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Simplification of 2D shapes with equivalent rectangles

Kwinta Andrzej, Bac-Bronowicz Joanna

Advances in Geodesy and Geoinformation

2022

Vol. 71, no. 1

art. no. e14, 2022

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.

3D representation of geological observations in underground mine workings of the Upper Silesian Coal Basin

Marcisz M., Probierz K., Ostrowska-Łach M.

Journal of Sustainable Mining

2018

Vol. 17, iss. 1

34--39

The purpose of the paper is to present the possibilities of the three-dimensional representation of geological strata in underground (access) workings in a hard coal deposit in the SW part of the Upper Silesian Coal Basin, using CAD software and its flagship program AutoCAD. The 3D visualization of the results of underground workings’ mapping is presented and illustrated on two opening out workings (descending galleries). The criteria for choosing these workings were based on their length and the complexity of geological settings observed while they were driven. The described method may be applied in spatial visualization of geological structures observed in other deposits, mines and existing workings (it is not applicable for designing mine workings), also beyond the area of the Upper Silesian Coal Basin (USCB). The method presented describes the problem of the visualization of underground mine workings in a typical geological aspect, considering (aimed at) detailed visualization of geological settings revealed on the side walls of workings cutting the deposit.