Geometrically continuous splines for surfaces of arbitrary topology - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Computer Aided Geometric Design Year : 2016

Geometrically continuous splines for surfaces of arbitrary topology


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.
Fichier principal
Vignette du fichier
paper-hal.pdf (557.84 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-01196996 , version 1 (10-09-2015)
hal-01196996 , version 2 (23-03-2016)




Bernard Mourrain, Raimundas Vidunas, Nelly Villamizar. Geometrically continuous splines for surfaces of arbitrary topology. Computer Aided Geometric Design, 2016, 45, pp.108-133. ⟨10.1016/j.cagd.2016.03.003⟩. ⟨hal-01196996v2⟩
752 View
318 Download



Gmail Mastodon Facebook X LinkedIn More