U3D_无限阶贝塞尔曲线

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 do
        t[i] = {}
        for j = 1,i do
            if j == 1 or j == i then
                t[i][j] = 1
            else
                t[i][j] = t[i - 1][j - 1] + t[i - 1][j]
            end
        end
    end
    for i = 1,n do
        table.insert(ret,t[n][i])
    end
    t = nil
    return ret
end

------------------------测试函数------------------------

function Bezier.TEST()
    local go = GameObject()
    go.name = "测试点"
    go.transform.position = Vector3.zero

    local go1  = GameObject()
    go1.name = "测试点1"
    go1.transform.position = Vector3(-17.4,0,0)
    go1.transform:SetParent(go.transform)

    local go2  = GameObject()
    go2.name = "测试点2"
    go2.transform.position = Vector3(-9.52,0,-3.84)
    go2.transform:SetParent(go.transform)

    local go3  = GameObject()
    go3.name = "测试点3"
    go3.transform.position = Vector3(-2.88,0,5.94)
    go3.transform:SetParent(go.transform)

    local go4  = GameObject()
    go4.name = "测试点4"
    go4.transform.position = Vector3(1.7,0,0)
    go4.transform:SetParent(go.transform)

    local go5  = GameObject()
    go5.name = "测试点5"
    go5.transform.position = Vector3(9.95,0,-4.91)
    go5.transform:SetParent(go.transform)

    local go6  = GameObject()
    go6.name = "测试点6"
    go6.transform.position = Vector3(15.38,0,5.46)
    go6.transform:SetParent(go.transform)

    local lineCount = 20

    go:AddComponent(typeof(UnityEngine.LineRenderer))
    local lr = go:GetComponent("LineRenderer")
    lr.positionCount = lineCount + 1
    for i = 0,lineCount do
        lr:SetPosition(i,Bezier.BezierCurve(i / lineCount,go1.transform.position,
                                                           go2.transform.position,
                                                           go3.transform.position,
                                                           go4.transform.position,
                                                           go5.transform.position,
                                                           go6.transform.position))
    end
end

return Bezier