U3D_无限阶贝塞尔曲线

 Lua版

local Bezier = {}

--【无限阶贝塞尔曲线】
--@params t    整条线上对应的百分比位置{0-1}
--@params node 起点,控制点1,控制点2,控制点3......,结束点
--@return ret  返回对应的点/值
function Bezier.BezierCurve(t, node)
    local vecs  = node
    local count = #vecs
    local rank  = count - 1
    local ret   = Vector3.zero
    local pts   = Bezier.GetPascalTriangle(count)
    local fs    = {}

    for i = 1,count do
        local f = Bezier.GetFormula(vecs[i],rank,i,pts[i],t)
        table.insert(fs,f)
    end
    for i = 1,#fs do
        ret = ret + fs[i].Caclu()
    end
    return ret
end

-------------------------Private---------------------------------
function Bezier.Exponentiation(num,power)
    local n = 1
    if power == 0 then return n end
    for i = 1,power do
        n = n * num
    end
    return n
end

function Bezier.GetFormula(point,rank,index,ptValue,t)
    local ret   = {}
    ret.point   = point
    ret.rank    = rank
    ret.index   = index - 1
    ret.ptValue = ptValue
    ret.t       = t
    ret.Caclu   = function()
        local t1 = Bezier.Exponentiation((1 - ret.t),(ret.rank - ret.index))
        local t2 = Bezier.Exponentiation(ret.t,ret.index)
        return ret.point * t1 * t2 * ret.ptValue
    end
    return ret
end

function Bezier.GetPascalTriangle(n)
    local ret = {}
    local t = {}
    for i = 1,n