Many large scale physics-based simulations which take place on PC clusters or supercomputers produce huge amounts of data including vector fields. While these vector data such as electromagnetic fields, fluid flow fields, or particle paths can be represented by lines, the sheer number of the lines overwhelms the memory and computation capability of a high-end PC used for visualization. Further, very dense or intertwined lines, rendered with traditional visualization techniques, can produce unintelligible results with unclear depth relationships between the lines and no sense of global structure. Our approach is to apply a lighting model to the lines and sample them into an anisotropic voxel representation based on spherical harmonics as a preprocessing step. Then we evaluate and render these voxels for a given view using traditional volume rendering. For extremely large line based datasets, conversion to anisotropic voxels reduces the overall storage and rendering for O(n) lines to O(1) with a large constant that is still small enough to allow meaningful visualization of the entire dataset at nearly interactive rates on a single commodity PC.