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minmax - optimal spherical tesselations

Usage    |    Examples    |    Notes


Usage: minmax [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 regular polyhedron. If input_file is not given the program reads
from standard input.

  -h,--help this help message (run 'off_util -H help' for general help)
  --version version information
  -n <itrs> number of iterations (default 1000)
  -s <perc> percentage to shorten longest edges on iteration (default: 1)
  -l <perc> percentage to lengthen shortest edges (-a a/v) on iteration 
            (default: 0.0)
  -k <perc> percentage to reduce polygon radius (-a u) on iteration
            (default: value of -s)
  -f <perc> percentage to reduce distance of vertex from face plane (-a u)
            on iteration (default: value of -s)
  -a <alg>  length changing algorithm
              v - shortest and longest edges attached to a vertex (default)
              a - shortest and longest of all edges
              u - make faces into unit-edged regular polygons (-l controls
                  planarity, ignore -p, -E)
  -p <mthd> method of placement onto a unit sphere:
              n - project onto the sphere (default)
              r - random placement
              u - unscramble: place a small polygon on one side and the
                  rest of the vertices at a point on the other side
  -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: 16 giving 1e-16)
  -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)


Turn an icosahedron 3-fold axis into a six-fold axis, and make the resulting faces regular
off_trans -y D3v ico | to_nfold 6 | minmax -a u -s 20 -n 10000 | 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 >
minmax -p u -n 100000 >

Run for a bit longer, don't need -p u this time
minmax -n 100000 >


Doesn't always succeed. Experiment with option -s, -l, 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 (-a v/a) or the maximum distance a vertex moved (-a u).

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Contact:      -      Modified 27.3.2019