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unitile2d - make uniform tilings on a surface

Usage    |    Examples    |    Notes


Usage: unitile2d [options] [pattern]

Makes uniform tilings on a surface. Surfaces include plane or cylinder
section, torus, Klein bottle, and many others.
Patterns are (default: 1)
   1 - 4,4,4,4      {4,4}    5 - 3,3,3,4,4      9  - 4,8,8
   2 - 3,3,3,3,3,3  {3,6}    6 - 3,3,4,3,4      10 - 3,4,6,4
   3 - 6,6,6        {6,3}    7 - 3,3,3,3,6      11 - 4,6,12
   4 - 3,6,3,6               8 - 3,12,12

  -h,--help this help message (run 'off_util -H help' for general help)
  --version version information
  -s <type> surface type:
        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)
        T - trefoil (-R ring radius, -r tube radius. -T X,Y,0, -d N,D)
        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
        y - 4D Klein bottle (-W rotatation in 4D before projection onto xyz)
  -w <wdth> width of tiling (default: 20)
  -l <ht>   height of tiling (default: width)
  -g        use given height and width, don't increase to make
            rectangular tile
  -r <rad>  'minor' radius of surface
  -R <rad>  'major' radius of surface
  -d <dist> height of conic frustrum (-s C, default: 5.0) or parameter for
            Roman to Boy's surface (-s R, default 0.0)
  -T <tran> translate 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 <rot>  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 (default: write to standard output)


Display a chunky figure-8 Klein bottle
unitile2d -s K -R 1.5 6 | off_color -f N | antiview -t no_tri

Display the Roman surface, using a larger number of tiles
unitile2d -s r -l 40 -w 40 9 | off_color -f N | antiview -t no_tri

General "trefoil" with triangle tiling and 7/3 path
unitile2d -s T -w 12 -l 160 -r 0.6 -d 7,3 2 | off_color -f P | antiview -xev -t no_tri


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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Contact:      -      Modified 1.6.2022