preprints.org > computer science and mathematics > other > doi: 10.20944/preprints202311.0201.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 2 November 2023 / Approved: 3 November 2023 / Online: 3 November 2023 (04:19:05 CET)

Descriptive geometry has indispensable applications in many engineering activities, some of which are presented in the first chapter of this paper in order to place the development presented here among them. As a result of the continuous variability of the technological environment according to various optimization aspects, the engineering activities must also be continuously adapted to the changes, which an appropriate approach and formulation are required from the practitioners of descriptive geometry, and can even lead to improvement in the field of descriptive geometry. The imaging procedures are always based on the methods and theorems of descriptive geometry. Resolving contradictions in spatial geometry reconstruction research is a constant challenge, to which a possible answer in many cases is the search for the right projection direction. A special method of enumerating the possible infinite viewpoints for the representation of the surface edge curves is presented in another part of the paper. The procedure for determining the correct directions in a mathematically exact way is also presented through examples. The analysis and some of the results of the Monge mapping, which is suitable for the solution of a mechanical engineering task to be solved in a specific technical environment, are also presented.

tool wear measurement; CCD cameras positioning; digitized images; reconstruction problem; Monge mapping; projector lines; mathematical correspondence; directed angle triple; Monge cuboid; bijective subset

Computer Science and Mathematics, Other

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