Generates a rounded rectangle n-gon, renderable with a triangle fan.

rounded_rect_ngon.lua

function roundrectpoly(x, y, w, h, r, n)

	-- required args
	assert(x ~= nil and type(x) == "number")
	assert(y ~= nil and type(y) == "number")
	assert(w ~= nil and type(w) == "number")
	assert(h ~= nil and type(h) == "number")

	-- optional args
	assert(r == nil or type(r) == "number")
	assert(n == nil or type(n) == "number")
	r = math.min(r or 10, math.min(w * 0.5, h * 0.5))
	n = math.max(n or 5, 2)

	-- corner sector angle
	local ang = math.pi / 2 / (n - 1)

	-- angular starting offsets
	local br_ang = math.pi * 2.0 - ang
	local bl_ang = math.pi * 1.5 - ang
	local tl_ang = math.pi * 1.0 - ang
	local tr_ang = math.pi * 0.5 - ang

	-- x and y positions to rotate around
	local x_lft = x + r
	local x_rgt = x + w - r
	local y_top = y + r
	local y_btm = y + h - r

	local poly = {}

	for i = 1, n do
		local xi = i * 2 - 1
		local yi = i * 2
		-- bottom-right corner
		poly[n * 0 + xi] = x_rgt + math.sin(br_ang + ang * i) * r
		poly[n * 0 + yi] = y_btm + math.cos(br_ang + ang * i) * r
		-- top-right corner
		poly[n * 2 + xi] = x_rgt + math.sin(tr_ang + ang * i) * r
		poly[n * 2 + yi] = y_top + math.cos(tr_ang + ang * i) * r
		-- top-left corner
		poly[n * 4 + xi] = x_lft + math.sin(tl_ang + ang * i) * r
		poly[n * 4 + yi] = y_top + math.cos(tl_ang + ang * i) * r
		-- bottom-left corner
		poly[n * 6 + xi] = x_lft + math.sin(bl_ang + ang * i) * r
		poly[n * 6 + yi] = y_btm + math.cos(bl_ang + ang * i) * r
	end

	return poly
end