Клячин А.А. Triangulation of a flat region given in obj format

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https://doi.org/10.15688/mpcm.jvolsu.2025.4.3

Aleksey A. Klyachin
Doctor of Physical and Mathematical Sciences, Head of Department of Mathematical Analysis and Function Theory, Volgograd State University
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Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Abstract. This paper describes a method for triangulating a flat region defined by its boundary as a set of closed polygonal lines. Information about these lines is stored in verb’obj files. The algorithm is based on the idea of ??shifting the extreme points of the initial triangulation to the region’s boundary. To perform this shift, a single vector field directed toward the region’s boundary is constructed. Corresponding software was developed, and a triangulation of two regions, the boundaries of which were obtained through modeling in the verb’Blender environment, was constructed. The approach discussed in this paper enables the automation of the triangulation process without the labor-intensive step of writing out mathematical formulas defining the region’s boundary. The region is constructed in a visual modeling environment, and the file saved in verb’obj format is passed for processing to the algorithm presented in the paper, which completes the triangulation process.

Key words: triangulation of a region, shift of extreme nodes, computational grid, plane partitioning.

Triangulation of a flat region given in obj format by Клячин А.А.  is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Mathematical Physics and Computer Simulation. Vol. 28 No. 4 2025, pp. 43-53

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