<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The research of modern cartography in the field of digital generalisation focuses on the development of such methods that would be fully automatic and give an unambiguously objective result. Devising them requires specific standards as well as unique and verifiable algorithms. In metric space, a proposal for such a method, based on contractive mapping, the Lipschitz and Cauchy conditions and the Banach theorem, using the Salishchev metric, was presented in the publication (Barańska et al., 2021). The method formulated there is dedicated to linear objects (polylines). The current work is a practical supplement to it. It presents the practical implementation of the algorithm for automatic and objective generalisation. The article describes an operational diagram of the subsequent stages of the proposed generalisation method. In the test example, a binary tree structure of an ordered polyline was created. It was simplified in two selected scales and its shape after generalisation was illustrated. The resulting polyline obtained by the fully automatic method was verified in terms of accuracy.</p>
</abstract>

The research of modern cartography in the field of digital generalisation focuses on the development of such methods that would be fully automatic and give an unambiguously objective result. Devising them requires specific standards as well as unique and verifiable algorithms. In metric space, a proposal for such a method, based on contractive mapping, the Lipschitz and Cauchy conditions and the Banach theorem, using the Salishchev metric, was presented in the publication (Barańska et al., 2021). The method formulated there is dedicated to linear objects (polylines). The current work is a practical supplement to it. It presents the practical implementation of the algorithm for automatic and objective generalisation. The article describes an operational diagram of the subsequent stages of the proposed generalisation method. In the test example, a binary tree structure of an ordered polyline was created. It was simplified in two selected scales and its shape after generalisation was illustrated. The resulting polyline obtained by the fully automatic method was verified in terms of accuracy.

Algorithm of automatic digital cartographic generalisation with the use of contractive self-mapping

AGH University of Science and Technology Kraków

student AGH University of Science and Technology

Polish Cartographical Review

This work is licensed under the Creative Commons Attribution 4.0 International License.

The research of modern cartography in the field of digital generalisation focuses on the development of such methods that would be fully automatic and give an...

Algorithm of automatic digital cartographic generalisation with the use of contractive self-mapping

Published Online: Apr 05, 2022

Page range: 1 - 10

Received: Jan 27, 2022

Accepted: Mar 17, 2022

DOI: https://doi.org/10.2478/pcr-2022-0001

Keywords
digital generalisation, contractive self-mapping, minimum dimensions of Salishchev, polyline (segmented line) of binary tree structure, contraction triangles

© 2022 Piotr Banasik et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Algorithm of automatic digital cartographic generalisation with the use of contractive self-mapping

Published Online: Apr 05, 2022

Page range: 1 - 10

Received: Jan 27, 2022

Accepted: Mar 17, 2022

DOI: https://doi.org/10.2478/pcr-2022-0001

Keywordsdigital generalisation, contractive self-mapping, minimum dimensions of Salishchev, polyline (segmented line) of binary tree structure, contraction triangles

© 2022 Piotr Banasik et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
digital generalisation, contractive self-mapping, minimum dimensions of Salishchev, polyline (segmented line) of binary tree structure, contraction triangles