bezier.lua

--a line from x1, y1 to x2, y2 as t varies from 0 to 1
function line(x1, y1, x2, y2)
        return function(t)
                return x1 + (x2 - x1) * t, y1 + (y2 - y1) * t
        end
end

--the Bezier curve formed by interpolating between multiple given curves or lines
function curve(c1, c2, c3, ...)

        if not c2 then return c1 end    --sanity check

        local c1c2 = function(t) 
                local x1, y1 = c1(t)
                return line(x1, y1, c2(t))(t)
        end

        return c3 and curve(c1c2, curve(c2, c3, ...)) or c1c2
end

--the Bezier curve determined by given control points
function bezier(xv, yv)
        lines = {}
        for i = 1, #xv-1 do
                lines[i] = line(xv[i], yv[i], xv[i+1], yv[i+1])
        end
        return curve(unpack(lines)) or lines[1]
end