Investigating the Effectiveness of an Efficient Label Placement Method Using Eye Movement Data

Abstract

This paper focuses on improving the efficiency and effectiveness of dynamic and interactive maps in relation to the user. A label placement method with an improved algorithmic efficiency is presented. Since this algorithm has an influence on the actual placement of the name labels on the map, it is tested if this efficient algorithms also creates more effective maps: how well is the information processed by the user. We tested 30 participants while they were working on a dynamic and interactive map display. Their task was to locate geographical names on each of the presented maps. Their eye movements were registered together with the time at which a given label was found. The gathered data reveal no difference in the user’s response times, neither in the number and the duration of the fixations between both map designs. The results of this study show that the efficiency of label placement algorithms can be improved without disturbing the user’s cognitive map. Consequently, we created a more efficient map without affecting its effectiveness towards the user.     

公元1430年前中国测绘美洲——《坤舆万国全图》探秘

定性与定量分析《坤舆万国全图》和同时期的欧洲绘世界地图:墨卡托(1569)、奥特里乌斯(1570)、墨卡托(1595)北极圈地图和普兰修斯(1594)地图,揭示《坤舆万国全图》内容并非采自欧洲地图.《坤舆万国全图》显示文艺复兴前的欧洲,而美洲一半的地名在同时期的欧洲绘地图上没有出现,部分是利玛窦去世至少200年后欧洲人才知道的地理.《坤舆万国全图》准确标示今日的加利福尼亚、雷尼尔山(雪山)、阿拉斯加的冰川峡湾(美湾)、安克拉治附近的水潮与北美最高峰迪纳利(水潮峰)纬度与地理特征完全符合,南美智利与秘鲁的经度比较正确.普兰修斯与墨卡托的地图严重错误和不确定.《坤舆万国全图》的中国地名地理不是利玛窦年代的,是公元1430年以前的,比哥伦布到达美洲早60年以上.传教士卫匡国1655年出版的《中国新地图集》不可能是他测绘,只能翻译中国原数据,说明明代中国有能力测绘大面积有准确经纬度和球形投影的地图.这两种地图证实中国的世界地理知识和地图学并非来自西方.《坤舆万国全图》证明中国明代大航海是世界地理大发现与地图学的先行者.     

GRID BEARINGS AND DISTANCES ON THE CONICAL ORTHOMORPHIC PROJECTION

Abstract

When computing and adjusting traverses or secondary and tertiary triangulation in countries to which the Transverse Mercator projection has been applied, it is often more convenient to work directly in terms of rectangular co-ordinates on the projection system than it is to work in terms of geographical coordinates and then convert these later on into rectangulars. The Transverse Mercator projection is designed in the first place to cover a country whose principal extent is in latitude and hence work on it is generally confined to a belt, or helts, in which the extent of longitude on either side of the central meridian is so limited as seldom to exceed a width of much more than about 200 miles.     

THE TRANSVERSE MERCATOR PROJECTION OF THE SPHEROID

Abstract

In January 1940, in a paper entitled “The Transverse Mercator Projection: A Critical Examination” (E.S.R., v, 35, 285), the late Captain G. T. McCaw obtained expressions for the co-ordinates of a point on the Transverse Mercator projection of the spheroid which appeared to cast suspicion on the results originally derived by Gauss. McCaw considered, in fact, that his expressions gave the true measures of the co-ordinates, and that the Gauss method contained some invalidity. He requested readers to report any flaw that might be discovered in his work, but apparently no such flaw had been detected at the time of his death. It can be shown, however, that the invalidities are in McCaw's methods, and there seems no reason for doubting the results derived by the Gauss method.     

Geodetic grids in authoritative maps – new findings about the origin of the UTM Grid

ABSTRACT

Recent discoveries of Wehrmacht Maps in the Military Archive of the Federal Archive of Germany in Freiburg im Breisgau raised the motivation for further investigations into the history of the internationally employed Universal Transverse Mercator (UTM) projection which actually represents a prerequisite for the global use of Global Positioning System (GPS) – and thus of any type of navigation – instruments. In contrast to the frequently stated opinion that this map projection was first operationally used by U.S. Americans it turned out that presumably the first operational maps with indication of the orthogonal UTM grid were produced by German Wehrmacht officers prior to the post World War (WW) II triumph of this projection. Based on the authors´ recent discoveries this article reveals some hitherto hardly known facts concerning the history of cartography of the 1940s.     

SOUTH AND EAST AFRICA AND THE INTERNATIONAL UNION OF GEODESY AND GEOPHYSICS

Abstract

THE resolutions and pious hopes (væux) passed by the International Union of Geodesy and Geophysics at Edinburgh in September 1936 have just been circulated in a formidable document of 8 pages and XXIX commandments. Of these, two affect the Cape-to-Cairo line particularly and they seem to deserve special study. The first of these, Number III—on systems of Projections—applies the meridional strips of the Transverse Mercator Projection apparently to all maps, topographical as well as cadastral.     

