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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 Options -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) 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> distance (height of conic frustrum) -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)
unitile2d -s K -R 1.5 6 | off_color -f N -s 5 | antiview
unitile2d -s r -l 40 -w 40 9 | off_color -f N -s 2 | antiview
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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