中点変位法

midpoint_displacement.rb

def midpoint_displacement(size, rect = [], x = 0, y = 0, depth = 0)
  result = {}

  avg_height = ->(heights) {
    heights.sum / heights.size.to_f
  }

  rand_height = ->(h) {
    (rand - 0.5) * (2.0 ** -(depth * h))
  }

  crop_height = ->(height) {
    [[height, 1.0].min, 0.0].max
  }

  mid_height = ->(heights) {
    crop_height[avg_height[heights] + rand_height[0.3]]
  }

  if (size <= 1)
    result[[x       , y        ]] = rect[0]
    result[[x + size, y        ]] = rect[1]
    result[[x + size, y + size ]] = rect[2]
    result[[x       , y + size ]] = rect[3]
    return result
  end

  4.times { rect << rand } if rect.empty?

  center = mid_height[rect]
  mid01 = mid_height[[rect[0], rect[1]]]
  mid12 = mid_height[[rect[1], rect[2]]]
  mid23 = mid_height[[rect[2], rect[3]]]
  mid30 = mid_height[[rect[3], rect[0]]]

  next_size = size >> 1
  next_depth = depth + 1

  result.merge! midpoint_displacement(next_size, [ rect[0], mid01  , center , mid30   ], x            , y            , next_depth)
  result.merge! midpoint_displacement(next_size, [ mid01  , rect[1], mid12  , center  ], x + next_size, y            , next_depth)
  result.merge! midpoint_displacement(next_size, [ center , mid12  , rect[2], mid23   ], x + next_size, y + next_size, next_depth)
  result.merge! midpoint_displacement(next_size, [ mid30  , center , mid23  , rect[3] ], x            , y + next_size, next_depth)

  return result
end

loop do
  n = 100
  result = midpoint_displacement(n)

  File.open('data.dat', 'w') do |file|
    result.each do |(x, y), z|
      file.puts [x, y, z].join(' ')
    end
  end

  IO::popen('gnuplot', 'w') do |io|
    m = [n, 20].max
    io.puts "set dgrid3d #{m},#{m}"
    io.puts 'splot "data.dat" u 1:2:3 with pm3d'
    gets
  end
end