#!/usr/bin/ruby -w
# Generate input text for testing rotation angles.
#
# The goal is to generate something that will retain all character
# locations after a single rotation step, such that after 26 rotation
# steps we get back the original input.

# Rotation angle.
ANGLE = Math::PI / 13

# Radii where output characters will be inserted.  Only some subset of radii
# are stable.
RADII = [8, 14, 16, 20]

# List of (x, y) pairs.
points = []
RADII.each{|x|
   points += [[x, 0]]
}

# Collect rotated points into list of (y, x, character) tuples.
output_points = []
occupied_points = {}
rx = Math::tan(ANGLE / 2)
ry = Math::sin(ANGLE)
26.times{|i|
   # Add unrotated points.
   points.size.times{|j|
      x, y = points[j]
      if occupied_points[[x, y]]
         raise "Overlapping point at (#{x}, #{y})\n"
      end
      c = j == 0 ? ('a'.ord + (26 - i) % 26).chr : ('A'.ord + i).chr
      output_points += [[y, x, c]]
      occupied_points[[x, y]] = true
   }

   # Apply rotation.
   points.map!{|t|
      x, y = t
      x -= (rx * y).round
      y += (ry * x).round
      x -= (rx * y).round
      [x, y]
   }
}

# Add center point.
output_points += [[0, 0, '+']]

# Output final set of points.
min_x = min_y = 0
output_points.each{|t|
   y, x = t
   min_x = [min_x, x].min
   min_y = [min_y, y].min
}

cursor_x = min_x
cursor_y = min_y
text = ""
output_points.sort.each{|t|
   y, x, c = t
   if cursor_y < y
      text += "\n" * (y - cursor_y)
      cursor_y = y
      cursor_x = min_x
   end

   text += " " * (x - cursor_x) + c
   cursor_x = x + 1
}
puts text