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1

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

Bac-Bronowicz Joanna, Banasik Piotr, Chrobak Tadeusz

Polish Cartographical Review

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2023

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Vol. 55, No. 1

73--86

EN

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. This article presents a transition from the DLM (Digital Landscape Model) to the DCM (Digital Cartographic Model). It demonstrates an algorithm with independent solutions for the band axis and both its edges. The presented example was performed for the so-called polyline band, which can represent real topographic linear objects such as rivers and boundaries of closed areas (buildings, lakes, etc.). An unambiguous representation of both edges of the band is its axis, represented in DLM, which can be simplified to any scale. A direct consequence of this simplification is the shape of the band representing the actual shape of both edges of the object that is classified in the database as a linear object in DCM. The article presents an example performed for the so-called polyline band, which represents real topographic linear objects (roads, rivers) and area boundaries. The proposed method fulfils the following conditions: the Lipschitz condition, the Cauchy condition, the Banach theorem, and the Salichtchev’s standard for object recognition on the map. The presented method is objective in contrast to the previously used approximate methods, such as generalisations that use graph theory and fractal geometry, line smoothing and simplification algorithms, statistical methods with classification of object attributes, artificial intelligence, etc. The presented method for changing the geometry of objects by any scale of the map is 100% automatic, repeatable, and objective; that is, it does not require a cartographer’s intervention.

2

Mapa ma być dobra i ładna

Bac-Bronowicz Joanna, Chrobak Tadeusz, Kowalski Paweł, Głażewki Andrzej, Pędzich Paweł, Pasławski Jacek, Krzywicka-Blum Ewa, Ostrowski Wiesław, Siwek Jerzy, Spallek Waldemar, Bauer Robert, Dukaczewski Dariusz, Markowska Anna, Krupski Jan, Nakonieczna Iwona, Janusiewicz Roman, Górecki Adam, Golba Radosław, Szombara Stanisław, Kozioł Krystian, Krauze-Tomczyk Izabella, Traczyk Dorota, Zieliński Jerzy, Markowski Maciej, Krukowski Mirosław, Bidzińska Paulina, Wojtysiak-Kotlarska Maria, Stankiewicz Michał, Kaczyński Andrzej

Geodeta : magazyn geoinformacyjny

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2022

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nr 5

8--14

3

Simplification of 2D shapes with equivalent rectangles

Kwinta Andrzej, Bac-Bronowicz Joanna

Advances in Geodesy and Geoinformation

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2022

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Vol. 71, no. 1

art. no. e14, 2022

EN

Real objects in horizontal projection often have a complex geometry. Their irregular shape causes issues during analyses and calculations that consider their geometry. The paper proposes the replacement of real-world objects with equivalent rectangles (ER). The paper also defines the geometric criteria of ER as well as ER parameters and methods for calculating them. The paper also demonstrates the difference in the duration of calculations for different types of rectangles (equivalent rectangle with the same area, surrounding rectangle with the smallest area, inscribed rectangle with the largest area). The presented approach has been illustrated with three case studies. The first one is the application of ER to underground mining cavities to determine post-mining deformations of the ground surface. In the second study, an ER was applied to analyse the geometry of agricultural parcels in a selected part of a rural settlement. ER can help assess whether the spatial layout is faulty and if a planning intervention is necessary. The third example describes a building’s geometry with an ER. Regarding the simplification of building’s geometry, it is crucial to replace a simplified building with a model that has the same centroid location and the same area. It is the perfect solution for rapid analyses of displaying objects on maps in various scales.

