Klyachin V.A. Chain Algorithm for Compressing 3D-Models

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https://doi.org/10.15688/mpcm.jvolsu.2025.2.2

Vladimir A. Klyachin
Doctor of Sciences (Physics and Mathematics), Head of the Department of Computer Sciences and Experimental Mathematics, Volgograd State University
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https://orcid.org/0000-0003-1922-7849
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Abstract. The article describes in detail the algorithm for compressing information about the geometric structure of three-dimensional spatial models and multidimensional triangulations based on the use of adjacency of faces. This algorithm transforms a set of 3D-model faces into a list of chains sequentially located in space and adjacent to each other. Information compression occurs due to the absence of duplication of the numbers of vertices that form the model faces. The algorithm described in the article consists of three main parts. In the first part, a special graph of faces is constructed based on the set of model faces, the edges of the graph correspond to adjacent faces. Using the algorithm of traversal of graph vertices in depth, this graph is divided into simple chains. The second part of the algorithm transforms each chain of the graph into a sequence of numbers of vertices participating in the formation of the faces of this chain. The third part of the algorithm is designed to perform the reverse action – to translate the constructed sequence of vertex numbers back into sets of tuples consisting of the numbers of vertices that form the faces of the 3D-model. This algorithm is also extended to the case of spatial triangulations of polygonal areas. The software implementation of the algorithm for the special case of 3D-models is made in the form of built-in modules in the Blender program. The archives of the modules are freely available in the repository of the author of the article at https://github.com/KlyachinVA/LocFile.

Key words: triangulation, model graph, face chain, depth-first graph traversal, face adjacency.

Chain Algorithm for Compressing 3D-Models by Klyachin V.A.   is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Mathematical Physics and Computer Simulation. Vol. 27 No. 4 2024, pp. 15-26

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