canonical - canonicalize a polyhedon

Usage | Examples | Notes

Usage



Usage: canonical [options] [input_file]

Read a polyhedron from a file in OFF format. Canonicalize or planarize it.
Uses algorithms by George W. Hart, http://www.georgehart.com/
http://www.georgehart.com/virtual-polyhedra/conway_notation.html
http://www.georgehart.com/virtual-polyhedra/canonical.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
  -e <opt>  edge distribution (default : none)
               s - project vertices onto a sphere
  -s <opt>  shuffle model indexes
               v - vertices, e - edges, f - faces, a - all (default: none)
  -r <opt>  initial radius
               e - average edge near points radius = 1 (default)
               v - average vertex radius = 1
               x - not changed
  -C <opt>  initial centering
               e - edge near points centroid (default)
               v - vertex centroid
               x - not moved
  -p <opt>  planarization (done before canoncalization. default: none)
               q - face centroids magnitude squared
               m - mathematica planarize
               a - sand and fill planarize
               p - fast planarize (poly_form -a p)
  -i <itrs> maximum planarize iterations. -1 for unlimited (default: -1)
            WARNING: unstable models may not finish unless -i is set
  -c <opt>  canonicalization
               m - mathematica version (default)
               b - base/dual version (reciprocate on face normals)
               a - moving edge version
               x - none (default, if -p is set)
  -n <itrs> maximum canonical iterations. -1 for unlimited (default: -1)
            WARNING: unstable models may not finish unless -n is set
  -O <args> output b - base, d - dual, i - intersection points (default: b)
               n - base edge near points, m - dual edge near points
               p - base near points centroid, q - dual near points centroid
               u - minimum tangent sphere, U - maximum; o - origin point
               s - base incircles, S - rings; t - dual incircles, T - rings
  -q <dist> offset for incircles to avoid coplanarity e.g 0.0001 (default: 0)
  -g <opt>  roundness of tangent sphere, positive integer n (default: 8)
  -x <opt>  Normals: n - Newell's, t - triangles, q - quads (default: Newell's)
  -d <perc> radius test. percent difference between minimum and maximum radius
               checks if polyhedron is collapsing. 0 for no test 
               (default: 80 for canonicalizing, not used for planarizing)
  -l <lim>  minimum distance change to terminate, as negative exponent
               (default: 12 giving 1e-12)
            WARNING: high values can cause non-terminal behaviour. Use -n
  -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)

Extra Options
  for (-c m, -p m, and -p p)
  -E <perc> percentage to scale the edge tangency (default: 50) 
  -P <perc> percentage to scale the face planarity (default: 20) (also -p p)
  -A        alternate algorithm. try if imbalance in result (-c m only)

Coloring Options (run 'off_util -H color' for help on color formats)
  -I <col>  intersection points and/or origin color (default: yellow)
  -N <col>  base near points, centroid, incircles color (default: red)
  -M <col>  dual near points, centroid, incircles color (default: darkgreen)
  -B <col>  base edge color (default: unchanged)
  -D <col>  dual edge color (default: unchanged)
  -U <col>  unit sphere color (default: white)
  -T <tran> base/dual transparency. range from 0 (invisible) to 255 (opaque)

Examples

Make a cube, distort it, and canonicalize it back into a cube

off_util cube | off_trans -S 1,2,3 | canonical | antiview

Make a geodesic sphere, canonicalize it, and add it to it reciprocal

geodesic -c 2 ico | canonical -O bd | antiview

The program will not always converge, and produce the canonical form. In this cases it may help to distort the polyhedron before running canonical. This could be done with off_util -S, repel, poly_form, off_trans or even editing the OFF file by hand.

George Hart has a page on canonicalization.

Uses algorithms by George W. Hart, http://www.georgehart.com/. The 'Mathematica' algorithms have been written to follow George Hart's Mathematica implementation

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