A Mathematical Model for Determining Coordinates of Points in a Desired Trimetric Projection of a Three-Dimensional Object

Nebojša Nikolić, Dragi Radomirović, Pavel Benka and Boris Stojić ()
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Nebojša Nikolić: Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21102 Novi Sad, Serbia
Dragi Radomirović: Faculty of Agriculture, University of Novi Sad, Trg Dositeja Obradovića 8, 21102 Novi Sad, Serbia
Pavel Benka: Faculty of Agriculture, University of Novi Sad, Trg Dositeja Obradovića 8, 21102 Novi Sad, Serbia
Boris Stojić: Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21102 Novi Sad, Serbia

Mathematics, 2025, vol. 13, issue 6, 1-23

Abstract: The aim of this paper is to develop a mathematical model for determining coordinates of points in a desired trimetric projection of a three-dimensional object. The desired trimetric projection is quantitatively specified according to the observer’s preference to emphasize one face of the object more than another. Within the mathematical model, equations defining the interdependencies of trimetric parameters are derived first. It is then demonstrated how the projection of an arbitrary point of the observed object can be determined based on these trimetric parameters. Subsequently, equations are derived that enable the calculation of the necessary trimetric parameters to achieve a desired projection. By employing the developed model, one can accurately determine the coordinates of points in the desired trimetric projection, provided that the corresponding spatial coordinates are known, as demonstrated through several examples.

Keywords: trimetric projection; trimetric parameters; axonometry; mathematical model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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