Mapping Worlds With Irregular Shapes

Abstract

Near‐spherical worlds may be mapped using conventional techniques, but many solar system objects with diameters less than 500 km have very irregular shapes and pose special problems for cartographers. I describe the history and current status of exploration and mapping of these bodies with emphasis on cartographic problems, their solutions, and unusual cases requiring novel approaches to mapping. These include binary and multi‐lobed objects, and faceted shapes for which near‐global maps may be simultaneously equivalent and conformal. On peut faire des cartes de corps célestes qui ont une forme presque sphérique en utilisant des techniques conventionnelles, mais la plupart des petits corps célestes (diamètre de moins de 500 km) sont loin d'être sphériques et présentent des problèmes particuliers pour les cartographes. Je discute de l'histoire et de l'état actuel de l'exploration et de la cartographie de ces corps célestes ‐ et j'examine de près les problèmes cartographiques, leurs solutions, et des cas particuliers qui doivent être examinés d'un nouveau point de vue. Ceux‐ci incluent les objets avec deux lobes ou plus ainsi que les formes à facettes, dont les cartes peuvent être équivalentes et conformes en même temps.

An illustrated introduction to general geomorphometry

“…Formulae for the solution of this problem are used to determine parameters of moving windows in morphometric calculations (Florinsky, 2017a). At the same time, it is advisable to apply a triaxial ellipsoid for describing forms of small moons and asteroids (Bugaevsky, 1999; Stooke, 1998; Thomas, 1989). However, for the case of a triaxial ellipsoid, solutions of the inverse geodetic problem are presented in general form only (Bespalov, 1980; Jacobi, 1839; Karney, 2012; Krasovsky, 1902; Panou, 2013; Shebuev, 1896).…”

Assessing mango anthracnose using a new three‐dimensional image‐analysis technique to quantify lesions on fruit

“…The accuracy of the method also depends on the number of images forming the pseudocylindrical projection, and the correction performed to compensate for the distortion required for a 3D irregular surface projected in a two‐dimensional map (Stooke, 1998). In this work, a maximal rotation resolution of 1° was used to create a highly accurate projection from 360 images.…”

“…However, this kind of projection is not of the equal‐area type. Here we describe the implementation of an equal‐area pseudocylindrical projection that takes into account the three‐dimensional irregularities (Stooke, 1998) of each particular fruit, correcting the vertical and horizontal area deformations due to the inherent curves of the fruit envelope.…”