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

<p>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.</p>
</abstract>

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.

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

Faculty of Geodesy and Cartography Department of Cartography Warsaw

Polish Cartographical Review

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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...

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

Published Online: Sep 08, 2022

Page range: 35 - 53

Received: May 25, 2022

Accepted: Jul 21, 2022

DOI: https://doi.org/10.2478/pcr-2022-0004

Keywords
cartographic projections, conformal projections, conformal coordinates, tri-axial ellipsoid

© 2022 Paweł Pędzich, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Sep 08, 2022

Page range: 35 - 53

Received: May 25, 2022

Accepted: Jul 21, 2022

DOI: https://doi.org/10.2478/pcr-2022-0004

Keywordscartographic projections, conformal projections, conformal coordinates, tri-axial ellipsoid

© 2022 Paweł Pędzich, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
cartographic projections, conformal projections, conformal coordinates, tri-axial ellipsoid