A simple Vector2D class used in Corona SDK games.

Vector2D.lua

Vector2D = {}

function Vector2D:new(x, y)  
  local object = { x = x, y = y }
  setmetatable(object, { __index = Vector2D })  
  return object
end

function Vector2D:copy()
	return Vector2D:new(self.x, self.y)
end

function Vector2D:magnitude()
	return math.sqrt(self.x^2 + self.y^2)
end

function Vector2D:normalize()
	local temp
	temp = self:magnitude()
	if temp > 0 then
		self.x = self.x / temp
		self.y = self.y / temp
	end
end

function Vector2D:limit(l)
	if self.x > l then
		self.x = l		
	end
	
	if self.y > l then
		self.y = l		
	end
end

function Vector2D:equals(vec)
	if self.x == vec.x and self.y == vec.y then
		return true
	else
		return false
	end
end

function Vector2D:add(vec)
	self.x = self.x + vec.x
	self.y = self.y + vec.y
end

function Vector2D:sub(vec)
	self.x = self.x - vec.x
	self.y = self.y - vec.y
end

function Vector2D:mult(s)
	self.x = self.x * s
	self.y = self.y * s
end

function Vector2D:div(s)
	self.x = self.x / s
	self.y = self.y / s
end

function Vector2D:dot(vec)
	return self.x * vec.x + self.y * vec.y
end

function Vector2D:dist(vec2)
	return math.sqrt( (vec2.x - self.x) + (vec2.y - self.y) )
end

-- Class Methods

function Vector2D:Normalize(vec)	
	local tempVec = Vector2D:new(vec.x,vec.y)
	local temp
	temp = tempVec:magnitude()
	if temp > 0 then
		tempVec.x = tempVec.x / temp
		tempVec.y = tempVec.y / temp
	end
	
	return tempVec
end

function Vector2D:Limit(vec,l)
	local tempVec = Vector2D:new(vec.x,vec.y)
	
	if tempVec.x > l then
		tempVec.x = l		
	end
	
	if tempVec.y > l then
		tempVec.y = l		
	end
	
	return tempVec
end

function Vector2D:Add(vec1, vec2)
	local vec = Vector2D:new(0,0)
	vec.x = vec1.x + vec2.x
	vec.y = vec1.y + vec2.y
	return vec
end

function Vector2D:Sub(vec1, vec2)
	local vec = Vector2D:new(0,0)
	vec.x = vec1.x - vec2.x
	vec.y = vec1.y - vec2.y
	
	return vec
end

function Vector2D:Mult(vec, s)
	local tempVec = Vector2D:new(0,0)
	tempVec.x = vec.x * s
	tempVec.y = vec.y * s
	
	return tempVec
end

function Vector2D:Div(vec, s)
	local tempVec = Vector2D:new(0,0)
	tempVec.x = vec.x / s
	tempVec.y = vec.y / s
	
	return tempVec
end

function Vector2D:Dist(vec1, vec2)
	return math.sqrt( (vec2.x - vec1.x) + (vec2.y - vec1.y) )
end

return Vector2D

Here's how to limit the actual magnitude of a vector (the limit function in the code above only deals with individual components, not magnitude). I ported this from the openFrameworks ofVec3f class (https://github.com/openframeworks/openFrameworks/blob/master/libs/openFrameworks/math/ofVec3f.h#L931)

function Vector2D:LimitMagnitude(vec, max)
    local tempVec = Vector2D:new(vec.x, vec.y)
    local lengthSquared = tempVec.x * tempVec.x + tempVec.y * tempVec.y
    if lengthSquared > max * max and lengthSquared > 0 then
        local ratio = max / math.sqrt(lengthSquared)
        tempVec.x = tempVec.x * ratio
        tempVec.y = tempVec.y * ratio
    end

    return tempVec
end