4

Analysis of hyperboloid cooling tower projection on 2D shape

Kwinta Andrzej, Bac-Bronowicz Joanna

Geomatics, Landmanagement and Landscape

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2021

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no. 3

25--40

EN

This paper undertakes the problem of mapping a hyperboloid cooling tower on a single plane. Measurements performed by ground-based laser scanning technology quickly deliver substantial amounts of geometric data of the tower’s outer wall. The essence of the article is projection of the rotational hyperboloid on a plane. The shape of the hyperboloid cooling tower is not directly expandable to a single plane. Mapping a hyperboloid shape on a plane is, therefore, associated with distortions. This paper presents a comparison between cylindrical and conic projection of a hyperboloid cooling tower. The most popular method of mapping hyperboloid is cylindrical projection. The cylinder’s side surface is easily developed on the drawing sheet. For the hyperboloid cooling tower, the biggest distortions occur in the latitudinal direction and reach the highest values at the top and bottom edges. The equation (13) describe distortion for the cylindrical projection. The equation (18) describe distortion for the conical projection. This paper presents results obtained from the performed measurement. The analysis found that cone mapping produces less distortion than cylindrical projection for the hyperboloid cooling tower. We think, that in conical projection, the shape of a hyperboloid cooling tower and theoretical conic shape have better corresponding together than in cylindrical projection.

5

Risk Reduction of a Terrorist Attack on a Critical Infrastructure Facility of LGOM Based on the Example of the Żelazny Most Tailings Storage Facility (OUOW Żelazny Most)

Bac-Bronowicz Joanna, Kowalczyk Piotr, Bartlewska-Urban Monika

Studia Geotechnica et Mechanica

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2020

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Vol. 42, nr 4

367--387

EN

This paper identifies the threats and risks of a terrorist attack on a critical infrastructure facility based on the example of Żelazny Most Tailings Storage Facility (OUOW). The threat analysis primarily took into account the threats of deliberate human actions. Identification of potential threats concerning the infrastructure surrounding the facility was conducted based on information that is readily available on the Internet. The reasons why it may be a potential target were also justified. Numerical calculations of the stress–deformation scale of the initial state of the reservoir, based on the Biot model with the Kelvin–Voight rheological skeleton, were presented as a starting point for in-depth research on the scale of threats and risks to the reservoir. The presented numerical model can be a starting point for calculating the stability of a reservoir subjected to explosives. The facility constitutes a major element of Lubińsko-Głogowski Okręg Miedziowy (Lubin-Głogów Copper District). OUOW Żelazny Most is the biggest such facility in Europe and is utilized to collect tailing waist. When expanded in its southern quarter, the facility will be the biggest in the world.

6

SeKoZ - Ewaluacja usług ekosystemowych zieleni miejskiej w geoportalu przestrzennych zasobów pokrycia terenu oraz warunków glebowo-geologicznych

Bac-Bronowicz Joanna, Biernat Stanisław, Grzempowski Piotr, Uciechowska-Grakowicz Anna

Roczniki Geomatyki

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2020

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T. 18, z. 3(90)

187--197

PL

Celem projektu jest opracowanie systemu informatycznego "System oceny usług ekosystemowych zieleni miejskiej" (SekoZ). W procesie rozwoju systemu SekoZ wykorzystywana jest technologia GIS 3D, która umożliwi automatyczne modelowanie obiektów w miejskiej przestrzeni 3D oraz zastosowane zostanie modelowanie w wysokiej rozdzielczości parametrów meteorologicznych i parametrów jakości powietrza. Cel osiągnięty jest w wyniku następujących badań przemysłowych w zakresie automatyzacji inwentaryzacji ilościowej drzewostanów i innych struktur roślinnych w przestrzeni miejskiej w oparciu o technologię LIDAR oraz procedury analityczne w przestrzeni trójwymiarowej: badania wpływu zieleni miejskiej na jakość powietrza, temperaturę powietrza i retencję wody deszczowej. W ramach zadań związanych z pracami rozwojowymi realizowana będzie waloryzacja przestrzenna miasta w zależności od wartości wskaźników ilościowych usług ekosystemowych; opracowano prototyp oprogramowania, który automatyzuje inwentaryzację zieleni miejskiej.

