used for which there are no mapping equations, but at most a mapping description. As a surveying basis for the mapping, distances are used that have been determined with a high degree of probability since ancient times. Triangles are constructed from these lines and transferred directly to the plane without any reduction in the image. The result is a geometrically unambiguous field of support points of known ports. The missing coastal structures can be supplemented after the construction of the field of support points on the basis of traditional coastal descriptions (Portolani/Periploi).

Analiza kartografske projekcije karte Nova Lusitania

The map named Carta Geographica de Projecçaõ Espherica Orthogonal da Nova Lusitania ou America Portugueza e Estado do Brazil from 1798, together with its 1795 (?), 1797 and 1803 versions, is undoubtedly one of the cartographic monuments developed by Portuguese cartography from the late eighteenth century. Its organizer was the geographer, astronomer, and frigate captain Antonio Pires da Silva Pontes Leme, who relied on the work of 34 people, including astronomers, geographers, and engineers, who, although only mentioned in the 1798 version, contributed to the creation of all versions. All of them are similar in appearance, but differ in size, content, details, amount, and distribution of toponyms, which will be the subject of another paper. The greatest similarity, however, concerns the defined map projection. The objective of this paper is to analyse and present the possible hypotheses and conclusions about which map projection was adopted for all versions of Nova Lusitania, through the identification of characteristics that allowed to infer and prove the adopted projection. The applied methodology verified that in the bibliographic search, the information about the map structure is insufficient. An article presented by General Djalma Polli Coelho in October 1950 states that the projection suggested by its title, as orthogonal spherical, appeared to be the Sanson-Flamsteed equal-area projection. However, the expression Carta Geographica de Projecçaõ Espherica Orthogonal allows us to infer also the transverse orthographic projection. Through parameters defined for the two projections, it was possible to establish the comparative elements for a cartographic analysis, which would allow us to conclude and prove the structure adopted for the map, allowing to conclude if the adopted projection for the Nova Lusitania was an azimuthal orthographic equatorial projection, or a Sanson-Flamsteed, sinusoidal projection on the meridian 315°, defined west-east, (counterclockwise), from the El Hierro (Ferro) Island. This meridian is referenced approx. –62°39'46" off the Greenwich meridian.

Diagnosis of cylindrical projections and analysis of suitability for the territorial area of South America

Cartographic Projection can be defined as the mathematical relationship between the position of a model of the terrestrial surface and the flat surface. Cylindrical projections are employed around the world, taking into consideration their properties and special characteristics. The purpose of this study was to identify the cartographic projection that best represents South America terrestrial surface, focusing mainly on the area of the continent, determined by the South American Defense Council. Initially, the projections were selected based on a bibliographic review. Subsequently, a suitability judgment was made for South America applying Tissot Indicatrix, Isolines of Maximum Angular Distortion and Region of Acceptable Distortion. Finally, an assumption was drawn up among the best results. The study control was performed using the software Flex Projector and ArcGIS 10.1, computational resources of great use in Cartography. The study provided a clear, simple and objective understanding of how different projections behave. The motivation comes from the insufficiency of detailed information and applied to the choice of map projection in regions of large areas.