vector

local vector = {
    add = function( self, o )
        return vector.new(
            self.x + o.x,
            self.y + o.y,
            self.z + o.z
        )
    end,
    sub = function( self, o )
        return vector.new(
            self.x - o.x,
            self.y - o.y,
            self.z - o.z
        )
    end,
    mul = function( self, m )
        return vector.new(
            self.x * m,
            self.y * m,
            self.z * m
        )
    end,
    dot = function( self, o )
        return self.x*o.x + self.y*o.y + self.z*o.z
    end,
    cross = function( self, o )
        return vector.new(
            self.y*o.z - self.z*o.y,
            self.z*o.x - self.x*o.z,
            self.x*o.y - self.y*o.x
        )
    end,
    length = function( self )
        return math.sqrt( self.x*self.x + self.y*self.y + self.z*self.z )
    end,
    normalize = function( self )
        return self:mul( 1 / self:length() )
    end,
    round = function( self, nTolerance )
        nTolerance = nTolerance or 1.0
        return vector.new(
            math.floor( (self.x + (nTolerance * 0.5)) / nTolerance ) * nTolerance,
            math.floor( (self.y + (nTolerance * 0.5)) / nTolerance ) * nTolerance,
            math.floor( (self.z + (nTolerance * 0.5)) / nTolerance ) * nTolerance
        )
    end,
    tostring = function( self )
        return self.x..","..self.y..","..self.z
    end,
}

local vmetatable = {
    __index = vector,
    __add = vector.add,
    __sub = vector.sub,
    __mul = vector.mul,
    __unm = function( v ) return v:mul(-1) end,
    __tostring = vector.tostring,
}

function new( x, y, z )
    local v = {
        x = x or 0,
        y = y or 0,
        z = z or 0
    }
    setmetatable( v, vmetatable )
    return v
end