An Implementation of the Robinson Map Projection Based on Cubic Splines

The Robinson world map projection has been in existence since 1963. Mapping equations for the projection are based on table interpolation. Cubic splines with the choice of appropriate boundary conditions are shown to possess favorable characteristics as interpolative functions. The evaluation of cubic splines for given latitudes provides a basis for efficient forward mapping equations. Inverse mapping equations are based on an efficient inversion of the cubic spline functions utilizing Newton's method. Derivatives of the cubic spline functions lead to formulas for scale factors along projected meridians and parallels and for areal scale factors. Details for a computer implementation of the mapping equations and the computation of scale factors are given.     

The Miller Oblated Stereographic Projection for Africa,Europe, Asia and Australasia

The Miller Oblated Stereographic Projection, implemented by both the American Geographical Society and the Defense Mapping Agency in small-scale mapping of Africa, Europe, Asia and Australasia, is conformal for most land masses, reducing overall scale and area distortion by using a double projection. “Fill-in” sections are not conformal. Developed in 1953–1955 by O. M. Miller, the projection is implemented via tables for map construction. With the advent of computer-assisted intelligence and operations systems that use this projection to provide electronic images, the computation of rectangular projection coordinates from geographic locations via table look-up is no longer adequate. This paper presents an algorithm, based upon the original Miller work, which performs this transformation in a form applicable to scientific programming languages.     

The Generalized Conic Projection

The Equidistant Cylindric and the Equidistant Conic projections are reviewed as foundations for a series of new projections. The new projections are introduced as the Patchwork Conic, an amalgamation of Equidistant Conic projections; the Generalized Equidistant Cylindric, with a standard path, or conformal path of correct scale, that is definable by the projection designer; and the Generalized Equidistant Conic, having two definable standard paths. Several potential uses are mentioned. Maps, formulae, and computation examples are provided. It is concluded that the projection is unique in allowing tailoring without compromising desirable mathematical properties.     

Designing Effective Bivariate Symbols: The Influence of Perceptual Grouping Processes

The purpose of this research was to empirically assess perceptual groupings of various combinations of symbol dimensions (e.g., graphic variables) used in designing bivariate map symbols. Perceptual grouping ability was assessed using the theory of selective attention, a construct first proposed in psychological research. Selective attention theory contends that one's ability to analyze a symbol's dimensions—such as color or size—is affected by other dimensions present in the same symbol. Symbol dimensions are described as either separable (capable of being attended to independently of other dimensions), integral (cannot be processed without interference from other dimensions), or configural (i.e., show characteristics of both integrality and separability, which may also form new, emergent properties). Without empirical evidence describing such interactions for various combinations of symbol dimensions, cartographers cannot truly evaluate the functionality of the symbols they use on maps. The symbol dimensions or graphic combinations chosen for this study were selected to incorporate a wide range of traditional cartographic symbolization, including line and lettering symbolization, areal shading, dot patterns, and point symbols. Combinations were examined in an abstract setting using a speeded classification task, which is the traditional means of studying selective attention. Subject reaction times provided an assessment of the levels of integrality, separability, and configurality. Results suggest that most symbol dimension combinations are either separable or exhibit evidence of asymmetrical dimensional interactions. Findings from this study will be integrated into subsequent experiments, the results of which will assist cartographers in the design of complex map symbols.     

New Equal-Area Map Projections For Noncircular Regions

A series of new equal-area map projections has been devised. Called Oblated Equal-Area, its lines of constant distortion follow approximately oval or rectangular paths instead of the circles of the Lambert Azimuthal Equal-Area projection or the straight lines of the Cylindrical Equal-Area projection. The projection series permits design of equal-area maps of oblong regions with less overall distortion of shape and scale than equal-area maps on other projections.