Volume rendering techniques are conventionally classified as either direct or indirect methods. Indirect methods require to transform the initial volumetric model into an intermediate geometrical model in order to efficiently visualize it. In contrast, direct volume rendering (DVR) methods can directly process the volumetric data. Modern CT scanners usually provide data as a set of samples on a rectilinear grid, which is computed from the measured projections by discrete tomographic reconstruction. Therefore the rectilinear grid can already be considered as an intermediate volume representation. In this paper we introduce direct direct volume rendering (D2VR). D2VR does not require a rectilinear grid, since it is based on an immediate processing of the measured projections. Arbitrary samples for ray casting are reconstructed from the projections by using the Filtered Back-Projection algorithm. Our method removes a lossy resampling step from the classical volume rendering pipeline. It provides much higher accuracy than traditional grid-based resampling techniques do. Furthermore we also present a novel high-quality gradient estimation scheme, which is also based on the Filtered Back-Projection algorithm.