Multidimensional Transfer Functions for Volume Rendering

This chapter provides a detailed exposition of the multidimensional transfer function concept, a generalization of multidimensional transfer functions for both scalar and multivariate data as well as a novel technique for the interactive generation of volumetric shadows. To resolve the potential complexities in a user inter-face for multidimensional transfer functions, a set of direct manipulation widgets is introduced that make finding and experimenting with transfer functions an intuitive, efficient, and informative process. In order to make this process genuinely interactive, the chapter exploits the fast rendering capabilities of modern graphics hardware, especially 3D texture memory and pixel-texturing operations. Together, the widgets and the hardware form the basis for new interaction modes that can guide users towards transfer-function settings appropriate for their visualization and data-exploration interests. Using multidimensional transfer functions heightens the importance of densely sampling the voxel data in rendering. With each new axis in the transfer function, there is another dimension along which neighboring voxels can differ. It becomes increasingly likely that the data sample points at the corners of a voxel straddle an important region of the transfer function, such as a region of high opacity, instead of falling within it. Thus, in order for the boundaries to be rendered smoothly, the distance among view-aligned sampling planes through the volume must be very small.