Interpolation of syzygies for implicit matrix representations - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2016

Interpolation of syzygies for implicit matrix representations

Résumé

We examine matrix representations of curves and surfaces based on syzygies and constructed by interpolation through points. They are implicit representations of objects given as point clouds. The corresponding theory, including moving lines, curves and surfaces, has been developed for parametric models. Our contribution is to show how to compute the required syzygies by interpolation, when the geometric object is given by a point cloud whose sampling satisfies mild assumptions. We focus on planar and space curves, where the theory of syzygies allows us to design an exact algorithm yielding the optimal implicit expression. The method extends readily to surfaces without base points defined over triangular patches. Our Maple implementation has served to produce the examples in this paper and is available upon demand by the authors.
Fichier principal
Vignette du fichier
EGK-syzygies16.pdf (287.19 Ko) Télécharger le fichier
EGK-syzygies16.bbl (4.17 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01421866 , version 1 (27-12-2016)

Identifiants

  • HAL Id : hal-01421866 , version 1

Citer

Ioannis Z. Emiris, Konstantinos Gavriil, Christos Konaxis. Interpolation of syzygies for implicit matrix representations. 2016. ⟨hal-01421866⟩
332 Consultations
138 Téléchargements

Partager

Gmail Facebook X LinkedIn More