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Abstract <p>The present paper suggests a new approach for geometric representation of 3D spatial models and provides a new compression algorithm for 3D meshes, which is based on the mathematical theory of convex geometry. In our approach, we represent a 3D convex polyhedron by means of planes, containing only its faces. This allows us not to consider topological aspects of the problem (connectivity information among vertices and edges) since by means of the planes, we construct the polyhedron uniquely. Due to the fact that the topological data is ignored, this representation provides a high degree of compression. Also, plane-based representation provides a compression of geometrical data because most of the faces of the polyhedron are not triangles but polygons with more than three vertices.</p>

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Coding and Compression of Three-Dimensional Meshes

  • 期刊论文

  • 发表日期：

    2026年3月1日

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  • Rafik Aramyan,
  • Gagik Mkrtchyan,
  • Arman Karapetyan

摘要

Abstract

The present paper suggests a new approach for geometric representation of 3D spatial models and provides a new compression algorithm for 3D meshes, which is based on the mathematical theory of convex geometry. In our approach, we represent a 3D convex polyhedron by means of planes, containing only its faces. This allows us not to consider topological aspects of the problem (connectivity information among vertices and edges) since by means of the planes, we construct the polyhedron uniquely. Due to the fact that the topological data is ignored, this representation provides a high degree of compression. Also, plane-based representation provides a compression of geometrical data because most of the faces of the polyhedron are not triangles but polygons with more than three vertices.