EXTRA: mmop_origami  multimodular polyhedron origami
Usage: mmop_origami [options] [input_file]
Read a file in OFF format containing an oriented polyhedron, and try to
convert to a multimodular origami polyhedron form with unitedged polygons.
The form is described in Multimodular Origami Polyhedra: Archimedeans,
Buckyballs and Duality by Rona Gurkewitz, Bennett Arnstein
http://store.doverpublications.com/0486423174.html
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
n <itrs> number of iterations (default 10000)
s <perc> percentage to adjust corrections on iteration (default: 100)
t <val> truncate polygon edge to this length (default: no truncation
k keep orientation, affects face centre offset direction (default:
set positive orientation)
p <ht> set initial height of face centres (default: 0.5)
V colour units with base model vertex colour
m <maps> a comma separated list of colour maps used to transform colour
indexes (default: rand), a part consisting of letters from
v, e, f, selects the element types to apply the map list to
(default 'vef'). The 'compound' map should give useful results.
l <lim> minimum change of distance/width_of_model to
terminate, as negative exponent (default: 15 giving 1e15)
z <n> status checking and reporting every n iterations, 1 for no
status (default: 1000)
q quiet, do not print status messages
o <file> write output to file (default: write to standard output)
See also,
mmop_origami examples with images.
Cuboctahedron dual
mmop_origami cubo_d  antiview
Cuboctahedron dual, preserve base vertex colours
mmop_origami V cubo_d  antiview
Cuboctahedron dual, preserve base vertex colours, 'pop' face centres
a little
mmop_origami V p 0.1 cubo_d  antiview
Cuboctahedron dual, preserve base vertex colours, 'pop' face centres
a lot
mmop_origami V p 0.5 cubo_d  antiview
Rhombicosidodecahedron dual, truncate modules to 1/3
mmop_origami p 0.2 t 1/3 rhombicosid_d  antiview
mmop_origami creates models like those described in
Multimodular Origami
Polyhedra: Archimedeans, Buckyballs and Duality
by Rona Gurkewitz, Bennett Arnstein.
A solution will have vertex units made of regular polygons, which are
creased from centretovertex and centretomidedge. Solutions are
found by iteration. Multiple solutions may exist, and can be found by
raising or lowering face centres with option p. Other solutions
may exist by raising some centres and lowering others, but this is not
currently supported.
Sometimes the algorithm will 'jam' on a nonsolution, and some models do
not have geometrically realisable solutions.
Check the quality of solutions by seeing if the triangles have good angles.
The following is close to a solution, but icreasing the number of
iterations doesn't improve the solution, so it is probably jammed.
mmop_origami p 0.1 s 1 n 100000 tr_icosid_d  off_report C F
The following model does not have a (symmetrical) solution
mmop_origami pri7  off_report C F
Convergence is slow on models with flat hexagons in the solution
mmop_origami n 200000 tr_ico  off_report C F
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EXTRA: jitterbug  jitterbug transformation
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Programs and Documentation
