pyramid-y.lua

-- For the animation, run with the love2d game engine
-- For the SVG output, run with the standard Lua interpreter

local size = 14			-- This is the number of hexes on the side of the flat rhombus

local base_hex = {}
local s32 = math.sqrt(3)/2
local rad = 1/math.sqrt(3)

for i = 1,6 do
	local alpha = (i + 0.5) * 2 * math.pi / 6
	table.insert(base_hex, {rad * math.cos(alpha), rad * math.sin(alpha)})
end


local hexes = {}

for x = -size,size do
	for y = 0,size do
		if x - y >= -size and not (y == 0 and x < 0) then
			local y_shift = -0.5

			local dx = x + y_shift * y
			local dy = s32 * y
			local hex = {}

			for i = 1,6 do
				hex[i] = {
					base_hex[i][1] + dx,
					base_hex[i][2] + dy
				}
			end

			table.insert(hexes, hex)
		end
	end
end

local steps2 = 15

local function to_segments(hex)

	local coords = {}

	for i = 1,6 do
		local a = hex[i]
		local b = hex[(i % 6) + 1]

		for k = 0,steps2 do
			local s = k / steps2
			table.insert(coords, {
				(1-s) * a[1] + s * b[1],
				(1-s) * a[2] + s * b[2]
			})
		end
	end

	return coords
end


local function fold(p, factor)

	local d = math.sqrt(p[1]^2 + p[2]^2)
	local a = math.atan2(p[2], p[1])
	a = a * factor

	local x = d * math.cos(a)
	local y = d * math.sin(a)

	return {x,y}
end



local function toSVG()

	local svg = {}
	table.insert(svg, '<svg xmlns="http://www.w3.org/2000/svg" width="1500" height="1000" viewBox="0 0 1500 1000">')

	local factor = 2
	local scale = 20
	for _,hex in ipairs(hexes) do
		local coords = ""
		for _,p in ipairs(to_segments(hex)) do
			p = fold(p, factor)
			coords = coords .. string.format("%.2f,%.2f ", scale * p[1] + 600, scale * p[2] + 500)
		end

		table.insert(svg, string.format('<polygon points="%s" fill="white" stroke="black" stroke-width="3" />', coords))
	end

	table.insert(svg, "</svg>")
	return table.concat(svg, "\n")
end

if love then
	function love.load()
		love.window.setMode( 1500,1000 )
	end

	function love.draw()

		local max_factor = 1
		local factor = (math.sin(love.timer.getTime() / 10 * 2 * math.pi) + 1)/2 * max_factor + 1
		local scale = 20
		for _,hex in ipairs(hexes) do
			local coords = {}
			for _,p in ipairs(to_segments(hex)) do
				p = fold(p, factor)
				table.insert(coords, scale * p[1] + 600)
				table.insert(coords, scale * p[2] + 500)
			end
			love.graphics.polygon("line", coords)
		end
	end
else

	local fp = io.open("out.svg", "w")
	fp:write(toSVG())
	fp:close()
end