Lua angle class

_R = _R or debug.getregistry()

_R.Angle = {}
local meta = {}

function _R.Angle:Distance(other)
    local p = self.p - other.p
    local y = self.y - other.y
    local r = self.r - other.r

    return math.sqrt(p*p + y*y + r*r)
end

function meta:__mul(other)
    if type(other) == "number" then
        return Angle(self.p * other, self.y * other, self.r * other)
    end

    return Angle(self.p * other.p, self.y * other.y, self.r * other.r)
end

function meta:__add(other)
    if type(other) == "number" then
        return Angle(self.p + other, self.y + other, self.r + other)
    end

    return Angle(self.p + other.p, self.y + other.y, self.r + other.r)
end

function meta:__sub(other)
    if type(other) == "number" then
        return Angle(self.p - other, self.y - other, self.r - other)
    end

    return Angle(self.p - other.p, self.y - other.y, self.r - other.r)
end

function meta:__div(other)
    if type(other) == "number" then
        return Angle(self.p / other, self.y / other, self.r / other)
    end

    return Angle(self.p / other.p, self.y / other.y, self.r / other.r)
end

function meta:__pow(o)
    if type(o) ~= "number" then
        error("power not a number!")
    end
    return Angle(self.p ^ o, self.y ^ o, self.r ^ o)
end

function meta:__unm()
    return Angle(-self.p, -self.y, -self.r)
end

function meta:__eq(o)
    return self.p == o.p and self.y == o.y and self.r == o.r
end

function meta:__tostring()
    return tostring(self.p) .. ", " .. tostring(self.y) .. ", " .. tostring(self.r)
end

local members = { p = true, y = true, r = true }

function meta:__newindex(k, v)
    if members[k] then
        local nv = v % 360
        rawset(self._m, k, nv)
    end
end

function meta:__index(k)
    if not members[k] then
        return _R.Angle[k]
    end
    return self._m[k]
end


function Angle(p, y, r)
    local ret = {}
    ret._m = {}

    setmetatable(ret, meta)

    ret.p = p or 0
    ret.y = y or 0
    ret.r = r or 0

    return ret
end