-- Small package of 3D vector functions

local mt = {}

local function new(v)
   local vec = {v[1], v[2], v[3]}
   setmetatable(vec, mt)
   return vec
end

local function addvec(v, w)
   return new{v[1]+w[1], v[2]+w[2], v[3]+w[3]}
end

local function subvec(v, w)
   return new{v[1]-w[1], v[2]-w[2], v[3]-w[3]}
end

local function addnum(v, n)
   return new{v[1] + n, v[2] + n, v[3] + n}
end

local function subnum(v, n)
   return new{v[1] - n, v[2] - n, v[3] - n}
end

local function addany(v, x)
   if type(x) == "table" then
      return addvec(v, x)
   else
      return addnum(v, x)
   end
end

local function subany(v, x)
   if type(x) == "table" then
      return subvec(v, x)
   else
      return subnum(v, x)
   end
end

local function scale(v, n)
   return new{v[1]*n, v[2]*n, v[3]*n}
end

local function dot(v, w)
   return v[1]*w[1] +v[2]*w[2] + v[3]*w[3]
end

local function mulany(v, x)
   if type(x) == "table" then
      return dot(v, x)
   else
      return scale(v, x)
   end
end

local function cross(v, w)
   return new {v[2]*w[3] - w[2]*v[3],
               w[1]*v[3] - v[1]*w[3],
               v[1]*w[2] - w[1]*v[2]}
end

local function scaleinv(v,n)
   return new{v[1]/n, v[2]/n, v[3]/n}
end

local function neg(v)
   return v*(-1)
end

local function norm2(v)
   return dot(v,v)
end

local function norm(v)
   return math.sqrt(norm2(v))
end

local function normalize(v)
   return v/norm(v)
end

local function vectostring(v)
   return "{" .. v[1] .. ", " .. v[2] .. ", " .. v[3] .. "}"
end

mt.__add = addany
mt.__sub = subany
mt.__mul = mulany
mt.__div = scaleinv
mt.__unm = neg
mt.__tostring = vectostring

Vector = {
   new = new,
   norm = norm,
   norm2 = norm2,
   cross = cross,
   normalize = normalize,
   x = new{1,0,0},
   y = new{0,1,0},
   z = new{0,0,1},
   origin = new{0,0,0}
}

return Vector