No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Automating the Selection of Standard Parallels for Conic Map Projections
... Los productos cartográficos finales se desarrollaron en POSGAR 2007/Argentina Faja 2 (EPSG:5344). La determinación de superficies planas se realizó en el sistema Cónico de Albers (Snyder, 1987) que asegura una mínima distorsión en las áreas graficadas (Jenny, 2012;Šavrič & Jenny, 2016). Para el ajuste de paralelos de referencia ecuatorial y polar (ϕ1 y ϕ2) se aplicó la función dependiente de los paralelos extremos que alcanzó cada UH mapeada (ϕmin y ϕmáx), (Snyder, 1987;Bugayevskiy & Snyder, 1995;Šavrič & Jenny, 2016) y aplicando un valor K=4 de acuerdo con la propuesta de Kavrayskiy para las formas predominantes en esta región (Bugayevskiy & Snyder, 1995) Tabla 2. Parámetros utilizados para el cálculo de superficies mediante el sistema Equivalente Cónico de Albers, en superficies resultantes de cada UH, expresados en decimal de grado. ...
... La determinación de superficies planas se realizó en el sistema Cónico de Albers (Snyder, 1987) que asegura una mínima distorsión en las áreas graficadas (Jenny, 2012;Šavrič & Jenny, 2016). Para el ajuste de paralelos de referencia ecuatorial y polar (ϕ1 y ϕ2) se aplicó la función dependiente de los paralelos extremos que alcanzó cada UH mapeada (ϕmin y ϕmáx), (Snyder, 1987;Bugayevskiy & Snyder, 1995;Šavrič & Jenny, 2016) y aplicando un valor K=4 de acuerdo con la propuesta de Kavrayskiy para las formas predominantes en esta región (Bugayevskiy & Snyder, 1995) Tabla 2. Parámetros utilizados para el cálculo de superficies mediante el sistema Equivalente Cónico de Albers, en superficies resultantes de cada UH, expresados en decimal de grado. Donde: * Solo se consideró la Subregión Hidrográfica Río Chico, integrante de esta RH, que consiste en una región con recursos hídricos compartidos con la provincia de Santa Cruz. ...
Watershed definition is fundamental for integrated management of water
resources, considering the social, productive and environmental demands. The
watershed spatial delimitation is essential to understand eco-hydrological processes
in the territory and management. The objective of this work was to delineate and code
the hydrographic regions of Southern Patagonia under standardized procedures and
new geographic information technologies. The ALOS World 3D model, WorldView
high-resolution scenes and QGIS 3.12 free software algorithms were used to carry out
automated watershed delineations at various hydrological nesting levels, and
subsequent coding and nomenclature. A precise cartographic product was achieved at
a scale of 1: 25,000 on a territory of 366,357.4 km2. This results in 7,307 hydrographic
units distributed in 5 levels, with 14 large hydrographic regions (RH) in the upper
level, 46 sub-regions, 249 hydrographic basins, 1,110 sub-basins and 5,888 microbasins. The cartography achieved improved the resolution and precision of actual
available regional products, representing a valuable tool for the sustainable water
resources management at different levels of organization and complexity of natural
processes.
... Standard parallels are mentioned in some books, but not defined [1,2]. One whole article deals with the selection of standard parallels in conic projections, but in that article standard parallels are not defined [3]. Some authors equate standard and secant parallels [4][5][6][7]. ...
In the literature on map projections, we regularly encounter the name standard parallel or standard parallels. However, it is obvious that a unique definition of a standard parallel is not universally accepted. To fully clarify the meaning of standard parallels, the author proposes the notion of equidistantly mapped parallels, which has not been common in the literature so far. Equidistantly mapped parallels can be in the direction of the parallel or in the direction of the meridian. Here, it is shown that every standard parallel is also an equidistantly mapped parallel, but that the reverse need not be true. If the parallel is mapped equidistantly in the direction of the parallel, then its length in the projection plane is equal to the length of that parallel on the sphere. The opposite does not have to be true, i.e., if the length of the image of the parallel in the projection plane is equal to the length of the parallel on the sphere, this does not mean that the parallel was mapped equidistantly. In addition to standard and equidistant parallels, the concept of parallels of true length also appears in the theory of map projections. They should also be distinguished from standard and equidistant parallels.
... In the last century, almost all authors of textbooks on map projections wrote about the choice of standard parallels. This topic is still current [17]. ...
