convex_dynamics

Computation of the minimal convex invariant error set for the error-diffusion algorithm in 2D, given a collection of sets of points.

Uses the CGAL C++ library.

Point set can be given in a JSON object with the collection of point sets with key "point_sets" as an array of arrays of pairs of coordinates. Coordinates can be integers, or fractions, denoted as strings, like "4/5". Example: below we have a collection of three point sets:

{"point_sets":[
  [[-1,1],[1,1],[1,"-3/8"],[-1,-1],[-2,-1]],
  [[-1,1],[1,"1/2"],[1,-1],[-1,-1],[-2,-1],[-2,5]],
  [[-2,2],[1,5],[1,-1]]
]}

Save this in a file, and run ./iter <filename>

Options

The following options can be specified in the JSON object:

• "iteration" : specify which iteration to use:

  • "g" : the G-iteration (default)
  • "G" : the convexified G-iteration
  • "f" : the F-iteration
  • "F" : the convexified F-iteration

  For example,

  {
    "iteration":"G",
    "point_sets":[...] 
  }
  

• "A" : the initial set to use

  For example,

  {
    "A":[[1,1],[-1,1],[-1,-1],[1,-1]],
    "point_sets":[...] 
  }
  

  If "A" is omitted, the singleton set [0,0] is used for the "g" and "G" iterations, while the convex hull of the first point set is used for the "f" and "F" iterations.

• "digit_threshold" : threshold specifying how many digits the numerator or denominator of a vertex coordinate should have in order to enable coefficient rounding (defaults to 10)

• "rounding_error" : round a coordinate when it is within rounding_error from a small fraction (defaults to 1e-8)