D4G framework: a novel Voronoi diagram classification for decoding natural geometrics to enhance the built environment

F Habib, NA Megahed, N Badawy… - Architectural Science …, 2024 - Taylor & Francis
This study enhances designers' ability to decode natural geometric patterns, simplify their
descriptions, and apply them to the built environment using Voronoi diagram (VD) …

On polynomials associated to Voronoi diagrams of point sets and crossing numbers

M Claverol, A de las Heras-Parrilla… - Discrete …, 2024 - dmtcs.episciences.org
Three polynomials are defined for given sets S of n points in general position in the plane:
The Voronoi polynomial with coefficients the numbers of vertices of the order-k Voronoi …

Voronoi Diagrams of Arbitrary Order on the Sphere

M Claverol, AH Parrilla, C Huemer - arxiv preprint arxiv:2207.13788, 2022 - arxiv.org
For a given set of points $ U $ on a sphere $ S $, the order $ k $ spherical Voronoi diagram
$ SV_k (U) $ decomposes the surface of $ S $ into regions whose points have the same $ k …

Properties for Voronoi diagrams of arbitrary order on the sphere

M Claverol Aguas… - The 38th European …, 2022 - upcommons.upc.edu
For a given set of points U on a sphere S, the order k spherical Voronoi diagram SV_k (U)
decomposes the surface of S into regions whose points have the same k nearest points of U …

[PDF][PDF] Special constructions to understand the structure of higher order Voronoi diagrams

M Claverol, A de las Heras-Parrilla… - XX Spanish Meeting on …, 2023 - egc23.web.uah.es
We study the structure of faces in Voronoi diagrams of order k, Vk (S), of sets S of n points in
the plane. While the number of faces of Vk (S) is well known, not so much is known about the …

Properties for Voronoi diagrams of arbitrary order in the sphere

A Heras Parrilla - 2021 - upcommons.upc.edu
In this thesis we study properties for spherical Voronoi diagrams of order $ k $, SV_k (U) $
using different tools: the geometry of the sphere, a labeling for the edges of $ SV_k (U) …