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D4G framework: a novel Voronoi diagram classification for decoding natural geometrics to enhance the built environment
This study enhances designers' ability to decode natural geometric patterns, simplify their
descriptions, and apply them to the built environment using Voronoi diagram (VD) …
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 …
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 …
$ 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 …
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 …
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) …
using different tools: the geometry of the sphere, a labeling for the edges of $ SV_k (U) …