Geometrically continuous splines for surfaces of arbitrary topology

Abstract : We analyze the space of geometrically continuous piecewise polynomial functions or splines for quadrangular and triangular patches with arbitrary topology and general rational transition maps. To define these spaces of G 1 spline functions, we introduce the concept of topological surface with gluing data attached to the edges shared by faces. The framework does not require manifold constructions and is general enough to allow non-orientable surfaces. We describe compatibility conditions on the transition maps so that the space of differentiable functions is ample and show that these conditions are necessary and sufficient to construct ample spline spaces. We determine the dimension of the space of G 1 spline functions which are of degree k on triangular pieces and of bi-degree (k, k) on quadrangular pieces, for k big enough. A separability property on the edges is involved to obtain the dimension formula. An explicit construction of basis functions attached respectively to vertices, edges and faces is proposed and examples of bases of G 1 splines of small degree for topological surfaces with boundary and without boundary are detailed.
Type de document :
Article dans une revue
Computer Aided Geometric Design, Elsevier, 2016, 45, pp.108-133. 〈10.1016/j.cagd.2016.03.003〉
Liste complète des métadonnées
Contributeur : Bernard Mourrain <>
Soumis le : mercredi 23 mars 2016 - 11:09:23
Dernière modification le : mercredi 10 octobre 2018 - 10:10:36
Document(s) archivé(s) le : lundi 14 novembre 2016 - 02:03:53


Fichiers produits par l'(les) auteur(s)


Distributed under a Creative Commons Paternité - Pas d'utilisation commerciale - Pas de modification 4.0 International License



Bernard Mourrain, Raimundas Vidunas, Nelly Villamizar. Geometrically continuous splines for surfaces of arbitrary topology. Computer Aided Geometric Design, Elsevier, 2016, 45, pp.108-133. 〈10.1016/j.cagd.2016.03.003〉. 〈hal-01196996v2〉



Consultations de la notice


Téléchargements de fichiers