regions.lua composing bitmaps

regions.lua

local module = {}

function module.circle(cx, cy, radius)
  return function(x, y) return (x - cx)^2 + (y - cy)^2 < radius^2 end
end

function module.halfspace(rise, run, x0, y0)
  return function(x, y) return run*(y - y0) < rise*(x - x0) end
end


function module.complement(r)
  return function(x, y) return not r(x, y) end
end

function module.union(...)
  local region = {...};
  return function(x, y)
    local result = false;
    for i, r in ipairs(region) do
      result = result or r(x, y)
    end
    return result
  end
end

function module.intersection(...)
  local region = {...};
  return function(x, y)
    if #region == 0 then return false end
    local result = true;
    for i, r in ipairs(region) do
      result = result and r(x, y)
    end
    return result
  end
end

function module.difference(r1, r2)
  return function(x, y) return r1(x, y) and not r2(x, y) end
end

function module.xor(r1, r2)
  return function(x, y) return r1(x, y) ~= r2(x, y) end
end


function module.translate(r, tx, ty)
  return function(x, y)
    return r(x - tx, y - ty)
  end
end

function module.scale(r, s)
  return function(x, y)
    return r(x/s, y/s)
  end
end

function module.rotate(r, radians, cx, cy)
  cx = cx or 0
  cy = cy or 0
  return function(x, y)
    return r(
              (x - cx)*math.cos(-radians) - (y - cy)*math.sin(-radians) + cx,
              (y - cy)*math.cos(-radians) + (x - cx)*math.sin(-radians) + cy
            )
  end
end

function module.plot(r, output_width, output_height, x0, y0, x1, y1)
  x0, y0, x1, y1 = x0 or 0, y0 or 0, x1 or 1, y1 or 1

  local x, y
  io.write('P7\nWIDTH ', output_width, '\nHEIGHT ', output_height, '\nDEPTH 1\nMAXVAL 1\nTUPLTYPE BLACKANDWHITE_ALPHA\nENDHDR\n')
  -- io.write('P1\n', output_width, ' ', output_height, '\n')
  for i = 0, output_height - 1 do
    y = y1 - (y1 - y0)/output_height * i
    for j = 0, output_width - 1 do
      x = (x1 - x0)/output_width * j + x0
      if r(x, y) then
        io.write('\x00\x00')
      else
        io.write('\x00\x01')
      end
    end
  end
end

return module

-- main.lua
--[[
local regions = require 'regions'

local xor = regions.xor
local intersection = regions.intersection
local circle = regions.circle
local complement = regions.complement
local halfspace = regions.halfspace
local scale = regions.scale
local rotate = regions.rotate
local plot = regions.plot

local r =
  xor(
    intersection(
      circle(0, 0, 9/16),
      complement(circle(0, 1/3, 1/16)),
      complement(circle(0, -1/3, 1/16))
    ),
    intersection(
      halfspace(2, 1, 0, 0),
      circle(0, 0, 1/2)
    )
  )
--r = scale(r, 2)
--r = rotate(r, math.atan2(1, 2))

local width = arg[1] or 200
local height = arg[2] or 200
local subsamples = arg[3] or 4

plot(r, width, height)
]]

-- main2.lua
--[[
local regions = require "regions"

function square(x0, y0, x1, y1)
  return function(x, y) return x0 < x and x < x1 and y0 < y and y < y1 end
end

local linewidth = 2/81
local s = square(0 + linewidth/2, 0 + linewidth/2, 1/3 - linewidth/2, 1/3 - linewidth/2)

gliders = {
          regions.union(s,
                        regions.translate(s, 1/3, 0/3),
                        regions.translate(s, 1/3, 1/3),
                        regions.translate(s, 2/3, 1/3),
                        regions.translate(s, 0/3, 2/3)),

          regions.union(s,
                        regions.translate(s, 1/3, 0/3),
                        regions.translate(s, 2/3, 0/3),
                        regions.translate(s, 1/3, 2/3),
                        regions.translate(s, 2/3, 1/3)),

          regions.union(regions.translate(s, 1/3, -1/3),
                        regions.translate(s, 1/3, 0/3),
                        regions.translate(s, 2/3, 0/3),
                        regions.translate(s, 0/3, 1/3),
                        regions.translate(s, 2/3, 1/3)),

          regions.union(regions.translate(s, 1/3, -1/3),
                        regions.translate(s, 2/3, -1/3),
                        regions.translate(s, 2/3, 0/3),
                        regions.translate(s, 0/3, 0/3),
                        regions.translate(s, 2/3, 1/3)),
}

local framewidth = 1 + 2/3
for i, glider in ipairs(gliders) do
    gliders[i] = regions.translate(glider, (i-1)*framewidth, 0)
end

local r = regions.union(unpack(gliders))

local pixels_high = 108
local image_height = 1 + 1/3
local x0, y0 = 0 + 1/(2*pixels_high), - 1/3 - 1/(2*pixels_high) -- offset by half a pixel to avoid boundary issues
local aspect_ratio = 18/4

regions.plot(r, math.floor(pixels_high*aspect_ratio), pixels_high, x0, y0, x0+(image_height*aspect_ratio), y0+image_height)

]]