One of the common problems associated with large computer-based information systems is the relatively small window through which an information space can be viewed. Increasing interest in recent years has been focused on the development of distortion-oriented presentation techniques to address this problem. However, the growing number of new terminologies and techniques developed have caused considerable confusion to the graphical user interface designer, consequently making the comparison of these presentation techniques and generalization of empirical results of experiments with them very difficult, if not impossible. This article provides a taxonomy of distortion-oriented techniques which demonstrates clearly their underlying relationships. A unified theory is presented to reveal their roots and origins. Issues relating to the implementation and performance of these techniques are also discussed.

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A review and taxonomy of distortion-oriented presentation techniques

This paper presents efficient methods for implementing general non-linear magnification transformations. Techniques are provided for: combining linear and non-linear magnifications, constraining the domain of magnifications, combining multiple transformations, and smoothly interpolating between magnified and normal views. In addition, piecewise linear methods are introduced which allow greater efficiency and expressiveness than their continuous counterparts.

Techniques for non-linear magnification transformations

The notion of a cartogram is reviewed. Then, based on a presentation from the 1960s, a direct and simple introduction is given to the design of a computer algorithm for the construction of contiguous value-by-area cartograms. As an example, a table of latitude/longitude to rectangular plane coordinates is included for a cartogram of the United States, along with Tissot's measures for this map projection. This is followed by a short review of the subsequent history of the subject and includes citation of algorithms proposed by others. In contrast to the usual geographic map, the most common use of cartograms is solely for the display and emphasis of a geographic distribution. A second use is in analysis, as a nomograph or problem-solving device similar in use to Mercator's projection, or in the transform-solve-invert paradigm. Recent innovations by computer scientists modify the objective and suggest variation similar to Airy's (1861) “balance of errors” idea for map projections.

Thirty Five Years of Computer Cartograms

We introduce nonlinear magnification fields as an abstract representation of nonlinear magnification, providing methods for converting transformation routines to magnification fields and vice-versa. This new representation provides ease of manipulation and power of expression. By removing the restrictions of explicit foci and allowing precise specification of magnification values, we can achieve magnification effects which were not previously possible. Of particular interest are techniques we introduce for expressing complex and subtle magnification effects through magnification brushing, and allowing intrinsic properties of the data being visualized to create data-driven magnifications.

Nonlinear magnification fields

The paper describes a general formulation of the "detail-in-context" problem, which is a central issue of fundamental importance to a wide variety of nonlinear magnification systems. A number of tools are described for dealing with this problem effectively. These tools can be applied to any continuous nonlinear magnification system, and are not tied to specific implementation features of the system that produced the original transformation. Of particular interest is the development of "seamless multi level views", which allow multiple global views of an information space (each having different information content) to be integrated into a single view without discontinuity.

The generalized detail in-context problem

The evolution of a continuous projection for portraying the area of territorial units in proportion to a thematic variable has, in the past, eluded the cartographer. The present paper—resulting from postgraduate research in cartography by the second author under the supervision of the first—describes the development of such a projection and some of the possible applications.

Eli Shlomi

Papers

A Polyfocal Projection for Statistical Surfaces