Higher dimensional oogl objects...

[daeron]

This letter is in response to several inquiries I've received about creating a new oogl
format to handle higher dimensional objects. Here is my first stab at it. The format
doesn't really do much to resolve the solidity of the object since it merely stores
information up to one dimension less than the object itself. However, this could
perhaps be fixed by inserting a flag of some sort to indicate whether the object is hollow
or not. Geomview could interpret this by making the screen turn black whenever our
viewpoint enters the object (not particularly beneficial as far as I can see). The only
other use I can see for keeping track of solidity is for deciding what the object will
look like after being clipped, but this could just as easily be a flag directly to the clip
program. Anyway, take a look at the format and tell me what you think.

------ Cut Here ------

           # Sample of new format with a hypercube.

NOFF 4     # N-dimensional object, in this case 4.
16 32 24 8 # 16 vertices, 32 edges, 24 faces, 8 hyperfaces

# First, vertices:

-1 -1 -1 -1
-1 -1 -1  1
-1 -1  1 -1
-1 -1  1  1
-1  1 -1 -1
-1  1 -1  1
-1  1  1 -1
-1  1  1  1
 1 -1 -1 -1
 1 -1 -1  1
 1 -1  1 -1
 1 -1  1  1
 1  1 -1 -1
 1  1 -1  1
 1  1  1 -1
 1  1  1  1

# Then, edges specified by two connected vertices:

0 2
2 10
10 8
8 0
4 6
6 14
14 12
12 4
0 4
2 6
10 14
8 12
1 3
3 11
11 9
9 1
5 7
7 15
15 13
13 5
1 5
3 7
11 15
9 13
0 1
2 3
10 11
8 9
4 5
6 7
14 15
12 13

# Then, faces specified by connected edges:
# in this case always 4 edges, since each face of a hypercube is a square

0 1 2 3
4 5 6 7
0 9 4 8
1 10 5 9
2 11 6 10
3 8 7 11
12 13 14 15
16 17 18 19
12 21 16 20
13 22 17 21
14 23 18 22
15 20 19 23
0 25 12 24
1 26 13 25
2 27 14 26
3 24 15 27
16 29 4 28
17 30 5 29
18 31 6 30
19 28 7 31
8 24 20 28
9 25 21 29
10 26 22 30
11 27 23 31

# Then, hyperfaces specified by connected faces:
# always 6 faces since each hyperface is a cube

0 1 2 3 4 5
6 7 8 9 10 11
0 6 12 13 14 15
1 7 16 17 18 19
2 8 20 12 21 16
3 9 21 13 22 17
4 10 22 14 23 18
5 11 23 15 20 19

# After this we could have hyper-hyper faces and so on for higher dimensions.