Hypervolume visualization: a challenge in simplicity

Hyper-volume visualization is designed to provide simple and fully explanatory images that give comprehensive insights into the global structure of scalar fields of any dimension. The basic idea is to have a dimension independent viewing system that scales nicely with the geometric dimension of the dataset and that can be combined with classical approaches like isocontouring and animation of slices of <i>n</i>.D data. We completely abandon (for core simplicity) rendering techniques, such as hidden surface removal or lighting or radiosity, that enhance three dimensional realism and concentrate on the real-time display of images that highlight structural (topological) features of the <i>n</i>D dataset (holes, tunnels, cavities, depressions, extrema, etc). Hyper-volume visualization on the one hand is a generalization of direct parallel projection methods in volume rendering. To achieve efficiency (and real-time performance on a graphics workstation) we combine the advantages of (i) a hierarchical representations of the hyper-volume data for multiresolution display and (ii) generalized object space splatting combined with texture-mapped graphics hardware acceleration. The development of a system that implements display techniques for multidimensional datasets requires careful design of both algorithms and user interfaces that scale linearly with the dimension n of the input geometric space. This is a major challenge since straightforward generalizations of standard techniques that are suitable for display of 3D data yield exceedingly intricate interfaces. For example, a view manipulation graphical user interface is usually based on a rotation of the object about Cartesian rotation axes, with possibly unit quaternions internal representations for the rotation group. Unfortunately the number of independent rotation axes grows quadratically with dimension(three in 3D to six in 4D to ten in 5D to fifteen in 6D space). Going back to the basics of parallel projections, we develop an alternative scheme that is very simple to implement and immediately gives a view manipulation graphical user interface that scales linearly with the dimension. One can still utilize matrix or quaternion or higher dimensional rotational group representations, internally for calculations.The main results of our paper are thus both a multi-resolution direct rendering algorithm and scalable graphical user interface that provides insightfull global views of scalar fields in any dimension, while maintaining the fundamental characteristics of ease of use, and quick exploratory