The immersive visualization probe for exploring n-dimensional spaces

A new tool uses two types of dimensional navigation to display continuous 4D subsets of n-dimensional data. Thanks to the tool's embedded coordinate systems, researchers can better understand a model's underlying physical or mathematical process. Here, we describe a new method for visualizing data structure or models defined in higher-dimensional spaces. This technique is suitable for applications in which a scalar function, defined mathematically or procedurally, depends on n variables or parameters. The function's values essentially describe a set of points in n-dimensional space. To visualize these sets, we fix all but three of the parameters and then sample the resulting 4D set (the three parameters and the function's resulting value) on several discrete grids located on planes in the 3D space. We compose the image by using color to represent the fourth dimension (the function's value) at discrete locations on these grids. Interactive control over the way the parameters are fixed results in a highly dynamic system that researchers can easily use to explore the n-dimensional space's structure.