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Most direct volume renderings produced today employ 1D transfer functions which assign color and opacity to the volume based solely on the single scalar quantity which comprises the data set. Though they have not received widespread attention, multi-dimensional transfer functions are a very effective way to extract materials and their boundaries for both scalar and multivariate data. However, identifying good transfer functions is difficult enough in 1D, let alone 2D or 3D. This paper demonstrates an important class of 3D transfer functions for scalar data, and describes the application of multi-dimensional transfer functions to multivariate data. We present a set of direct manipulation widgets that make specifying such transfer functions intuitive and convenient. We also describe how to use modern graphics hardware to both interactively render with multidimensional transfer functions and to provide interactive shadows for volumes. The transfer functions, widgets and hardware combine to form a powerful system for interactive volume exploration.