#! /usr/bin/python3
# Last edited on 2023-06-12 17:05:48 by stolfi

# Compute a vector {v} with tree nonzero and distinct coordinates
# such that the 48 sign-flips and permutations are as separated as possible.

from math import inf, sqrt

def main():
  # v = (0.8343526900035698, 0.5094884257056673, 0.2104213220084118)
  # v = (0.8253501198358801, 0.5215643061465987, 0.21625876685284984)
  # v = (0.825883912599991, 0.5207186912677729, 0.2162586587235475)
  # v = (0.8259935240003327, 0.5207878011076222, 0.21567281823864468)
  # v = (0.8259577330612125, 0.5208243435244877, -0.21572164098362878)
  # v = (0.8259434156067079, 0.5208389595498422, -0.21574116999535153)
  # v = (0.8259418154023249, 0.5208414971364776, -0.21574116999438067)
  # v = (0.8259427137773173, 0.5208408814277186, -0.21573921709266863)
  # v = (0.8259425705997766, 0.5208410275849338, -0.21573941238286357)
  # v = (0.8259425705997767, 0.5208410275849339, -0.2157394123828636)
  # v = (0.8259425866018402, 0.5208410022090799, -0.2157394123828635)
  # v = (0.8259425901812791, 0.5208409985551501, -0.21573940750060858)
  # v = (0.8259425910796527, 0.5208409979394399, -0.21573940554770663)
  # v = (0.8259425911708956, 0.5208409979969779, -0.21573940505948114)
  # v = (0.825942591027718, 0.5208409981431351, -0.21573940525477134)
  # v = (0.825942591027718, 0.5208409981431351, -0.21573940525477134)
  v = (0.8259425910240683, 0.5208409981408336, -0.21573940527430036)
  print("v = ", v)
  print("|v| = ", vlen(v))
  
  u = vdir(( +v[1], -v[0], 0 ))
  w = vdir(vcross(u, v));
  
  dminmax = 0
  tminmax = None
  for ku in range(-10,11):
    for kw in range(-10,11):
      print("  k = ", ku, kw)
      t = vdir(vmix(vmix(v, 1, u, 0.00000000002*ku), 1, w, 0.00000000002*kw))
      print("  t = ", t)
      dmin = enum_trimmed_octahedron(None, t)
      print("dmin = ", dmin)
      if abs(dmin) > abs(dminmax):
        dminmax = dmin
        tminmax = t

  print("")
  print("dminmax = ", dminmax)
  print("tminmax = ", tminmax)
  return 0;
  # ----------------------------------------------------------------------
  
def enum_trimmed_octahedron(wr, v):  
  # Generate all permutations and sign-flips of {v}: 
  
  wmin = None
  dmin = +inf
  w = v;
  k = 0;
  for eo in range(2):
    for cy in range(3):
      for s0 in range(2):
        for s1 in range(2):
          for s2 in range(2):
            if wr != None:
              wr.write("#declare pt[%2d] = < %+19.16f, %+19.16f, %+19.16f >;\n" % (k, w[0], w[1], w[2]))
            if (v != w):
              d = vdist(v, w)
              if abs(d) < abs(dmin):
                dmin = d
                wmin = w
            k = k + 1
            w = ( +w[0], +w[1], -w[2] )
          w = ( +w[0], -w[1], +w[2] )
        w = ( -w[0], +w[1], +w[2] )
      w = ( w[1], w[2], w[0] )
    w = ( w[1], w[0], w[2] )

  print("")
  print("dmin = ", dmin)
  print("wmin = ", wmin)

  return dmin
  # ----------------------------------------------------------------------

def vcross(x, y):
  return(
    x[1]*y[2] - x[2]*y[1],
    x[2]*y[0] - x[0]*y[2],
    x[0]*y[1] - x[1]*y[0]
  )
  # ----------------------------------------------------------------------

main()