Visualizing n-Dimensional Virtual Worlds with n-Visio n Steven Feine r Clifford Beshers Department of Computer Scienc e Columbia Universit y New York . New York 1002 7 1 Introductio n There are many applications in science, mathematics , statistics, and business, in which it is important to explore an d manipulate clam in more than three dimensions . In thes e applications, data can be defined by points in Euclidean n-space . A point's position is then specified with it coordinates . each o f which determines its position relative to one of It mutuall y perpendicular axes . We describe here research that has as its goa l the development of interaction techniques and metaphors for th e 4D and higher-dimensional worlds that this data represents . 2 The n-Vision Testbe d n-Vision is a testbed for exploring n-dimensional virtua l worlds . It relies . in part, on techniques for Iransforming an d displaying 4D objects in real-time using 3D graphics hardware, a s described in [BESI-I881 . The system supports techniques such a s "near" and "far" hyperplane clipping, and shading (includin g the use of color to accomplish 4D depth cueing, in which th
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