The article belongs to the field of theoretical research on map projections. It is observed that there is no unique and generally accepted definition of standard parallels in the cartographic literature. For some authors, a standard line is a line along which there is no distortion, and for others, it is a line along which there is no distortion of length. At the same time, it is forgotten that the length distortions at any point generally change and depend on the direction. The main goal of this article is very simple: the sentence “linear deformation is zero in all directions” is expressed using a mathematical formula. Besides that, the paper introduces equidistance in a broader sense. This is a novelty in the theory of map projections. Equidistance is defined at a point, along a line and in an area, especially in the direction of the parallels and especially in the direction of the meridian. This enables an unambiguous definition of standard parallels. Theoretical considerations are illustrated with examples of cylindrical projections. The practical value of the proposed approach is manifested in the possibility of a better understanding of the distribution of distortions in any map projection used.
... and 2.1.3). All datasets were projected in an Albers equal-area projection [36]. of Hong Kong, Macao, and Taiwan are missing, and the GDP statistics of Tianjin Binhai New Area were not included due to its abnormality. In total, 2767, 2835, and 2793 GDP statistical data at the county level were collected in 2010, 2015, and 2020, respectively. ...
Accurate knowledge of the spatiotemporal distribution of gross domestic product (GDP) is critical for achieving sustainable development goals (SDGs). However, there are rarely continuous multitemporal gridded GDP datasets for China in small geographies, and less is known about the variable importance of GDP mapping. Based on remotely sensed and point-of-interest (POI) data, a geographical random forest model was employed to map China’s multitemporal GDP distribution from 2010 to 2020 and to explore the regional differences in the importance of auxiliary variables to GDP modeling. Our new GDP density maps showed that the areas with a GDP density higher than 0.1 million CNY/km2 account for half of China, mainly distributed on the southeast side of the Hu-line. The proportion of the areas with GDP density lower than 0.05 million CNY/km2 has decreased by 11.38% over the past decade and the areas with an increase of 0.01 million CNY/km2 account for 70.73% of China. Our maps also showed that the GDP density of most nonurban areas in northeast China declined, especially during 2015–2020, and the barycenter of China’s GDP moved 128.80 km to the southwest. These results indicate China’s achievements in alleviating poverty and the widening gaps between the South and the North. Meanwhile, the number of counties with the highest importance score for POI density, population density, and nighttime lights in GDP mapping accounts for 52.76%, 23.66%, and 23.56%, respectively, which suggests that they play a crucial role in GDP mapping. Moreover, the relationship between GDP and auxiliary variables displayed obvious regional differences. Our results provide a reference for the formulation of a sustainable development strategy.
... Given the continued application and research of map projections, more stringent requirements are required for accurate and efficient transformations between different projections. The key is to complete mutual transformation of important variables, such as common latitude, more efficiently to ensure high accuracy [8][9][10][11][12]. Much in-depth research has been conducted on this, leading to theories of latitude change. ...
Using the symbolic calculation program Mathematica and based on the power series expansions of the common latitude with geodetic latitude as a variable, power series expansions of the common latitude with geocentric latitude as the variable are derived. The coefficients of the two groups of formulas are based on the ellipsoid eccentricity e and the ellipsoid third flattening n, which make the expansions more uniform. Taking the CGCS2000 as an example, numerical analysis is applied to verify the accuracy and reliability of the derived power series expansions. By analyzing and calculating the truncation error of the common latitude based on ellipsoidal eccentricity e and the third flattening n expansion to different orders, we obtain simplified, practical formulas for the common latitude that satisfy the requirement of geodesic accuracy. Moreover, we show that the practical formula derived has higher calculation efficiency and easier dissemination, enriches the theory of map projection, and provides a basis for better display of remote sensing images.
... Given the continued application and research of map projections, more stringent requirements are required for accurate and efficient transformations between different projections. The key is to complete mutual transformation of important variables, such as common latitude, more efficiently to ensure high accuracy [8][9][10][11][12]. Much in-depth research has been conducted on this, leading to theories of latitude change. ...
Using the symbolic calculation program Mathematica, based on the power series expansions of common latitude with geodetic latitude as a variable, power series expansions of common latitude with geocentric latitude as variable are derived. The coefficients of the two groups of formulas are based on the ellipsoid eccentricity e and the ellipsoid third flattening n , which make the expansions more uniform. Taking CGCS2000 as an example, numerical analysis is applied to verify the accuracy and reliability of the derived power series expansions. By analyzing and calculating the truncation error of common latitude based on ellipsoidal eccentricity e and the third flattening n expansion to different orders, we obtain simplified practical formulas for common latitude that satisfy the requirement of geodesic accuracy. Moreover, we show that the practical formula derived has higher calculation efficiency and easier dissemination, enriches the theory of map projection, and provides a basis for better display of remote sensing images.
