4D to 3D Projection Animations

by John Dick

(5) Wheel Animation with added WY and XY Rotations

This animation shows added 180 degree WY and XY rotations of the viewpoint in 4D.

The thumbnail on the right shows the configuration halfway through the WY rotation where the W dimension is shown and the Y direction is "away".

This Animation

The rotations here are the same as for the previous animation, except that it's Y that turns into W rather than X. If you're having trouble following this one--during the WY rotation the top (orange) track is rotating "towards" you, eventually ending on the bottom.

(Following the discussion at the end of the previous animation.) Question: If you were controlling the motion of one of these wheel objects, how might you move your joystick to follow the various tracks?

Answer: Hard left or right on the bottom and top tracks; hard up or down on the 4 red tracks.

Beyond Wireframe

Might a true "picture" of a 4D world be possible if the objects were actual 4D solids, and not just line drawings? There's no computational problem in creating the 3D objects that would make up this picture. The problem is in the viewing of them. As mentioned previously here, a complete view could only be possible if everything were semi-transparent, allowing the viewer to perceive shading, shadows, and all the aspects of that drawing that allow us 3D folk to view into a 2D drawing to infer what is happening away from the viewer, in the 3rd dimension.

So, the problem is in the rendering--ordinary everyday 3D rendering. Not a 4D problem, but a 3D one. Creating a view of a 3D structure that shows all of the internal workings is not easy but it is not a a problem in principle. Of course, the "exploded view" showing an engine's parts won't do here--we need to preserve the geometry. And it may be that the transparency issue here is more difficult than has been previously dealt with.

However, imagine a view where the solids are strongly indicated on their boundaries, becoming more completely transparent as one moves into the solid, so as to allow a view of what's behind . . .