| Understanding geometric structures embedded in high dimensional spaces is a difficult and challenging task. A fundamental approach is to interactively search for informative low-dimensional projections. However, the manual interaction-based approach is limited in its scope, and often infeasible for exploring complex structures in very high dimensions.;We present a framework for visualizing and exploring high-dimensional geometry that employs an automatic method to expose interesting and informative projections of geometric structures. The method is based on optimizing a set of numerical measures or indices that recognize potentially significant geometric features and topological properties. Several such measures are presented and are used to identify informative projections. We investigate also the visualizability of the optimization problem itself to expose additional features of the viewfinding process.;Another component of the overall framework supports view exploration by navigating among optimal projections selected by the view-finding system. The problem of navigation and camera control in three dimensions is well understood; in higher dimensions, however, the problem of moving among viewpoints is complex. Our navigation and exploration framework is based on smooth interpolation of projection matrices corresponding to optimal views.;An important complementary problem is to evaluate the perceptual effectiveness of high-dimensional visualization methods. Preliminary studies suggest that naive observers can be trained to discriminate properties of objects projected in certain ways from four dimensions to three dimensions. |