EN

The aim of the project is to develop an IT system “System for evaluation of ecosystem services of urban greenery “(SekoZ). In the process of developing the SekoZ system, GIS 3D technology is used, which will enable automatic modelling of objects in urban 3D space, and high-resolution modeling of meteorological parameters and air quality parameters will be applied. The goal is achieved as a result of the following industrial research in the field of automation of quantitative inventory of tree stands and other plant structures in urban space based on LIDAR technology and analytical procedures in three-dimensional space: studies of the impact of urban greenery on air quality, air temperature and rainwater retention. Within the scope of tasks related to development works, the spatial valorisation of the city will be carried out depending on the value of quantitative indicators of ecosystem services; a software prototype has been developed that automates urban greenery inventory.

7

Regular polygons in 2D objects shape description

Kwinta Andrzej, Bac-Bronowicz Joanna

Geomatics, Landmanagement and Landscape

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2020

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no. 4

43--61

EN

Many real 3D objects have complex geometric shapes in various types of analyses. Image of these objects is recorded in the form of a 2D map. In the analysis, a simplification of this image to basic 2D figures with defined geometry is often needed. The paper presents an analysis of the geometry of a flat image (an image of a 3D object) using regular polygons. Geometry properties (F form, C centroid, S size) were determined to describe the object. Various criteria of selection of the ‘best’ regular n-sided polygon for a given 2D object (solved theoretically) were put forward. In the paper, criteria for describing a 2D object by regular n-sided polygons were defined on the basis of determining the measure of object shape elongation (e). In the ‘blind’ theoretical example, it was tested whether the individual shape measures listed in the paper allow for correct identification of the shapes of given 2D objects. The practical application of measures is illustrated by two actual examples. While in the first example the shape of the Canary Islands is analysed, the second example describes the shape of Poland’s borders. Actual examples deliver different results for different measures. In effect, there is no clear objective criterion for selecting a polygon shape. The simplifications of the shape of an object presented in the paper should not be equated with the object's generalization. Such simplifications are used in GIS to visualize geographic analyses based on the data available in the primary database, because the object will retain the character of the shape in the simplest possible geometry and neighborhood, and does not lose any of the scope and accuracy of the attributes assigned to a given object in the database.

PL

Wiele rzeczywistych obiektów 3D poddawanych różnym analizom ma skomplikowany kształt geometryczny. Obraz tych obiektów jest zapisany w postaci mapy 2D. Niejednokrotnie w trakcie analizy istnieje potrzeba uproszczenia tego obrazu do prostych figur 2D o zdefiniowanej geometrii. Autorzy pracy przedstawiają analizę geometrii obiektu płaskiego (obrazu obiektu 3D) poprzez wielokąty foremne. Określono własności geometrii służące do opisu obiektu (kształt F, położenie C, wymiar S). Przedstawiono różne kryteria (rozwiązania teoretyczne) doboru „najlepszego” wielokąta n foremnego dla danego obiektu 2D. W pracy zdefiniowano kryteria stosowania opisu obiektu 2D przez wielokąty n foremne na bazie wyznaczenia miary wydłużenia kształtu obiektu (e). W przykładzie teoretycznym „ślepym” sprawdzono, czy poszczególne wymienione w pracy miary kształtu prawidłowo identyfikują zadane kształty obiektów 2D. Praktyczne zastosowanie miar zostało zilustrowane dwoma przykładami praktycznymi. Przykład 1 dotyczy analizy kształtu wysp Kanaryjskich. Przykład praktyczny 2 dotyczy opisu kształtu granic Polski. Przykłady praktyczne dały różne wyniki dla różnych miar. Co powoduje brak jednoznacznego obiektywnego kryterium doboru kształtu wielokąta. Przedstawione w pracy uproszczenia kształtu obiektu nie należy utożsamiać z jego generalizacją. Tego rodzaju uproszczenia są używane w GIS do wizualizacji analiz geograficznych na podstawie danych dostępnych w bazie pierwotnej, gdyż obiekt zachowa charakter kształtu w możliwie prostej geometrii i sąsiedztwo, a nie traci nic z zakresu i dokładności atrybutów przypisanych do danego obiektu w bazie danych.