AoE4 Generated Map Function: Quadratic Bezier Curve

--[[
Creates a quadratic bezier curve
coord1, coord2, coord3: tables with x and y values
finesse: controls how many steps are calculated, suggested 100
    if there are gaps in the line you can try to increase this
    
Returns a array of xy coords
]]
local function CreateQuadraticBezierCurve(coord1, coord2, coord3, finesse)
    local line = {}
    local x1 = nil
    local y1 = nil
    for i = 0, finesse do
        local percent = i / finesse
	    local x2 = (1 - percent)^2 * coord1.x + 2 * (1 - percent) *
	        percent * coord2.x + percent^2 * coord3.x
	    local y2 = (1 - percent)^2 * coord1.y + 2 * (1 - percent) *
	        percent * coord2.y + percent^2 * coord3.y
	    
	    x2 = x2>=0 and math.floor(x2+0.5) or math.ceil(x2-0.5)
	    y2 = y2>=0 and math.floor(y2+0.5) or math.ceil(y2-0.5)

	    if (not(x1 == x2 and y1 == y2))
	        and (terrainLayoutResult[x2] ~= nil and terrainLayoutResult[y2] ~= nil)
	         then
	        x1 = x2
	        y1 = y2
	        table.insert(line, {x = x1, y = y1})
        end
    end
    return line
end

--[[Example
local line = CreateQuadraticBezierCurve({x=1, y=gridSize}, {x=1, y=1}, {x=gridSize, y=1}, 100)
for l in pairs(line) do
    local coord = line[l]
    terrainLayoutResult[coord.x][coord.y].terrainType = tt_plains
end
]]