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A Study of the Local Geometric Accuracy of Count de Ferraris's Carte de cabinet (1770s) Using Differential Distortion Analysis

(2018) CARTOGRAPHIC JOURNAL. 55(1). p.16-35
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Abstract
The eighteenth century Carte de cabinet of count de Ferraris is the first large-scale (1: 11 520) topographic map of the entire Belgian territory, making it a valuable source of historical information. In the past, a number of studies have tried to assess the geometric accuracy of this map, but they all suffer from restricted technical capabilities for computing and visualizing the distortions, and most of them only focus on a limited number of the 275 map sheets. This paper therefore seeks to provide the first systematic and in-depth investigation of the map's local geometric accuracy. Recently, two Belgian government agencies georeferenced the Flemish and Walloon part of the Carte de cabinet with a high level of detail, using some 30,000 ground control points to link the old map to the modern topographic map of Belgium. These data sets represent a new and unprecedented potential source of accuracy information. However, the high number of control points and our desire to compute distortions in an exact, local, quantitative and continuous way meant prominent techniques for studying the geometric accuracy of old maps, such as displacement vectors, distortion grids, triangular nets and the popular MapAnalyst software, were unsuited for this task. To meet all our requirements a new technique called Differential Distortion Analysis, which is influenced by the treatment of distortions in map projection theory, was used instead. Its advantages, structure and application to the Carte de cabinet are discussed in detail. The new technique allows calculating and displaying the map's local angular and surface distortions with a very high spatial resolution. Consequently, it was possible to identify trends in the obtained levels of accuracy and to relate these to historical facts about the Carte de cabinet's production process. This has resulted in important new insights into the map's geometric accuracy.
Keywords
MAPS, History of cartography, count de Ferraris, Carte de cabinet (1777), geometric accuracy, Differential Distortion Analysis, thin plate spline, area scale factor, maximum angular distortion

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Chicago
Vervust, Soetkin, Manuel Claeys Boùùaert, Bernard De Baets, Nico Van de Weghe, and Philippe De Maeyer. 2018. “A Study of the Local Geometric Accuracy of Count De Ferraris’s Carte De Cabinet (1770s) Using Differential Distortion Analysis.” Cartographic Journal 55 (1): 16–35.
APA
Vervust, S., Claeys Boùùaert, M., De Baets, B., Van de Weghe, N., & De Maeyer, P. (2018). A Study of the Local Geometric Accuracy of Count de Ferraris’s Carte de cabinet (1770s) Using Differential Distortion Analysis. CARTOGRAPHIC JOURNAL, 55(1), 16–35.
Vancouver
1.
Vervust S, Claeys Boùùaert M, De Baets B, Van de Weghe N, De Maeyer P. A Study of the Local Geometric Accuracy of Count de Ferraris’s Carte de cabinet (1770s) Using Differential Distortion Analysis. CARTOGRAPHIC JOURNAL. Abingdon: Taylor & Francis Ltd; 2018;55(1):16–35.
MLA
Vervust, Soetkin, Manuel Claeys Boùùaert, Bernard De Baets, et al. “A Study of the Local Geometric Accuracy of Count De Ferraris’s Carte De Cabinet (1770s) Using Differential Distortion Analysis.” CARTOGRAPHIC JOURNAL 55.1 (2018): 16–35. Print.
@article{8569040,
  abstract     = {The eighteenth century Carte de cabinet of count de Ferraris is the first large-scale (1: 11 520) topographic map of the entire Belgian territory, making it a valuable source of historical information. In the past, a number of studies have tried to assess the geometric accuracy of this map, but they all suffer from restricted technical capabilities for computing and visualizing the distortions, and most of them only focus on a limited number of the 275 map sheets. This paper therefore seeks to provide the first systematic and in-depth investigation of the map's local geometric accuracy. Recently, two Belgian government agencies georeferenced the Flemish and Walloon part of the Carte de cabinet with a high level of detail, using some 30,000 ground control points to link the old map to the modern topographic map of Belgium. These data sets represent a new and unprecedented potential source of accuracy information. However, the high number of control points and our desire to compute distortions in an exact, local, quantitative and continuous way meant prominent techniques for studying the geometric accuracy of old maps, such as displacement vectors, distortion grids, triangular nets and the popular MapAnalyst software, were unsuited for this task. To meet all our requirements a new technique called Differential Distortion Analysis, which is influenced by the treatment of distortions in map projection theory, was used instead. Its advantages, structure and application to the Carte de cabinet are discussed in detail. The new technique allows calculating and displaying the map's local angular and surface distortions with a very high spatial resolution. Consequently, it was possible to identify trends in the obtained levels of accuracy and to relate these to historical facts about the Carte de cabinet's production process. This has resulted in important new insights into the map's geometric accuracy.},
  author       = {Vervust, Soetkin and Claeys Bo{\`u}{\`u}aert, Manuel and De Baets, Bernard and Van de Weghe, Nico and De Maeyer, Philippe},
  issn         = {0008-7041},
  journal      = {CARTOGRAPHIC JOURNAL},
  keyword      = {MAPS,History of cartography,count de Ferraris,Carte de cabinet (1777),geometric accuracy,Differential Distortion Analysis,thin plate spline,area scale factor,maximum angular distortion},
  language     = {eng},
  number       = {1},
  pages        = {16--35},
  publisher    = {Taylor \& Francis Ltd},
  title        = {A Study of the Local Geometric Accuracy of Count de Ferraris's Carte de cabinet (1770s) Using Differential Distortion Analysis},
  url          = {http://dx.doi.org/10.1080/00087041.2017.1323148},
  volume       = {55},
  year         = {2018},
}

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