It is shown that there is an optimal finite linear combination of B-splines, denominated modified B-splines, such that a pertinent low frequency condition called M−flatness is satisfied. A profound relationship of the modified B-splines with the Beta distribution implies an asymptotic sampling theorem with exact reconstruction requiring only small oversampling.

This paper presents a new kind of uniform splines, called hyperbolic polynomial B-splines, generated over the space Ω = span{sinh t, cosh t, tk−3, tk−4, . . . , t,1} in which k is an arbitrary integer larger than or equal to 3. Hyperbolic polynomial B-splines share most of the properties as those of the B-splines in the polynomial space. We give the subdivision formulae for this new kind of cur...

Easy to construct and optimally convergent generalisations of B-splines unstructured meshes are essential for the application isogeometric analysis domains with non-trivial topologies. Nonetheless, especially hexahedral meshes, construction smooth basis functions is still an open question. We introduce a simple partition unity that yields blended B-splines, referred as SB-splines, on semi-struc...