Pencils of CGA for Voronoi and Power Diagrams - Archive ouverte HAL
Communication Dans Un Congrès Année : 2024

Pencils of CGA for Voronoi and Power Diagrams

Faiceaux de CGA pour les diagrammes de Voronoi et les power diagrammes

Stéphane Breuils
Venceslas Biri
Vincent Nozick

Résumé

Geometric Algebra can be considered as a very useful language for dealing with mathematics, physics and computer science. Among the various algebras commonly used by practitioners of GA, Conformal Geometric Algebra (CGA) is of special interest for its powerful transformations and its ability to represent any hypersphere or hyperplane. Moreover, CGA is an algebra capable of representing pencils of hyperspheres. This paper presents an approach for constructing Voronoi diagrams by using pencils of CGA to build cell interfaces from centroid positions. Power, multiplicatively weighted Voronoi and multiplicatively weighted power diagrams are also supported by the presented method. This allows the use of circles as centroids to add control to the weights of the cells and to the curvatures of their borders.
Fichier principal
Vignette du fichier
camera-ready-engage24.pdf (424.03 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-04636752 , version 1 (05-07-2024)

Licence

Identifiants

  • HAL Id : hal-04636752 , version 1

Citer

Clément Chomicki, Stéphane Breuils, Venceslas Biri, Vincent Nozick. Pencils of CGA for Voronoi and Power Diagrams. CGI ENGAGE 2024, Jul 2024, Genève, Switzerland. ⟨hal-04636752⟩
35 Consultations
19 Téléchargements

Partager

More