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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.