Cartographic communication through crisis maps takes place in a unique environment characterised by the immediate risks of considerable loss and stress. Many such maps are designed by practitioners with limited resources, pressured for time, and who often fail to pay the necessary attention to map graphics. This can reduce map clarity and make orientation to and understanding of essential crisis information difficult. To identify the most frequent shortcomings that may compromise the interpretation of depicted objects, phenomena presented, and actions required, we assessed the map graphics of 106 maps specifically designed for communication and action in crises. The results showed that they were often visually overloaded. Crisis data were not conveyed by appropriate cartographic representations, and due to the inappropriate use of visual variables, the associative and selective properties of cartographic symbols were overlooked, and their ordered and quantitative features ignored. The use of colour was often not adapted to conventional visual language, and colour symbolism was not always taken into account. The cartographic symbols used were often incomprehensible, illegible, ambiguous, and unclassified, and they lacked symbolism and hierarchical organisation. The article aims to address these problems by proposing guidelines which do not require much time or expertise, but which would ensure that cartographically correct crisis maps are well designed. Objects, phenomena or actions specific to crisis management would be indicated using appropriate map graphics and their importance highlighted, so as to make interpretation easier for all participants in a crisis event, and so facilitate crisis communication and response.

A projection aspect is usually defined in references as the relation to the so-called auxiliary surface. However, such surfaces do not usually exist in map projection theory, which raises the issue of defining projection aspects without reference to auxiliary surfaces. This paper explains how projection aspects can be defined in two ways which are not mutually exclusive. According to the first definition, the aspect is the position of a projection axis in relation to the axis of geographic parameterization of a sphere. The projection axis is the axis of the pseudogeographic parameterization of a sphere, based on which the basic equations of map projection are defined. The basic equations of map projection are selected according to agreement and/or custom. According to this definition, aspects can be normal, transverse or oblique. According to the second definition, an aspect is the representation of the area in the central part of a map, and can be polar, equatorial or oblique. Therefore, it is possible for a map projection to have a normal and polar aspect, but it can also have a normal and equatorial aspect. The second definition is not recommended for use, due to its ambiguity.

Many books, textbooks and papers have been published in which the classification of map projections is based on auxiliary (developable) surfaces and projections are divided into conic, cylindrical and azimuthal projections. We argue that such a classification of map projections is unacceptable and give many reasons for that. Many authors wrote in more detail about the classification of map projections, and our intention is to give a new refined and rectified insight into the classification of map projections. Our approach can be included in map projection publications of general and thematic cartography. Doing this, misconceptions and unnecessary insistence on conceptuality instead of reality will be avoided.

This paper explains that the terms “horizontal and vertical scales” are not appropriate in map projections theory. Instead, the authors suggest using the term “scales in the direction of coordinate axes.” Since it is not possible to read a local linear scale factor in the direction of a coordinate axis immediately from the definition of a local linear scale factor, this paper considers the derivation of new formulae that enable local linear scale factors in the direction of coordinate x and y axes to be calculated. The formula for computing the local linear scale factor in any direction defined by dx and dy is also derived. Furthermore, the position and magnitude of the extreme values of the local linear scale factor are considered and new formulas derived.

The Web Mercator projection is a projection of a relatively recent date. There has been a lot of controversy about its application. Some believe that this projection is not a projection of either the sphere or the surface of the ellipsoid. Therefore, in this paper, several projections of the surface of a rotational ellipsoid into a plane are investigated and it is shown that the Web Mercator projection is one of such projections. Namely, although the equations of this projection are identical to the equations for the projection of the sphere, the basic difference is in the choice of the area of definition, i.e., the domain of the projection. Furthermore, we have shown that the Web Mercator projection can also be interpreted as double mapping: mapping an ellipsoid to a sphere according to the normals and then mapping the sphere to the plane according to the formulas of the Mercator projection for the sphere. The Web Mercator projection is not a conformal projection, but it is close in properties to the Mercator projection.

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.