unitile2d - makes uniform tilings on a surface
unitile2d [options] [pattern]
Makes uniform tilings on a surface. Surfaces include plane or cylinder
section, torus, Klein bottle, and many others.
- pattern
- Patterns are (default: 1)
- 1 - 4,4,4,4 {4,4}
- 2 - 3,3,3,3,3,3 {3,6}
- 3 - 6,6,6 {6,3}
- 4 - 3,6,3,6
- 5 - 3,3,3,4,4
- 6 - 3,3,4,3,4
- 7 - 3,3,3,3,6
- 8 - 3,12,12
- 9 - 4,8,8
- 10 - 3,4,6,4
- 11 - 4,6,12
- -h
- program help
- -s <type>
- surface type, and any extra options for the surface
- p - plane (default)
- c - conical frustum (-R bottom radius, -r top radius, -d height, -T X,Y,0)
- m - mobius strip (-R ring radius, -r strip width, -T X,0,0)
- t - torus (-R ring radius, -r tube radius. -T X,Y,0)
- k - Klein bottle (-r tube radius, -T X,0,0)
- K - figure-8 Klein bottle (-R ring radius, -r tube radius, -T X,0,0)
- C - cross-cap (needs tile vertices at tiling rectangle corners)
- w - cross-cap (does not preserve tiling, only works with pattern 1!)
- r - Roman (does not preserve tiling)
- b - Boy's (does not presere tiling)
- R - Roman to Boy's (-d stage of tansformation, range 0.0-1.0, does not preserve tiling)
- x - 4D torus (-W rotatation in 4D before projection onto xyz, -T X,Y,0)
- R - 4D Klein bottle (-W rotatation in 4D before projection onto xyz)
- -w <width>
- width of tiling (default: 20)
- -l <height>
- height of tiling (default: width)
- -g
- use given height and width, don't increase to make
rectangular tile
- -R <radius>
- "major" radius of surface
- -r <radius>
- "minor" radius of surface
- -d <dist>
- distance (see particular surface)
- -T <tran>
- translation of pattern, three numbers separated by commas which are
used as the x, y and z displacements
- -S <X,Y>
- "shear" the base rectangular tiling pattern by X units in the
w direction and Y units in the l direction (used with -s t)
- -W <rot4d>
- rotation of 4D surface before projection, six angles
separated by commas to rotate in planes xy,yz,zw,wx,xz,yw
- -o <file>
- write output to file, if this option is not used
the program writes to standard output
Display a chunky figure-8 Klein bottle
unitile2d -s K -R 1.5 6 | off_color -f N -s 5 | antiview
Display the Roman surface, using a larger number of tiles
unitile2d -s r -l 40 -w 40 9 | off_color -f N -s 2 | antiview
This program is work in progress, and may change considerably in
future releases.
If a pattern doesn't mesh on a surface you may have to change options
-l or -w slightly. Pattern 7 won't mesh on any non-orientable surface.
Using values for option -T which are inappropriate for a particular
surface may cause the tiling not to mesh.
Some of the projective plane surfaces don't preserve the tiling as
they map a line of the tiling rectangle onto a single point of the
surface.
Unused options are silently ignored.
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