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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. [ABSTRACT FROM AUTHOR]

For centuries, people have been intrigued by map projections upon polyhedra--the surface of the Earth laid out on the faces of polyhedral bodies (beautiful in themselves)--which are then unfolded to make flat maps of the world. This paper describes a simple 'slice-and-dice' method to obtain area equivalence, which is applied to polyhedral globes. The implementations of this method include a projection that is equivalent to Snyder's equal-area projection for Platonic bodies, an equal-area projection with far smaller cusps, and an equal-area projection that obtains constant scale along the polyhedron's edges. The latter two are presented in terms of exact equations and are compared with Snyder's projection., Introduction Polyhedral globes (Figure 1) go as far back as to at least the times when the artist Albrecht Durer (1525) suggested the projection of a sphere upon polyhedra. They [...]

Sometimes map projection designers need to create equal-area projections to best fill the projections' purposes. However, unlike for conformal projections, few transformations have been described that can be applied to equal-area projections to develop new equal-area projections. Here, I survey area-preserving transformations, giving examples of their applications and proposing an efficient way of deploying an equal-area system for raster-based Web mapping. Together, these transformations provide a toolbox for the map projection designer working in the area-preserving domain. [ABSTRACT FROM AUTHOR]

Equivalence (the equal-area property of a map projection) is important to some categories of maps. However, unlike for conformal projections, completely general techniques have not been developed for creating new, computationally reasonable equal-area projections. The literature describes many specific equal-area projections and a few equal-area projections that are more or less configurable, but flexibility is still sparse. This work develops a tractable technique for generating a continuum of equal-area projections between two chosen equal-area projections. The technique gives map projection designers unlimited choice in tailoring the projection to the need. The technique is particularly suited to maps that dynamically adapt optimally to changing scale and region of interest, such as required for online maps. [ABSTRACT FROM AUTHOR]

One method for working with large, dense sets of spatial point data is to aggregate the measure of the data into polygonal containers, such as political boundaries, or into regular spatial bins such as triangles, squares, or hexagons. When mapping these aggregations, the map projection must inevitably distort relationships. This distortion can impact the reader’s ability to compare count and density measures across the map. Spatial binning, particularly via hexagons, is becoming a popular technique for displaying aggregate measures of point data sets. Increasingly, we see questionable use of the technique without attendant discussion of its hazards. In this work, we discuss when and why spatial binning works and how mapmakers can better understand the limitations caused by distortion from projecting to the plane. We introduce equations for evaluating distortion’s impact on one common projection (Web Mercator) and discuss how the methods used generalize to other projections. While we focus on hexagonal binning, these same considerations affect spatial bins of any shape, and more generally, any analysis of geographic data performed in planar space. [ABSTRACT FROM PUBLISHER]

In 1989, Herbert Hufnagel introduced a mathematical model for a family of equal-area, pseudocylindric projections, which includes the Mollweide, Wagner IV, and Eckert IV projections as specializations. Hufnagel’s contribution has received very little attention, and his projections are not available in any of the commonly used cartographic software packages. This article makes three contributions: The Hufnagel family is introduced to the English-speaking community; algorithms for computing the forward and reverse projections are presented; and the eight new projections proposed by Hufnagel are analyzed. [ABSTRACT FROM PUBLISHER]

As mapmakers we are invested in the importance of our craft. We bemoan the tragic state of geographic and map literacy, and advocate better education. Names like Robinson, Harley, and Wood have asserted the great power of maps. Are we guilty of seeing everything as a nail because we make hammers? In this rhetorical presentation, I argue for humility in our endeavor, recognizing that many people simply do not need maps. They meet their way finding needs using other efficient, utilitarian skills and devices. Could we improve our map designs for those who do use maps by disregarding the (non-)needs of those who do not? [ABSTRACT FROM AUTHOR]

Presents a letter to the editor in response to the paper "A Geodetic Approach: Universal No-Projection Seamless Mapping," by Muneendra Kumar, which appeared in a previous issue of "Surveying and Land Information Science."