Earlier this year, I started working through the online book Ray Tracing In One Weekend (Book 1). I have been following along with it in Common Lisp, and I have been extending it all from 3-dimensional to n-dimensional.

I reproduced 4-dimensional versions of all of the book images which you can see on my weekend-raytracer github page.

Here is the final image. This is a 250-samples-per-pixel, 640x360x10 image plane of three large hyperspheres (one mirrored, one diffuse, one glass) atop a very large, diffuse hypersphere. Also atop this very large hypersphere are a bunch of smaller hyperspheres of varying colors and materials. The image is rendered with some defocus-blur.

Final image of 4-dimensional scene

Caveat: This depends on a patched version of the policy-cond library that is not in the current Quicklisp distribution but should be in the next.

A machine-implemented display method that, with respect to a volume dataset being rendered, enables a user to navigate to any position in space and look in any direction. Preferably, the volume dataset is derived from a computer tomography (CT) or magnetic resonance imaging (MRI) scan. With the described approach, the user can see details within the dataset that are not available using conventional visualization approaches. The freedom-of-motion capability allows the user to go to places (positions) within the volume rendering that are not otherwise possible using conventional “orbit” and “zoom” display techniques. Thus, for example, using the described approach, the display image enables a user to travel inside physical structures (e.g., a patient's heart, brain, arteries, and the like).