Multivariate Generalized Hermite Subdivision Schemes

Due to properties such as interpolation, smoothness, and spline connections, Hermite subdivision schemes employ fast iterative algorithms for geometrically modeling curves/surfaces in CAGD building wavelets numerical PDEs. In this paper, we introduce a notion of generalized (dyadic) then characterize their convergence, smoothness underlying matrix masks with or without interpolation properties. We also the linear-phase moments achieving polynomial-interpolation property. For any given integer $$m\in \mathbb {N}$$ , constructively prove that there always exist convergent smooth basis vector functions are $$\mathscr {C}^{m}(\mathbb {R}^d)$$ have linearly independent shifts. As by-products, our results resolve existence Lagrange, Hermite, Birkhoff schemes. Even dimension one significantly generalize extend many known on extensively studied univariate To illustrate theoretical provide examples symmetric having short support