by quickfur » Thu Jan 14, 2016 12:20 am
Yeah I think any projection-based 4D visualization method must, at the very least, be based on polygon-rendering rather than wireframe renderings. However, polygon renderings are more tricky to program, and one runs into performance issues, such as the large number of polygons that need to be drawn, how to clip 4D and 3D volumes in real-time, as well as clarity issues (generally, after about 3-4 layers of filled polygons, the visual field is saturated and any deeper polygons will likely be either invisible, or clutter up the image and make it incomprehensible).
Of course, even after those obstacles are overcome, there's still the problem of features of the projections that are 4D-specific, with no direct 3D analogue, so our brain has a hard time interpreting them. One prominent example of this is when you're looking down a corrider that has a T-junction opening into a perpendicular corridor. In the analogous 3D situation, you'd see 3 elements of the opening: part of the side corridor's ceiling, floor, and far wall. Because of this, our brain has come to expect exactly one of each element when recognizing a side corridor. However, in 4D, there are not 3, but 5 visible elements: the first 3 have 3D analogues: part of the side corridor's ceiling, floor, and the far wall. But parts of two of the side walls are also visible! This is something with no direct analogue in 3D, and it looks very confusing to our 3D-centric brain. What happens next is that our brain says "square tube surrounded by 2 side elements, a ceiling, and a floor -- that's not a corridor, that's a tube floating in space". So it fails to recognize the "square tube" as the far wall of a side corridor.
Even after you have trained yourself to interpret this combination of elements differently, the instinct of "X surrounded by sides, top, bottom elements == protruding object" is so strong, that you'd probably just lapse into thinking about it abstractly, rather than truly visualizing the side-corridor for what it is. The most common misinterpretation at this point is to equate the square tube (i.e., the far wall of the side corridor) with the corridor itself, rather than a wall that's part of the real corridor. So far, I have not been able to truly surmount this difficulty mentally, without using abstract analogies as workarounds.