The literature usually calls downscaled versions of basic conformal map projections “secant”, referring to conceptual developable map surfaces that intersect the reference frame. However, recent ...studies pointed out on the examples of various mappings of the sphere that this model may lead to incorrect conclusions. In this study, we examine the paradigm of secant surfaces for two popular map projections of the ellipsoid, the UTM (Universal Transverse Mercator) and the UPS (Universal Polar Stereographic) projections. Results will show that ellipsoidal map projections can exhibit further anomalies. To support the shift to a paradigm avoiding developable map surfaces, this study recommends the new term reduced map projection with a proper and simple definition to be used instead of secant map projections.
In previous papers that have dealt with cylindrical map projections as limiting cases of conical projections, standard or equidistant parallels were used in the derivations. This paper shows that ...this is not necessary and that it is sufficient to use parallels that preserve length. In addition, unlike other approaches, in this article the limiting cases of conic projections are derived in the most natural way, by deriving the equations of cylindrical projections from the equations of conic projections in a rectangular system in the projection plane using a mathematical concept of limits. It is shown that such an approach is possible, but not always, so it should be used carefully, or even better, avoided in teaching and studying map projections.
Notes on the Eisenlohr Projection Strebe, Daniel
Cartographic journal,
01/2023, Letnik:
ahead-of-print, Številka:
ahead-of-print
Journal Article
Recenzirano
Friedrich Eisenlohr presented a map projection in 1870 that is optimal for a conformal world map of the sphere interrupted along an entire meridian. The projection has received little attention in ...the literature despite its theoretical importance. This paper gives alternative formulations for the projection and its scale factors and develops an efficient inverse for the projection.
Proxemic maps for immersive visualization Ghaemi, Zeinab; Engelke, Ulrich; Ens, Barrett ...
Cartography and geographic information science,
05/2022, Letnik:
49, Številka:
3
Journal Article
Recenzirano
In human computer interaction, proxemics describes the ways that people use space to interact with other people or objects. We focus on proxemic maps, which are virtual maps in immersive environments ...that react to proxemic interaction. Proxemic maps take advantage of new opportunities brought about by immersive visualization, where virtual maps can be freely positioned in virtual or physical space and adapt themselves relative to the spatial position of the viewer. We discuss proxemic interactions that alter the content and type of maps, including changing scale, symbolization, type of visualization and geometry. We propose a novel transformation that changes the geometry of maps based on their proximity to users. Users move the map back and forth and the map transitions between ring, horizontal, vertical and cylindrical geometries. The ring geometry surrounds the user and aligns features on the map with features in the real world. We implemented the map transformation in virtual reality and conducted a user study to evaluate it. The results of the user study indicate that participants preferred the ring and horizontal geometries. The ring geometry is useful because it simplifies connecting virtual features on the map with real features in the landscape, while the horizontal geometry provides an overall view of the landscape. We further found that combination of different geometries helped the study participants to overcome the limitations of each geometry.
We compare the processing of Persistent Scatterer Interferometry data in map geometry versus their processing in slant-range/azimuth radar coordinates. In mountainous areas, using the map geometry ...significantly reduces the geometric distortion of radar coordinates that places scatterers that are actually widely separated in altitude in very close proximity in terms of slant-range. Processing in slant-range coordinates over mountainous regions introduces distortion in the distances used for estimation and filtering of tropospheric phase and phase unwrapping. Spatial filtering, interpolation of missing values, and phase unwrapping have better performance in map geometry because the distances between points are closer to reality. Performing these steps in a map geometry results in a more robust and more reliable processing chain.
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 paper presents a method of construction of cylindrical and azimuthal equalarea map projections of a triaxial ellipsoid. Equations of a triaxial ellipsoid are a function of reduced coordinates and ...functions of projections are expressed with use of the normal elliptic integral of the second kind and Jacobian elliptic functions. This solution allows us to use standard methods of solving such integrals and functions. The article also presents functions for the calculation of distortion. The maps illustrate the basic properties of developed map projections. Distortion of areas and lengths are presented on isograms and by Tissot’s indicatrixes with garticules of reduced coordinates. In this paper the author continues his considerations of the application of reduced coordinates to the construction of map projections for equidistant map projections. The developed method can be used in planetary cartography for mapping irregular objects, for which tri-axial ellipsoids have been accepted as reference surfaces. It can also be used to calculate the surface areas of regions located on these objects. The calculations were carried out for a tri-axial ellipsoid with semi-axes a = 267:5 m, b = 147 m, c = 104:5 m accepted as a reference ellipsoid for the Itokawa asteroid.
This paper explores scholarly literature published since the 1960s that examines peoples' cognitive and perceptual understanding of map projections. Map projections present challenges to virtually ...everyone who uses them. Some of the challenges include selecting a projection, specifying projection parameters, and understanding distortion patterns. Broadly speaking, cartographic inquiry has addressed many topics in cognition and perception; yet, research focused on projections remains scarce. We surveyed the body of research studies incorporating projections or a projection-related topic (e.g. distortion) as a variable in the experimental design. Topics included asking participants to estimate areas, conceptualize travel paths, or identify preferred graticule aesthetics. Despite the conclusions reported by these studies, we noted three general concerns that may diminish the accuracy of results from research in this area. First, projection-specific terminology or properties critical to the studies and analysis that may be misunderstood by researchers and/or participants. Second, study participants were largely homogenous. Third, most of the studies were not designed for replication or reproducibility. Given our critique, we offer six suggestions for those who are interested in new cognitive and perceptual projection research.
In books and textbooks on map projections, cylindrical, conic and azimuthal projections are usually considered separately. It is sometimes mentioned that cylindrical and azimuthal projections can be ...interpreted as limiting cases of conic, but this is rarely proven. The goal of this article is to show in a rigorous and systematic way how to generally approach solving the problem of transition from a conic to a corresponding cylindrical projection. This article points to the fact that J. H. Lambert showed as early as 1772 that a conformal cylindrical projection is created from a conformal conic projection. Following his idea, this paper shows that not only conformal, but also equal-area and equidistant cylindrical projections can be derived from corresponding conic map projections. Although it seems that the paper deals with quite well known and intuitive property of conic projections, it will also show that the transition from the conic to the corresponding cylindrical projection is not always possible.
PDF
