Derivatives of isogeometric functions on n-dimensional rational patches in Rd

As a first application of the presented formula we derive conditions which guarantee C1 and C2 smoothness for isogeometric functions on several singularly parametrized planar and volumetric domains as well as on embedded surfaces. It is interesting to note that the presented conditions depend not only on the general structure of the patch, but on the exact representation of the interior of the given geometry mapping.