Presented in this work is the Non-Cartesian Distributed Approximation Functional (NCDAF). It is a multi-dimensional generalization of the (one-dimensional) Hermite DAF that is non-separable and isotropic. Demonstrated here is an approximation method based on the NCDAF that can construct a continuous approximation of a function and derivatives from a discrete sampling of points. Under appropriate choice of conditions this approximation is free from artifacts originating from (1) the sampling scheme, and (2) the orientation of the sampled data. The NCDAF is also viewed as a compromise between the minimum uncertainty state (i.e. Gaussian) and the ideal filter. The NCDAF (kernel) is shown (1) to have a very small uncertainty product, (2) to be infinitely smooth, (3) to possess the same set of invariances as the minimum uncertainty state, (4) to propagates in convenient closed form under quantum mechanical free propagation, and (5) can be made arbitrarily close to the ideal filter.