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Radial Basis Functions (RBFs) have become a popular rendering primitive, both in surface and in volume rendering. This paper focuses on volume visualization, giving rise to 3D kernels. RBFs are especially convenient for the representation of scattered and irregularly distributed point samples, where the RBF kernel is used as a blending function for the space in between samples. Common representations employ radially symmetric RBFs, and various techniques have been introduced to render these, also with efficient implementations on programmable graphics hardware (GPUs). In this paper, we extend the existing work to more generalized, ellipsoidal RBF kernels, for the rendering of scattered volume data. We devise a post-shaded kernel-centric rendering approach, specifically designed to run efficiently on GPUs, and we demonstrate our renderer using datasets from subdivision volumes and computational science.