The aim of this doctoral dissertation was to investigate and resolve cartographical issues in maritime delimitation, to determine the limitations of existing software solutions and to develop and implement a comprehensive methodology to address them in a digital environment. Its findings comprise three automated methodologies -and their implementation in digital environment- namely that of the identification and determination of juridical bays according to the UN Convention on the Law of the Sea, that for the Voronoi Tessellation on the ellipsoidal Earth and that for the automated delimitation of maritime zones and boundaries for all coastal states in the dataset and for any combination of normal and straight baselines, as well as the selection of the most appropriate cartographic projection for the presentation of maritime zones and boundaries. The findings of this dissertation contribute to cartographers’ work and substantially improve the accuracy and reliability of the end-results as they examine all available spatial information and are independent of user’s perception. Furthermore, they significantly reduce the time of maritime delimitation as they comprise fully automated processes with no need for supervised intervention and, finally, contribute to the correct cartographic portrayal of maritime zones and boundaries.
The adaptive composite map projection technique changes the projection to minimize distortion for the geographic area shown on a map. This article improves the transition between the Lambert azimuthal projection and the transverse equal-area cylindrical projection that are used by adaptive composite projections for portrait-format maps. Originally, a transverse Albers conic projection was suggested for transforming between these two projections, resulting in graticules that are not symmetric relative to the central meridian. We propose the alternative transverse Wagner transformation between the two projections and provide equations and parameters for the transition. The suggested technique results in a graticule that is symmetric relative to the central meridian, and a map transformation that is visually continuous with changing map scale.
The selection of map projections is difficult and confusing for many. This article introduces Projection Wizard, an online map projection selection tool available at projectionwizard.org that helps mapmakers select projections. The user selects the desired distortion property, and the area to be mapped on an interactive web map. Projection Wizard then proposes a projection, along with projection parameters (such as standard parallels). The tool also creates a preview map with the proposed projection, and provides the corresponding projection code in PROJ.4 format, if applicable. The automated selection process is based on John P. Snyder’s selection guideline with a few adjustments. This article discusses the automated selection process, and the map projections suggested. Projection Wizard solves the problem of map projection selection for many applications and helps cartographers and GIS users choose appropriate map projections.
There are two problems with current cylindrical projections for world maps. First, existing cylindrical map projections have a static height-to-width aspect ratio and do not automatically adjust their aspect ratio in order to optimally use available canvas space. Second, many of the commonly used cylindrical compromise projections show areas and shapes at higher latitudes with considerable distortion. This article introduces a new compromise cylindrical map projection that adjusts the distribution of parallels to the aspect ratio of a canvas. The goal of designing this projection was to show land masses at central latitudes with a visually balanced appearance similar to how they appear on a globe. The projection was constructed using a visual design procedure where a series of graphically optimized projections was defined for a select number of aspect ratios. The visually designed projections were approximated by polynomial expressions that define a cylindrical projection for any height-to-width ratio between 0.3:1 and 1:1. The resulting equations for converting spherical to Cartesian coordinates require a small number of coefficients and are fast to execute. The presented aspect-adaptive cylindrical projection is well suited for digital maps embedded in web pages with responsive web design, as well as GIS applications where the size of the map canvas is unknown a priori. We highlight the projection with a height-to-width ratio of 0.6:1, which we call the Compact Miller projection because it is inspired by the Miller Cylindrical projection. Unlike the Miller Cylindrical projection, the Compact Miller projection has a smaller height-to-width ratio and shows the world with less areal distortion at higher latitudes. A user study with 448 participants verified that the Compact Miller - together with the Plate Carrée projection - is the most preferred cylindrical compromise projection.
The recently introduced adaptive composite map projection technique changes the projection to the geographic area shown on a map. It is meant as a replacement for the commonly used web Mercator projection, which grossly distorts areas when representing the entire world. The original equal-area version of the adaptive composite map projection technique uses the Lambert azimuthal projection for regional maps and three alternative projections for world maps. Adaptive composite map projections can include a variety of other equal-area projections when the transformation between the Lambert azimuthal and the world projections uses Wagner’s method. To select the most suitable pseudocylindrical projection, the distortion characteristics of a pseudocylindrical projection family are analyzed, and a user study among experts in the area of map projections is carried out. Based on the results of the distortion analysis and the user study, a new pseudocylindrical projection is recommended for extending adaptive composite map projections. The new projection is equal-area throughout the transformation to the Lambert azimuthal projection and has better distortion characteristics then small-scale projections currently included in the adaptive composite map projection technique.
Flex Projector is a free, open-source, and cross-platform software application that allows cartographers to interactively design custom projections for small-scale world maps. It specializes in cylindrical, and pseudocylindrical projections, as well as polyconical projections with curved parallels. Giving meridians non-uniform spacing is an option for all classes of projections. The interface of Flex Projector enables cartographers to shape the projection graticule, and provides visual and numerical feedback to judge its distortion properties. The intended users of Flex Projector are those without specialized mathematical expertise, including practicing mapmakers and cartography students. The pages that follow discuss why the authors developed Flex Projector, give an overview of its features, and introduce two new map projections created by the authors with this new software: the A4 and the Natural Earth projection.
