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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Nebojša Nikolić & Dragi Radomirović & Pavel Benka & Boris Stojić, 2025. "A Mathematical Model for Determining Coordinates of Points in a Desired Trimetric Projection of a Three-Dimensional Object," Mathematics, MDPI, vol. 13(6), pages 1-23, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:6:p:1006-:d:1616345
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    References listed on IDEAS

    as
    1. Shouxia Wang & Shuxia Wang & Weiping He, 2020. "Multistroke Grouping of Online Freehand Axonometric Sketches for Mechanical Models," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-13, May.
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