  We introduce new manifold-based splines that are able to exactly reproduce
B-splines on unstructured surface meshes. Such splines can be used in
isogeometric analysis (IGA) to represent smooth surfaces of arbitrary topology.
Since prevalent computer-aided design (CAD) models are composed of
tensor-product B-spline patches, any IGA suitable construction should be able
to reproduce B-splines. To achieve this goal, we focus on univariate
manifold-based constructions that can reproduce B-splines. The manifold-based
splines are constructed by smoothly blending together polynomial interpolants
defined on overlapping charts. The proposed constructions automatically
reproduce B-splines in regular parts of the mesh, with no extraordinary
vertices, and polynomial basis functions in the remaining parts of the mesh. We
study and compare analytically and numerically the finite element convergence
of several univariate constructions. The obtained results directly carry over
to the tensor-product case.
