Multidimensional transfer functions for interactive volume rendering

Most direct volume renderings produced today employ one-dimensional 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, multidimensional 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 one dimension, let alone two or three dimensions. This paper demonstrates an important class of three-dimensional transfer functions for scalar data, and describes the application of multidimensional 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.