Section:
New Results
-smooth splines on quad meshes with 4-split macro-patch elements
Participants :
Ahmed Blidia, Bernard Mourrain.
We analyze the space of differentiable functions on a quad-mesh
, which are composed of 4-split spline macro-patch
elements on each quadrangular face. We describe explicit transition
maps across shared edges, that satisfy conditions which ensure that
the space of differentiable functions is ample on a quad-mesh of
arbitrary topology. These transition maps define a finite dimensional
vector space of spline functions of bi-degree on each
quadrangular face of . We determine the dimension of this
space of spline functions for big enough and provide explicit
constructions of basis functions attached respectively to vertices,
edges and faces. This construction requires the analysis of the module
of syzygies of univariate b-spline functions with b-spline function
coefficients. New results on their generators and dimensions are
provided. Examples of bases of splines of small degree for
simple topological surfaces are detailed and illustrated by parametric
surface constructions.
This is a joint work with Nelly Villamizar