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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 -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) p - face centroids (magnitude squared) q - face centroids (magnitude) f - face centroids m - mathematica planarize a - sand and fill planarize u - make faces into unit-edged regular polygons (minmax -a u) -i <itrs> maximum number of planarize iterations (default: no limit) -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 number of canonical iterations (default: no limit) -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 centeroid, 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: 0.0) -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. precent difference between minumum and maximum radius checks if polyhedron is collapsing. 0 for no test (default: 80) -z <n> status reporting every n lines. -1 for no status. (default: 1000) -l <lim> minimum distance change to terminate, as negative exponent (default: 12 giving 1e-12) -o <file> write output to file (default: write to standard output) Mathematica Canonicalize Options (-c m and -p m) -E <perc> percentage to scale the edge tangency error (default: 50) -P <perc> percentage to scale the face planarity error (default: 20) -A alterate 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)
off_util cube | off_trans -S 1,2,3 | canonical | antiview
geodesic -c 2 ico | canonical -O bd | antiview
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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