(Lua) Doing mathematical operations with non-number values - lua

Question

I want to make some sort of a Vector3 library for Lua which could let you make simple 3D position operations with simple syntax. I'll mention that I'm using Luaj for running Lua code for Java manipulation.
Here's my beginning code:
Vector3 = {
new = function (x1, y1, z1)
return {x = x1, y = y1, z = z1}
end
}
Position1 = Vector3.new(1, 5, 8)
Position2 = Vector3.new(4, 7, 2)
And here's what I want to be able to happen:
Subtraction = Position1 - Position2
print(Subtraction.x, Subtraction.y, Subtraction.z) -- prints "-3, -2, 6"
Any idea on making EXACT code to work?

Answer 1

This is what metatables and metamethods are for. You should have a read in the documentation.
Basically, they let you redefine what operators (and some other things) do on your values. What you want right now is to define the __sub metamethod, which defines how to handle the - operator. I guess in the future you'll want to redefine the other metamethods as well.
First, define a subtraction function in your Vector3 "class" that takes two vectors:
function Vector3.subtract(u,v)
return Vector3.new(u.x - v.x, u.y - v.y, u.z - v.z)
end
Then create let Vector3 know the metatable it should give all vectors:
Vector3.mt = {__sub = Vector3.subtract}
And when you create a new vector:
new = function (x1, y1, z1)
local vec = {x = x1, y = y1, z = z1}
setmetatable(vec, Vector3.mt)
return vec
end
You could also make the metatable (mt) a local variable inside your new function - that would prevent external code from messing with the metatable (as it would be only accessible by your new function). However, having it inside Vector3 allows you to check against usages like v - "string":
function Vector3.subtract(u,v)
if getmetatable(u) ~= Vector3.mt or
getmetatable(v) ~= Vector3.mt then
error("Only vectors can be subtracted from vectors", 2)
end
return Vector3.new(u.x - v.x, u.y - v.y, u.z - v.z)
end

Answer 2

You could do something like this:
Vector3 = {}
mt = {}
function Vector3:new(_x, _y, _z)
return setmetatable({
x = _x or 0,
y = _y or 0,
z = _z or 0
}, mt)
end
mt.__sub = function(v1, v2) return Vector3:new(v1.x - v2.x, v1.y - v2.y, v1.z - v2.z) end
mt.__tostring = function(v) return "Vector3=(" .. v.x .. "," .. v.y .. "," .. v.z .. ")" end
mt.__index = Vector3 -- redirect queries to the Vector3 table
-- test Vector3
Position1 = Vector3:new(1, 5, 8)
Position2 = Vector3:new(4, 7, 2)
Sub = Position1 - Position2
print(Sub)
which would print:
Vector3=(-3,-2,6)
More on Lua & OO, see: http://lua-users.org/wiki/ObjectOrientationTutorial