All major web mapping services use the web Mercator projection. This is a poor choice for maps of the entire globe or areas of the size of continents or larger countries because the Mercator projection shows medium and higher latitudes with extreme areal distortion and provides an erroneous impression of distances and relative areas. The web Mercator projection is also not able to show the entire globe, as polar latitudes cannot be mapped. When selecting an alternative projection for information visualization, rivaling factors have to be taken into account, such as map scale, the geographic area shown, the map's height-to-width ratio, and the type of cartographic visualization. It is impossible for a single map projection to meet the requirements for all these factors. The proposed composite map projection combines several projections that are recommended in cartographic literature and seamlessly morphs map space as the user changes map scale or the geographic region displayed. The composite projection adapts the map's geometry to scale, to the map's height-to-width ratio, and to the central latitude of the displayed area by replacing projections and adjusting their parameters. The composite projection shows the entire globe including poles; it portrays continents or larger countries with less distortion (optionally without areal distortion); and it can morph to the web Mercator projection for maps showing small regions.
The design of new map projections has up until now required mathematical and cartographic expertise that has limited this activity to a small group of specialists. This article introduces the background mathematics for a software-based method that enables cartographers to easily design new small-scale world map projections. The software is usable even by those without mathematical expertise. A new projection is designed interactively in an iterative process that allows the designer to graphically and numerically assess the graticule, the representation of the continents, and the distortion properties of the new projection. The method has been implemented in Flex Projector, a free and open-source application enabling users to quickly create new map projections and modify existing projections. We also introduce new tools that help evaluate the distortion properties of projections, namely a configurable acceptance index to assess areal and angular distortion, a derived acceptance visualization, and interactive profiles through the distortion space of a projection. To illustrate the proposed method, a new projection, the Cropped Ginzburg VIII projection, is presented.
New metrics are introduced for tracking pixel loss and duplication during the transformation of discrete raster data sets by map projection. The metrics, PL and PD, successfully measure pixel loss and pixel duplication, respectively, throughout the spatial realm and provide evidence of the property of equal area. PL and PD are applied to the examination of world equal-area map projections. Traditional map projection distortion evaluation addresses scale, area, shape, and directional distortion, which is appropriate to point-by-point analytical projection methods used for vector data. PL and PD provide an additional means for evaluating map projection distortion for discrete raster data. Data producers and data users, including researchers and policy makers, are often unaware that the choice of a map projection may affect the content of data sets and, possibly, research results. Pixel duplication may be reversed in some cases, but lost pixels mean that data has been lost forever. The results of this work indicate the need for a change in cartographic recommendations for selecting global raster data map projections. The Sinusoid projection, with the greatest angular distortion of the projections studied, would be an unlikely choice for a global equal-area data set, but it exhibits no pixel loss or duplication.
The suitability of some form of conic projection for the representation of a territory in temperate latitudes is well known. In consequence, much of the work which has been done by Russian cartographers has been directed towards the investigation of the conic graticules which give the most suitable small-scale representation of the U.S.S.R. for particular purposes. The majority of the projections which will be described are modifications of the three general expressions for equidistant, equal area and conformal conic projections with one standard parallel.
After decades of using only one map projection, the Polyconic, for its mapping program, the U.S. Geological Survey (USGS) now uses several of the more common projections for its published maps. For larger scale maps, including topographic quadrangles and the State Base Map Series, conformal projections such as the Transverse Mercator and the Lambert Conformal Conic are used. Equal-area and equidistant projections appear in the National Atlas. Other projections, such as the Miller Cylindrical and the Van der Grinten, are chosen occasionally for convenience, sometimes making use of existing base maps prepared by others. Some projections treat the Earth only as a sphere, others as either ellipsoid or sphere. The USGS has also conceived and designed several new projections, including the Space Oblique Mercator, the first map projection designed to permit mapping of the Earth continuously from a satellite with low distortion. The mapping of extraterrestrial bodies has resulted in the use of standard project
The World in Perspective: A Directory of World Map Projections
- F Canters
- H Decleir
Canters, F., Decleir, H., 1989. The World in Perspective: A Directory of World Map
Projections. John Wiley and Sons, Chichester, p. 181.
Izbiranje ekvivalentne kartografske projekcije za kartiranje kontinentov (Selecting a Cartographic Equivalent Projection For Mapping Continents)
- U Hrvatin
Hrvatin, U., 2011. Izbiranje ekvivalentne kartografske projekcije za kartiranje kontinentov (Selecting a Cartographic Equivalent Projection For Mapping Continents). University of Ljubljana, Faculty of Civil and Geodetic Engineering,
Ljubljana, Slovenia, p. 93.