Automatic simplification of the geometry of a cartographic line using contractive self-mapping – illustrated with an example of a polyline band

Abstract

The present article is another attempt to adapt map geometry to automatic digital cartography. The paper presents a method of digital polyline generalisation that uses contractive self-mapping. It is a method of simplification, not just an algorithm for simplification. This method in its 1996 version obtained a patent entitled “Method of Eliminating Points in the Process of Numerical Cartographic Generalisation” – Patent Office of the Republic of Poland, No. 181014, 1996. The first results of research conducted using the presented method, with clearly defined data (without singular points of their geometry), were published in the works of the authors in 2021 and 2022.

Keywords

• digital generalisation
• contractive self-mapping
• salichtchev’s minimum measures
• geometry of a polyline in the binary tree structure
• lipschitz’s contraction triangle
• banach theorem