A low distortion conformal projection of a tri-axial ellipsoid and its application for mapping of extra-terrestrial objects

Pędzich, Paweł

doi:10.1016/j.pss.2019.104697

Cited by 3 publications

(2 citation statements)

References 8 publications

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“…These studies describe methods of creating maps that meet the requirements of Chebyshev's principle for various areas for an oblate ellipsoid. On the other hand, the work (Pędzich, 2019) describes the application of the theorem for mapping areas situated on a tri-axial ellipsoid.…”

Section: Modifications Of Azimuthal Projections Low-distortion Confor...mentioning

confidence: 99%

“…(13) According to the conformal projections theory (Pędzich, 2019) the scale of length distortions in the projection (12) takes the form: (14) where ds is the arc element on the original surface equal to: and ds' is the arc element on the image surface equal to . For the tri-axial ellipsoid and the method described here, the formula to calculate r has the following form (Bugayevskiy, 1998):…”

Section: Initial Information and Assumptions Concerning Conformal Pro...mentioning

confidence: 99%

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

Pędzich

2022

Polish Cartographical Review

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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.

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Section: Modifications Of Azimuthal Projections Low-distortion Confor...mentioning

confidence: 99%

Section: Initial Information and Assumptions Concerning Conformal Pro...mentioning

confidence: 99%

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

Pędzich

2022

Polish Cartographical Review

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Analytical and numerical methods of converting Cartesian to ellipsoidal coordinates

Πάνου

Korakitis

2021

Journal of Geodetic Science

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In this work, two analytical and two numerical methods of converting Cartesian to ellipsoidal coordinates of a point in space are presented. After slightly modifying a well-known exact analytical method, a new exact analytical method is developed. Also, two well-known numerical methods, which were developed for points exactly on the surface of a triaxial ellipsoid, are generalized for points in space. The four methods are validated with numerical experiments using an extensive set of points for the case of the Earth. Then, a theoretical and a numerical comparative assessment of the four methods is made. Furthermore, the new exact analytical method is applied for an almost oblate spheroid and for the case of the Moon and the results are compared. We conclude that, the generalized Panou and Korakitis’ numerical method, starting with approximate values from the new exact analytical method, is the best choice in terms of accuracy of the resulting ellipsoidal coordinates.

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Meridian section projections: a new class of the triaxial ellipsoid projections

Nyrtsov

Fleis

Sokolov

2021

G&C

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Historically the conformal projections have been used for mapping not only the Earth, but other celestial bodies as well. Their application enables preserving the shape of the relief features on the maps, which is extremely important for various analyses of celestial bodies’ surfaces. For many small bodies of the Solar system the International Astronomical Union recommends to apply a triaxial ellipsoid as a reference surface. But if the conformal projections for the reference surfaces of a sphere and an ellipsoid of revolution already exist, obtaining these projections for a triaxial ellipsoid will be significantly complicated, and the task of preserving the shape of relief features still actual. In general, the article deals with cylindrical and azimuthal projections of the meridian section for global mapping the celestial body surface in accordance with the idea formulated by prof. L. M. Bugaevsky. The projections are implemented for mapping of Phobos, moon of Mars.

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A low distortion conformal projection of a tri-axial ellipsoid and its application for mapping of extra-terrestrial objects

Cited by 3 publications

References 8 publications

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

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

Analytical and numerical methods of converting Cartesian to ellipsoidal coordinates

Meridian section projections: a new class of the triaxial ellipsoid projections

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