# Last edited on 2021-07-31 15:37:23 by jstolfi

from math import hypot, floor

def basis_2d_hartley_choose(fxm,fym,iso):
  # Returns a list of pairs ({fx,fy)} which are
  # the integer frequency vectors for a 2d Hartley basis 
  # with max absolute frequency {fxm} along the {x} axis and {fym} 
  # along the {y} axis.
  #
  # If {iso} is false, includes all frequency vectors with {|fx| <= fxm}
  # and {|fy| <= fym}.
  #
  # If {iso} is true, considers only frequency vectors such that {(fx/fxm,fy/fym)}
  # is inside or on the unit circle. Beware of roundoff errors; use fractional
  # {fxm,fym} if necessary to overcome them.
  
  nfx = 2*int(floor(fxm)) + 1;
  nfy = 2*int(floor(fym)) + 1;
  fr = []   # Frequency vectors.
  for kfx in range(nfx):
    fx = kfx - fxm
    for kfy in range(nfy):
      fy = kfy - fym
      ok = (not iso) or (hypot(fx/fxm,fw/fym) <= 1.0)
      if ok: fr.append((fx,fy))
  return fr
  # ----------------------------------------------------------------------