local math = require "math"

local concat = require "table".concat

local format = require "string".format

local setmetatable = setmetatable

local type, error = type, error

local rawset, rawget = rawset, rawget

-- One of those cases where you really miss the "using" keyword.

local pow, sqrt, max, floor, acos, sin, cos, modf, pi = math.pow, math.sqrt, math.max, math.floor, math.acos, math.sin, math.cos, math.modf, math.pi

math = nil

local vector

local function check(o) -- Vector type check

local t = type(o)

if not (t == "table" and o.object == "vector") then

error("attempt to perform arithmetic on a "..t.." value", 3)

end

end

local __index = {

tostring = function(self, f)

f = type(f) == "number" and f >= 0 and f or 3

f = "%."..f.."f"

local r = { }

for i = 1, self.n do

local n = self[i]

r[i] = format(modf(n) == n and "%1d" or f, n)

end

return "{"..concat(r, "; ").."}"

end;

add = function(a, b)

check(a)

check(b)

local v = { }

for i = 1, max(a.n, b.n) do

v[i] = (a[i] or 0) + (b[i] or 0)

end

return vector(v)

end;

sub = function(a, b)

check(a)

check(b)

local v = { }

for i = 1, max(a.n, b.n) do

v[i] = (a[i] or 0) - (b[i] or 0)

end

return vector(v)

end;

mul = function(a, b)

local t1 = type(a)

local t2 = type(b)

local v = { }

if t1 == "number" then

check(b)

for i = 1, b.n do

v[i] = b[i] * a

end

elseif t2 == "number" then

check(a)

for i = 1, a.n do

v[i] = a[i] * b

end

else

check(a)

check(b)

v = a:cross(b)

end

return vector(v)

end;

div = function(a, b)

check(a)

local t = type(b)

if t ~= "number" then

error("attempt to perform arithmetic on a "..t.." value", 3)

end

local v = { }

for i = 1, a.n do

v[i] = a[i] / b

end

return vector(v)

end;

len = function(self)

local r = 0

for i = 1, self.n do

r = r + pow(self[i], 2)

end

return sqrt(r)

end;

dot = function(a, b)

check(a)

check(b)

local r = 0

for i = 1, max(a.n, b.n) do

r = r + (a[i] or 0) * (b[i] or 0)

end

return r

end;

cross = function(a, b)

check(a)

check(b)

local v = {

(a[2] or 0) * (b[3] or 0) - (a[3] or 0) * (b[2] or 0);

(a[3] or 0) * (b[1] or 0) - (a[1] or 0) * (b[3] or 0);

(a[1] or 0) * (b[2] or 0) - (a[2] or 0) * (b[1] or 0);

}

return vector(v)

end;

normalize = function(self)

return self / #self

end;

angle = function(a, b)

check(a)

check(b)

a, b = a:normalize(), b:normalize()

return acos(a:dot(b))

end;

rotate = function(v, g, a, b)

local r = { }

local c, s = cos(g), sin(g)

for i = 1, v.n do

r[i] = i == a and v[a] * c - v[b] * s or b == i and v[a] * s + v[b] * c or v[i]

end

return vector(r)

end;

round = function(self, d)

local v = { }

d = type(d) == "number" and d or 0.5

for i = 1, self.n do

local a, b = modf(self[i])

v[i] = b < d and a or a + 1

end

return vector(v)

end;

eq = function(a, b)

if not (type(a) == "table" and a.object == "vector") or not (type(a) == "table" and a.object == "vector") then

return false

end

local r = true

for i = 1, max(a.n, b.n) do

if a[i] ~= b[i] then

r = false

break

end

end

return r

end;

object = "vector"; -- Object type

}

local meta = {

__index = __index;

__tostring = __index.tostring;

__add = __index.add;

__sub = __index.sub;

__mul = __index.mul;

__div = __index.div;

__len = __index.len;

__eq = __index.eq;

__newindex = function(self, d, n)

local a = type(d)

local b = type(n)

if not (a == "number" and d == floor(d) and d > 0) then

error("invalid dimension type (signed integer expected, got "..(a == "number" and d ~= floor(d) and "float" or a)..")", 2)

end

if b ~= "number" then

error("invalid coordinate type (number expected, got "..b..")")

end

d = floor(d)

for i = 1, d-1 do

if not rawget(self, i) then

rawset(self, i, 0)

end

end

rawset(self, d, n)

rawset(self, "n", d)

end;

}

vector = function(v) -- Creates a new vector

v.n = #v

return setmetatable(v, meta)

end

return function(...) -- The same as above, but with additional checks

local v = { ... }

for i=1, #v do

local t = type(v[i])

if t ~= "number" then

error("bad argument #"..i.." (number expected, got "..t..")")

end

end

return vector(v)

end