Interpolation of syzygies for implicit matrix representations

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.
Type de document :
Pré-publication, Document de travail
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Contributeur : Christos Konaxis <>
Soumis le : mardi 27 décembre 2016 - 19:09:34
Dernière modification le : mercredi 17 octobre 2018 - 17:02:07
Document(s) archivé(s) le : mardi 21 mars 2017 - 05:22:56


  • HAL Id : hal-01421866, version 1



Ioannis Emiris, Konstantinos Gavriil, Christos Konaxis. Interpolation of syzygies for implicit matrix representations. 2016. 〈hal-01421866〉



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