Interpolation of syzygies for implicit matrix representations - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :

Interpolation of syzygies for implicit matrix representations

(1, 2) , (3) , (1, 2)
1
2
3

Abstract

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
Vignette du fichier
EGK-syzygies16.bbl (4.17 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)

Dates and versions

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

Identifiers

  • HAL Id : hal-01421866 , version 1

Cite

Ioannis Z. Emiris, Konstantinos Gavriil, Christos Konaxis. Interpolation of syzygies for implicit matrix representations. 2016. ⟨hal-01421866⟩
308 View
131 Download

Share

Gmail Facebook Twitter LinkedIn More