In the field of scientific visualization, the term
"four dimensional visualization" usually refers to the process of rendering a
three dimensional field of scalar values. While this paradigm applies to many
different data sets, there are also uses for visualizing data that correspond to
actual four-dimensional structures. Four dimensional structures have typically
been visualized via wireframe methods, but this process alone is usually
insufficient for an intuitive understanding; all but the most simple datasets
easily overwhelm the viewer. This research covers the visualization of four
dimensional objects through wireframe methods with extended visualization cues,
and through raytracing methods. Both the wireframe and raytracing methods employ
true four-space viewing parameters and geometry. The raytracing approach easily
solves the hidden surface and shadowing problems of 4D objects, and yields an
image in the form of a three-dimensional field of RGB values, which can be
rendered with a variety of existing methods. The 4D raytracer also supports true
four-dimensional lighting, reflections and refractions.