Coding and Compression of Three Dimensional Meshes by Planes

TL;DR

This paper introduces a novel geometric representation and compression algorithm for 3D convex polyhedra using planes, which simplifies topology and enhances compression efficiency.

Contribution

The paper presents a new plane-based representation for 3D convex polyhedra that ignores topological data, enabling high compression and simplified geometric encoding.

Findings

High compression rates achieved by ignoring topological data.

Efficient encoding of polygonal faces with more than three vertices.

Unique reconstruction of polyhedra from plane-based representation.

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 mathematical theory of convex geometry. In our approach we represent a 3D convex polyhedron by means of planes, containing only its faces. This allows 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 high degree of compression. Also planes 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.