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unitile2d - makes uniform tilings on a surface

Usage

Synopsis

Description

Options

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

Examples

   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

Notes

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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