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1

Cartometric analysis of selected works by Leonardo da Vinci

Pędzich Paweł

Polish Cartographical Review

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2023

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Vol. 55, No. 1

1--10

EN

This research presents the results of the cartometric analysis of two Leonardo da Vinci’s works, i.e. the Mapa mundi and A map of Imola. The analysis of the Mapa mundi was conducted by employing various distortion measures and creating maps to show their distribution by distortion isograms. A map of Imola was analysed utilising MapAnalyst, taking advantage of the software’s tools, such as distortion grids, isolines of scale and local map rotation angles.

2

Koncepcja analitycznego odwzorowania kartograficznego o minimalnych zniekształceniach długości dla obszaru Polski

Kadaj Roman

Inżynieria i Budownictwo

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2023

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R. 79, nr 1-2

35--39

PL

W pracy przedstawiono koncepcję konforemnego, analitycznego i jednostrefowego odwzorowania i układu kartograficznego dla obszaru Polski, charakteryzującego się mniejszymi o ok. 50% zniekształceniami długości niż np. układ PL-1992. Proponowany układ może mieć zastosowanie w procesach projektowo-realizacyjnych obiektów o wysokiej precyzji geometrycznej (np. węzły kolejowe, obiekty przemysłowe).

EN

The paper presents the concept of a conformal, analytical and single-zone projection and cartographic system for the area of Poland, characterized by approx. 50% less length distortions than, for example, the PL-1992 system. The proposed system can be used in the design and implementation processes of objects with high geometric precision (e.g. railway junctions, industrial facilities).

3

Conformal projections of a tri-axial ellipsoid based on isometric coordinates: history, methodology, and examples

Pędzich Paweł

Polish Cartographical Review

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2022

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Vol. 54, No. 1

35--53

EN

The paper presents a review of the conformal projections of a tri-axial ellipsoid and the methodology of creating these projections with the use of isometric coordinates. The concept is very simple and has been known for a long time; if isometric coordinates are introduced on the surface of the original and on the plane of the image, then any analytical function of the complex variable, i.e. a function that has a continuous derivative, creates a conformal projection. The introduction presents the history of conformal projections. Then, existing projections are presented, including the Bugayevskiy projection and several projections developed by the author that apply selected functions of the complex variable. Scripts were prepared in the Octave software with the use of the presented methodology. Programming in Octave offers a possibility of a simple implementation of complex variable functions, which is also briefly discussed in the paper. The developed scripts were then used to perform calculations and to draw cartographic grids and distortion isolines in the selected conformal projections. The test object was the tri-axial ellipsoid that represents Phobos.

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

Image of the World on polyhedral maps and globes

Pędzich P.

Polish Cartographical Review

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2016

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Vol. 48, No. 4

197--210

EN

Application of polyhedrons as image surface in cartographic projections has a tradition of more than 200 years. The first maps relying on polyhedrons appeared in the 19th century. One of the first maps which based on an original polyhedral projection using a regular octahedron was constructed by the Californian architect Bernard Cahill in 1909. Other well known polyhedral projections and maps included Buckminster Fuller’s projection and map into icosahedron from 1954 and S. Waterman’s projection into truncated octahedron from 1996, which resulted in the “butterfly” map. Polyhedrons as image surface have the advantage of allowing a continuous image of continents of the Earth with low projection distortion. Such maps can be used for many purposes, such as presentation of tectonic plates or geographic discoveries. The article presents most well known polyhedral maps, describes cartographic projections applied in their preparation, as well as contemporary examples of polyhedral maps. The method of preparation of a polyhedral map and a virtual polyhedral globe is also presented.

6

Geoinformatyczne bezpośrednie opisywanie położenia

Pachelski W.

Geoinformatica Polonica

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2003

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T. 5

55-74

PL

Obszerna dziedzina modelowania informacji geograficznej ma na celu formułowanie w kategoriach informatycznych takich sformalizowanych opisów struktur informacyjnych, które mogłyby stanowić podstawę spójnych realizacji narzędziowych GIS w zróżnicowanych środowiskach oraz ułatwiać, a często nawet wręcz umożliwiać, komunikowanie informacji pomiędzy takimi realizacjami. Z tych względów dziedzina ta została objęta normalizacją w skali międzynarodowej (ISO), europejskiej (CEN), a ostatnio także krajowej (PKN). Przedmiotem niniejszego opracowania jest ta część metodologii modelowania informacji geograficznej, która dotyczy opisywania położenia obiektów geograficznych za pomocą współrzędnych w odpowiednio definiowanych systemach odniesienia. Przedstawia się w nim m.in.: 1. Niektóre pojęcia podstawowe i ich definicje, a mianowicie: - geodezyjny system odniesienia; układ odniesienia (datum), układ współrzędnych, odwzorowanie kartograficzne; 2. Skrótowy przegląd pojęć, metod i technologii geodezyjnych prowadzących zarówno do definiowania geodezyjnego systemu odniesienia, jak i położeń obiektów w tym systemie. 3. Podstawy notacji graficznej UML oraz diagram geodezyjnego systemu odniesienia, zapisany w tej notacji. Schemat pojęciowy bezpośredniego opisu położenia jest również przedstawiony w zapisie leksykalnym w języku EXPRESS. W opracowaniu wykorzystano normę międzynarodową ISO/FDIS 19111:2002 oraz Polską Normę PN-N-02270:2000.

EN

A large field of modelling geographic information aims at formulating in terms of computer science such formal descriptions of information structures, which could provide the basics for compatible implementations of GIS in diverse environments, as well as to facilitate, or even to make it possible, information communication or exchange between them. That is why the field became a subject of international (by the ISO), European (by the CEN) and national (Polish Committee ofStandardisation) activities. This paper deals with a part of the methodology of geographic information modelling, which concerns describing positions of geographic objects by means of co-ordinates in properly defined reference systems. There are considered, among others: 1. Some basic concepts and definitions, which include: geodetic reference system, datum, co-ordinate system, cartographic projection; 2. An overview of geodetic concepts, methods and technologies, which are used to define a geodetic reference system, as well as to determine object positions within it; 3. Basics of the graphic notation UML and a diagram of a geodetic reference system in this notation. A conceptual schema of a direct description of such a system is also presented in the lexical language EXPRESS. In the paper the International Standard ISO/FDIS 19111:2002 and the Polish Standard PN-N-02270:2000 have been used.