Nicolas-Auguste Tissot: A link between cartography and quasiconformal theory

Nicolas-Auguste Tissot (1824--1897) published a series of papers on cartography in which he introduced a tool which became known later on, among geographers, under the name of the "Tissot indicatrix." This tool was broadly used during the twentieth century in the theory and in the practical aspects of the drawing of geographical maps. The Tissot indicatrix is a graphical representation of a field of ellipses on a map that describes its distortion. Tissot studied extensively, from a mathematical viewpoint, the distortion of mappings from the sphere onto the Euclidean plane that are used in drawing geographical maps, and more generally he developed a theory for the distorsion of mappings between general surfaces. His ideas are at the heart of the work on quasiconformal mappings that was developed several decades after him by Gr{\"o}tzsch, Lavrentieff, Ahlfors and Teichm{\"u}ller. Gr{\"o}tzsch mentions the work of Tissot and he uses the terminology related to his name (in particular, Gr{\"o}tzsch uses the Tissot indicatrix). Teichm{\"u}ller mentions the name of Tissot in a historical section in one of his fundamental papers where he claims that quasiconformal mappings were used by geographers, but without giving any hint about the nature of Tissot's work. The name of Tissot is also missing from all the historical surveys on quasiconformal mappings. In the present paper, we report on this work of Tissot. We shall also mention some related works on cartography, on the differential geometry of surfaces, and on the theory of quasiconformal mappings. This will place Tissot's work in its proper context. The final version of this paper will appear in the journal Arch. Hist. Exact Sciences

Quasiconformal mappings, from Ptolemy's geography to the work of Teichmüller

The origin of quasiconformal mappings, like that of conformal mappings, can be traced back to old cartography where the basic problem was the search for mappings from the sphere onto the plane with minimal deviation from conformality, subject to certain conditions which were made precise. In this paper, we survey the development of cartography, highlighting the main ideas that are related to quasiconformality. Some of these ideas were completely ignored in the previous historical surveys on quasiconformal mappings. We then survey early quasiconformal theory in the works of Grötzsch, Lavrentieff, Ahlfors and Teichmüller, which are the 20th-century founders of the theory

A multi-disciplinary perspective on the built environment: Space Syntax and cartography – the communication challenge

8-11 June 2009

Rethinking Map Legends with Visualization

This design paper presents new guidance for creating map legends in a dynamic environment. Our contribution is a set of guidelines for legend design in a visualization context and a series of illustrative themes through which they may be expressed. These are demonstrated in an applications context through interactive software prototypes. The guidelines are derived from cartographic literature and in liaison with EDINA who provide digital mapping services for UK tertiary education. They enhance approaches to legend design that have evolved for static media with visualization by considering: selection, layout, symbols, position, dynamism and design and process. Broad visualization legend themes include: The Ground Truth Legend, The Legend as Statistical Graphic and The Map is the Legend. Together, these concepts enable us to augment legends with dynamic properties that address specific needs, rethink their nature and role and contribute to a wider re-evaluation of maps as artifacts of usage rather than statements of fact. EDINA has acquired funding to enhance their clients with visualization legends that use these concepts as a consequence of this work. The guidance applies to the design of a wide range of legends and keys used in cartography and information visualization

Trends and concerns in digital cartography

CISRG discussion paper ;

Embedding Spatial Software Visualization in the IDE: an Exploratory Study

Software visualization can be of great use for understanding and exploring a software system in an intuitive manner. Spatial representation of software is a promising approach of increasing interest. However, little is known about how developers interact with spatial visualizations that are embedded in the IDE. In this paper, we present a pilot study that explores the use of Software Cartography for program comprehension of an unknown system. We investigated whether developers establish a spatial memory of the system, whether clustering by topic offers a sound base layout, and how developers interact with maps. We report our results in the form of observations, hypotheses, and implications. Key findings are a) that developers made good use of the map to inspect search results and call graphs, and b) that developers found the base layout surprising and often confusing. We conclude with concrete advice for the design of embedded software maps.Comment: To appear in proceedings of SOFTVIS 2010 conferenc