Direct volume rendering of large volumetric data sets on programmable graphics hardware is often limited by the amount of available graphics memory and the bandwidth from main memory to graphics memory. Therefore, several approaches to volume rendering from compact representations of volumetric data have been published that avoid most of the data transfer between main memory and the graphics programming unit (GPU) at the cost of additional data decompression by the GPU. To reduce this performance cost, adaptive sampling techniques were proposed; which are, however, usually restricted to the sampling in view direction. In this work, we present a GPU-based volume rendering algorithm with adaptive sampling in all three spatial directions; i.e., not only in view direction but also in the two perpendicular directions of the image plane. This approach allows us to reduce the number of samples dramatically without compromising image quality; thus, it is particularly well suited for many comp...