In this paper we present a novel framework for direct volume rendering using a splatting approach based on elliptical Gaussian kernels. To avoid aliasing artifacts, we introduce the concept of a resampling filter combining a reconstruction with a low-pass kernel. Because of the similarity to Heckbert\'s EWA (elliptical weighted average) filter for texture mapping we call our technique EWA volume splatting. It provides high image quality without aliasing artifacts or excessive blurring even with non-spherical kernels. Hence it is suitable for regular, rectilinear, and irregular volume data sets. Moreover, our framework introduces a novel approach to compute the footprint function. It facilitates efficient perspective projection of arbitrary elliptical kernels at very little additional cost. Finally, we show that EWA volume reconstruction kernels can be reduced to surface reconstruction kernels. This makes our splat primitive universal in reconstructing surface and volume data.