Curve Fitting - Catmull-Rom spline

CatmullRomSpline.lua

function smooth( points, steps )

	if #points < 3 then
		return points
	end

	local steps = steps or 5

	local spline = {}
	local count = #points - 1
	local p0, p1, p2, p3, x, y

	for i = 1, count do

		if i == 1 then
			p0, p1, p2, p3 = points[i], points[i], points[i + 1], points[i + 2]
		elseif i == count then
			p0, p1, p2, p3 = points[#points - 2], points[#points - 1], points[#points], points[#points]
		else
			p0, p1, p2, p3 = points[i - 1], points[i], points[i + 1], points[i + 2]
		end	

		for t = 0, 1, 1 / steps do

			x = 0.5 * ( ( 2 * p1.x ) + ( p2.x - p0.x ) * t + ( 2 * p0.x - 5 * p1.x + 4 * p2.x - p3.x ) * t * t + ( 3 * p1.x - p0.x - 3 * p2.x + p3.x ) * t * t * t )
			y = 0.5 * ( ( 2 * p1.y ) + ( p2.y - p0.y ) * t + ( 2 * p0.y - 5 * p1.y + 4 * p2.y - p3.y ) * t * t + ( 3 * p1.y - p0.y - 3 * p2.y + p3.y ) * t * t * t )

			--prevent duplicate entries
			if not(#spline > 0 and spline[#spline].x == x and spline[#spline].y == y) then
				table.insert( spline , { x = x , y = y } )				
			end	
			
		end

	end	

	return spline

end

function draw( points ) 
	for i = 1, #points do
		local point = points[i]
		display.newCircle(point.x, point.y, 2)
	end 
end

local points = { {x = 100, y = 100}, {x = 100, y = 200}, {x = 200, y = 200}, {x = 200, y = 300} }
--draw(points)


local spline = smooth( points )
draw(spline)

So could this be used for an arc of throwing a grenade in a video game for example? If the known points are the start, end, and mid? If so, do you think you'd be able to translate this to 3D with x,y,z instead of just x & y?