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

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.