quickfur wrote:Wait, isn't cavalier projection just a kind of oblique projection? This can be done easily, of course. Now, understanding the result would be another matter, though. :-) Although, I did use oblique projections in my mind to visualize some of the tetracube-based uniform polychora (such as the runcinated/cantellated tesseracts, and other such cuties).
Dont know exactly about the naming, but for 3d->2d cavalier perspective is putting x and y as usual an z in 45 degrees between them. x and y has original length and z has half the length. So in 4d->3d you put x, y, z as usual and w in same angle to x,y,z. x,y,z in original length w in half the original length. This induces parallel lines remaining parallel after projection. I think its not even a parallel projection for any viewing angle. For an overview of axonometric projections look here.
Yes, cavalier perspective is how one usually draws a cube on paper. Two equally sized squares shifted half the edge length in 45 degrees. In 4d building blocks for example (where you can switch the 4d->3d projection type) the scene looks much more neatly with cavalier or similar projections where parallel lines remain parallel after projection.
In the next time I will add occlusion culling there, though I fear it will be quite slow.
Recently, much to my joy, I discovered that the "polytopes" hack in xscreensaver actually implements transparent surfaces for viewing the regular 4-polytopes!!
Will have a look at it, though linux is not my main system.
I also remember some guy named Tuvel, who used to post here, who had a website with animations of various polytopes using glass-like material for rendering polygons. Unfortunately, the website no longer exists, and I've been unable to find those animations anywhere else (except for the precious few I downloaded locally).
Damn, thats really a pitty. Can you make your (precious) downloaded ones available online? Am actually indeed intend to make a real world model of an impossible tesseract with glass or some transparent material. Would be interesting to know how much transparency helps understanding, or whether the transparency is rather irritating.
The other question about transparency is whether, one should really make the 3d facets transparent or only the 2d faces. Because making the 3d facets transparent could imho lead to something grey in grey (because every point in a 3d volume would then lower light intensity, contrary to only the points of its surface), and probably objects of complex scenes are no more discernable.
Though of course even opaque 2d faces are for a tetrionian kind of wireframe, so he would anyway look through.