This paper presents an interactive global visualization technique for dense vector fields using levels of detail. We introduce a novel scheme which combines an error-controlled hierarchical approach and hardware acceleration to produce high resolution visualizations at interactive rates. Users can control the trade-off between computation time and image quality, producing visualizations amenable for situations ranging from high frame-rate previewing to accurate analysis. Use of hardware texture mapping allows the user to interactively zoom in and explore the data, and also to configure various texture parameters to change the look and feel of the visualization. We are able to achieve sub-second rates for dense LIC-like visualizations with resolutions in the order of a million pixels for data of similar dimensions. Categories and Subject Descriptors (according to ACM CCS): I.3 [Computer Graphics]: Applications