THE PLACE OF MOUNT EVEREST IN HISTORY

Abstract

The Himalaya are known as the highest mountains of the earth; but they have another title to fame not generally recognized in that they have been the home of civilized man for a longer period than any other mountain range. When the monoliths of Stonehenge were being raised in England and when the Pyramids were being built in Egypt, the glaciers of the Himalaya were being explored. The geographical names which are entered upon modern maps of the Central Himalaya are very ancient memorials of civilization. The existence of a mountain nomenclature, Aryan in the west and centre, Mongolian in the east, has given rise to linguistic problems not less difficult than the topographical problems of the snows. In 1927 the volumes of the Linguistic Survey of India were published; they had been written by Sir George Grierson, an officer of the Indian Civil Service, and they dealt with 723 different languages and dialects. In the Himalaya there are now in use among the peoples seventy different languages, all of which (with one aboriginal exception) belong either to the Aryan or Mongolian family. Languages are historical monuments, and from them Sir George Grierson has been able to decipher the outlines of history.     

The oblique Mercator projection of the ellipsoid of revolution IE a 2 ,b

While the standardMercator projection / transverse Mercator projecton maps the equator / the transverse metaequator equivalent to the meridian of referenceequidistantly, theoblique Mercator projection aims at aconformal mapping of the ellipsoid of revolution constraint to anequidistant mapping of an oblique metaequator. Obliqueness is determined by the extension of the area to be mapped, e.g. determined by the inclination of satellite orbits: Satellite cameras map the area just under the orbit geometry. Here we derive themapping equations of theoblique Mercator projection being characterized to beconformal andequidistant on the oblique metaequator extending results ofM. Hotine (1946, 1947).     

A TRANSVERSE MERCATOR PROJECTION OF THE SPHEROID ALTERNATIVE TO THE GAUSS-KRÜGER FORM

Abstract

The excuse for yet another paper on the Transverse Mercator projection, which has already received what should be more than its fair share of space in this Review, can only be that there is a fresh viewpoint to offer. It is the purpose of this paper to show that there are, in fact, two “Transverse Mercator” projections of the spheroid, of which one has hitherto almost escaped notice.     

Remapping Fictional Worlds: A Comparative Reconstruction of Fictional Maps

ABSTRACT

This article presents a quantitative analysis of fictional maps and their relation to historic maps from different periods. Fictional maps are maps of imaginary territories. This type of map is now common in fiction, but they arose relatively late, in the second half of the nineteenth century, and are considered an independent branch of cartography today. They stand out through the way they are published because they are component parts of books and not independent cartographic works, and therefore their creators are not cartographers but rather the authors of these books. Fictional maps are mostly subordinate to the story, but they serve to give a sense of historical authenticity and draw the reader into the story. Without networks of coordinates and with labels such as ‘the end of the world’, they are spatially indeterminate, but they establish a connection between the fictional landscape and its identity. This study deals with 89 fictional maps from recent children’s and young adult literature. First we present a historical overview of these works and fictional maps, and then a cartographic analysis of fictional maps. We examined seventy-seven books with fictional maps and evaluated the maps according to five groups of standard cartographic elements: natural elements, built elements, toponyms, mathematical elements, and explanatory elements. We discuss the differences between cartographic representation of fictional maps and historic maps, and build a cartographic model based on the frequency of cartographic elements to put fictional maps into historic and geographical contexts.     

Shapes on a plane: evaluating the impact of projection distortion on spatial binning

ABSTRACT

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.     

Deconstructing Galbraith: A Geostatistical Analysis of Cartographic Intent

Abstract

This study uses cartometric techniques to reveal cartographic design considerations operative in Frank H. Galbraith’s 1897 railway mail service training maps. Galbraith’s maps make extensive use of humorous cartouches intended to serve as mnemonic devices for learning railway mail service routes. Poisson and quadrat point pattern analyses are performed on all eight maps in the series to determine whether the mimetic symbols are clustered along the railway mail routes or dispersed throughout the mapped spaces to achieve better graphic balance. Evidence overwhelmingly indicates that the placement of the mnemonic symbols was primarily driven by design considerations. The study therefore proves that it is possible to use cartometric techniques to deconstruct the map document to determine the cartographic design principles operative during the map's construction.     

A New Face for The Cartographic Journal

Abstract

The logic behind the placement of names on maps is investigated as part of a study, the object of which is the automation of map lettering. After describing the basic principles the author illustrates his solution.     

'Drawing the Coral Heads': Mental Mapping and its Physical Representation in a Polynesian Community

Abstract

Indigenous people throughout the world developed their own mapping skills and systems of knowledge. While Westerners are prone to overlook these communities' geographical knowledge and imagine their mapping activities to be primitive or non-existent, their mental maps are often impressive in sophistication and detailed even if based on cosmologies that are quite foreign to Western thinking. This article depicts a mental map of the ocean floor shared by Polynesians of Anuta, a remote community in the Solomon Islands. It situates Anuta's reef map in relation to academic discussions of indigenous cartography and describes the process that resulted in the map's physical representation.     

