poly_form  make faceregular and unscramble models
Usage: poly_form [options] [input_file]
Read a file in OFF format containing a graph of a polyhedron, with or
without vertex coordinates, and try to create a spherical or ellipsoidal
tesselation where the maximum edge is a minimum length, or try to make
into a regularfaced polyhedron. Option adjustment factors expressed as
a percentage are approximate. If input_file is not given the program reads
from standard input.
Options
h,help this help message (run 'off_util H help' for general help)
version version information
a <alg> model forming algorithm
r  make faces into unitedged regular polygons (default)
u  unscramble: place a small polygon on one side of a
sphere or ellipsoid and the rest of the vertices at a
point on the other side, then equalise shortest and
longest edges attached to a vertex
U  equalise shortest and longest edges attached to a vertex
on sphere or ellipsoid (use to continue unscrambling)
e  equalise edges on sphere or ellipsoid (default)
p  planarise
n <itrs> maximum number of iterations, 1 for unlimited (default: 10000)
s <perc> percentage to shorten longest edges on iteration (default: 1)
k <perc> a r  percentage to reduce polygon radius on iteration
(default: value of s)
a e  percentage to reduce minimum target length on iteration
(default: 1e6), will oscillate at certain precision,
process output with smaller value to improve solution
f <perc> percentage to reduce distance of vertex from face plane (a rp)
on iteration (default: value of s)
y maintain symmetry of the base model (with a e/r/p)
E <prms> use ellipsoid, three numbers separated by commas are the
axis lengths (for a superellipsoid an optional fourth number
gives the power)
l <lim> minimum change of distance/width_of_model to terminate, as
negative exponent (default: 14 giving 1e14)
z <nums> number of iterations between status reports (implies termination
check) (0 for final report only, 1 for no report), optionally
followed by a comma and the number of iterations between
termination checks (0 for report checks only) (default: 1000,100)
o <file> write output to file (default: write to standard output)
Turn an icosahedron 3fold axis into a sixfold axis, and make the
resulting faces regular
off_trans y D3v ico  to_nfold 6  poly_form s 15  antiview
Make the faces of a (3,5) icosahedral geodesic sphere into regular
triangles, while ensuring that the icosahedral symmetry is maintained,
set n and l higher for a better solution
poly_form n 100000 s 15 l 14 y geo_5_3  antiview
Make a geometric representation of a polyhedron having only face data,
in this case a geodesic sphere has all its coordinates set to the origin
and is then laid out again on a sphere
off_trans geo_3 S 0 > scrambled.off
poly_form a u scrambled.off > unscrambled.off
Run for a bit longer if necessary, don't use a u this time
as this includes an initial placement, instead use just the unscrambling
algorithm a U
poly_form n 100000 a U unscrambled.off > unscrambled2.off
Make an equal edge tiling on a sphere, and use y to constrain
to the original symmetry, which may also be faster
poly_form n 100000 a e s 100 geo_3_3_d  antiview
poly_form n 100000 a e s 100 y geo_3_3_d  antiview
An equaledge tiling on a sphere may not be solvable, but the result
might still be symmetric, which could then be used to speed up
a regularfaced solution
poly_form a u geo_3_3  poly_form a e s 100  antiview s a
poly_form a u geo_3_3  poly_form a e s 100  poly_form n 1 y  antiview
Solve an equaledge model on an ellipsoid
poly_form n 100000 a e E 1,1.2,1.5 y s 50 geo_3_3_d  antiview
Doesn't always succeed. Experiment with option s,
k and f to improve convergence, but setting them too
high may cause the model to scramble. Run the program for longer by
increasing option n. The program shows the progress every
1000 iterations (change with option z) by printing the
longest and shortest edge lengths and/or the maximum
distance a vertex moved.
Option y constrains the symmetry of a model, and
will also complete quicker for models with good symmetry and a
large number of elements.
The program was previously called minmax, but includes various
changes. Option p is gone, for p u use a u. Option
a parameters are renamed: a u is now a r (and is the
default), a v p u is a u, and a v is a U
for unscrambling and a e for equalising edges.
Option L is gone, and option l
is now used to specify precision (an option for lengthening edges
is no longer needed). The default for n is raised to 10000
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