EXTRA: mmop_origami - multimodular polyhedron origami

Usage

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 unit-edged 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
  -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.
  -s <perc> percentage to adjust corrections on iteration (default: 100)
  -n <itrs> maximum number of iterations, -1 for unlimited (default: 10000)
  -l <lim>  minimum change of distance/width_of_model to
            terminate, as negative exponent (default: 15 giving 1e-15)
  -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: 1000,1)
  -o <file> write output to file (default: write to standard output)

Examples

Cuboctahedron dual

mmop_origami cubo_d | antiview

mmop_origami -V cubo_d | antiview

mmop_origami -V -p 0.1 cubo_d | antiview

mmop_origami -V -p 0.5 cubo_d | antiview

mmop_origami -p -0.2 -t 1/3 rhombicosid_d | antiview

Notes

A solution will have vertex units made of regular polygons, which are creased from centre-to-vertex and centre-to-midedge. 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 non-solution, 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

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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