THE TRANSVERSE MERCATOR PROJECTION

Abstract

I. Introduction.—Map projection is a branch of applied mathematics which owes much to J. H. Lambert (v. this Review, i, 2, 91). In his “Beyträge zum Gebrauche der Mathematik und deren Anwendung” (Berlin, 1772) he arrived at a form of projection whereof the Transverse Mercator is a special case, and pointed out that this special case is adapted to a country of great extent in latitude but of small longitudinal width. Germain (“Traité des Projections”, Paris, 1865) described it as the Projection cylindrique orthomorphe de Lambert, but he also introduced the name Projection de Mercator transverse or renversée; he shows that Lambert's treatment of the projection was remarkably simple.     

Mapping for history: the influence of the 7th Field Survey Company’s 1917 operation maps on the historiography of the 3rd Battle of Gaza

ABSTRACT

During Palestine Campaign of World War I, the British Army’s Egyptian Expeditionary Force produced a series of operation maps to track and control the progress of their offensive into Palestine. These maps demonstrated innovation in both their form and function, and they have been referenced and reproduced by both map scholars and military historians ever since. Leaning on J.B. Harley and Matthew Edney’s ideas about critical map history, this essay provides a critical examination of these operation maps to illuminate the sociocultural context of their creation and examines the maps’ influence over the broader historiography of the Palestine Campaign. In doing so it highlights the interdisciplinary value of critical map histories.     

The optimal Mercator projection and the optimal polycylindric projection of conformal type – case-study Indonesia

As a conformal mapping of the sphere S ² _R or of the ellipsoid of revolution E ² _A , _B the Mercator projection maps the equator equidistantly while the transverse Mercator projection maps the transverse metaequator, the meridian of reference, with equidistance. Accordingly, the Mercator projection is very well suited to geographic regions which extend east-west along the equator; in contrast, the transverse Mercator projection is appropriate for those regions which have a south-north extension. Like the optimal transverse Mercator projection known as the Universal Transverse Mercator Projection (UTM), which maps the meridian of reference Λ₀ with an optimal dilatation factor &ρcirc;=0.999 578 with respect to the World Geodetic Reference System WGS 84 and a strip [Λ₀−Λ _W ,Λ₀ + Λ _E ]×[Φ _S ,Φ _N ]= [−3.5^∘,+3.5^∘]×[−80^∘,+84^∘], we construct an optimal dilatation factor ρ for the optimal Mercator projection, summarized as the Universal Mercator Projection (UM), and an optimal dilatation factor ρ₀ for the optimal polycylindric projection for various strip widths which maps parallel circles Φ₀ equidistantly except for a dilatation factor ρ₀, summarized as the Universal Polycylindric Projection (UPC). It turns out that the optimal dilatation factors are independent of the longitudinal extension of the strip and depend only on the latitude Φ₀ of the parallel circle of reference and the southern and northern extension, namely the latitudes Φ _S and Φ _N , of the strip. For instance, for a strip [Φ _S ,Φ _N ]= [−1.5^∘,+1.5^∘] along the equator Φ₀=0, the optimal Mercator projection with respect to WGS 84 is characterized by an optimal dilatation factor &ρcirc;=0.999 887 (strip width 3^∘). For other strip widths and different choices of the parallel circle of reference Φ₀, precise optimal dilatation factors are given. Finally the UPC for the geographic region of Indonesia is presented as an example. Received: 17 December 1997 / Accepted: 15 August 1997     

Generating and mapping population density surfaces within a geographical information system

Abstract

The spatially discontinuous choropleth map is a poor representation of the underlying continuous distribution of population density. A possible alternative is to derive dasymetric maps at a fine spatial resolution by making use of satellite imagery in a geographical information system. However, there are cartographic problems when these maps are displayed and further processing is needed in order to obtain approximations to a continuous density surface. Isarithmic maps of these density surfaces retain a high degree of spatial accuracy while providing pleasing and highly adaptable presentations.

The methods used to generate dasymetric and isarithmic maps are readily implemented in most raster based geographical information systems. For example, the classification of remotely sensed imagery, the subsequent processing and integration of data, and most of the cartographic display, were all undertaken in this work using the low cost IDRISI GIS that operates on standard IBM PC compatible hardware.     

Measuring the influence of map label density on perceived complexity: a user study using eye tracking

ABSTRACT

We combine eye tracking and a questionnaire-based approach to explore the influence of label density on the perceived visual complexity of maps. We design two experiments in which participants are asked to search for the names of point features on maps and to rate the map complexity and legibility for different label densities. Specifically, we conduct a highly controlled experiment in which all the map variables except the label density are held constant (the controlled experiment). Then, we conduct a second experiment following the same protocol but using real maps as visual stimuli (the real-map experiment) to verify if the results of the controlled experiment were applicable to real maps. The results of both experiments indicate a significantly positive correlation between perceived visual complexity and label density and between the response time in visual search tasks and label density. Surprisingly, we observe a significant inverse correlation between the label density and two eye movement parameters (fixation duration and fixation frequency) between the two experiments. We discuss how the variables of real maps might have affected these eye movement parameters and why the results of the two experiments are inconsistent. Our findings suggest that eye tracking parameters are not reliable indicators of map complexity. These empirical results can be helpful to future map design and map complexity investigation.