The quantitative assessment of the degree of order in a set of points is the subject of extensive investigation in discrete geometry. In this context, the Voronoi diagram finds applications across various fields, including medicine, biology, logistics, theoretical physics, and engineering. In the engineering domain, particularly in product design, the exploration of spatial order generates interest in the study and design of lattice structures or topological optimization. These specific applications contribute to enhancing certain characteristics of a structure or component, such as ergonomics, the quantity of material used, and mechanical properties. Delaunay triangulation, the dual of the Voronoi diagram, stands out as one of the most widely used algorithms for generating triangular meshes from point clouds. This work explores the analysis of primary entropic methods employed to evaluate the degree of order in Voronoi tessellation and Delaunay mesh. It Introduces an innovative approach centered on calculating the differential entropy of Voronoi seeds, which correspond to the vertices of Delaunay triangulation. The study shows the potential of the obtained results, both in terms of global and semi-local evaluations of the Delaunay mesh. It identifies novel usage scenarios within the context of product design. The results are thoroughly discussed and compared with other commonly utilized methodologies.

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Novel Differential Entropy-Based Approach for Delaunay Mesh Quality Assessment

  • Emmanuele Barberi,
  • Massimiliano Chillemi,
  • Filippo Cucinotta,
  • Felice Sfravara

摘要

The quantitative assessment of the degree of order in a set of points is the subject of extensive investigation in discrete geometry. In this context, the Voronoi diagram finds applications across various fields, including medicine, biology, logistics, theoretical physics, and engineering. In the engineering domain, particularly in product design, the exploration of spatial order generates interest in the study and design of lattice structures or topological optimization. These specific applications contribute to enhancing certain characteristics of a structure or component, such as ergonomics, the quantity of material used, and mechanical properties. Delaunay triangulation, the dual of the Voronoi diagram, stands out as one of the most widely used algorithms for generating triangular meshes from point clouds. This work explores the analysis of primary entropic methods employed to evaluate the degree of order in Voronoi tessellation and Delaunay mesh. It Introduces an innovative approach centered on calculating the differential entropy of Voronoi seeds, which correspond to the vertices of Delaunay triangulation. The study shows the potential of the obtained results, both in terms of global and semi-local evaluations of the Delaunay mesh. It identifies novel usage scenarios within the context of product design. The results are thoroughly discussed and compared with other commonly utilized methodologies.