Default: Prevent placing sapling if grown tree intersects protection

Add a global 'intersects protection' function to functions.lua for
checking if a specified volume intersects with a protected volume.
A 3D lattice of points are checked with an adjustable interval.
Add a global 'sapling on place' function to avoid duplicated code in
nodes.lua.

mods/default/functions.lua

@@ -481,3 +481,43 @@ minetest.register_abm({
 		end
 	end
 })
+
+
+--
+-- Checks if specified volume intersects a protected volume
+--
+
+function default.intersects_protection(minp, maxp, player_name, interval)
+	-- 'interval' is the largest allowed interval for the 3D lattice of checks
+
+	-- Compute the optimal float step 'd' for each axis so that all corners and
+	-- borders are checked. 'd' will be smaller or equal to 'interval'.
+	-- Subtracting 1e-4 ensures that the max co-ordinate will be reached by the
+	-- for loop (which might otherwise not be the case due to rounding errors).
+	local d = {}
+	for _, c in pairs({"x", "y", "z"}) do
+		if maxp[c] > minp[c] then
+			d[c] = (maxp[c] - minp[c]) / math.ceil((maxp[c] - minp[c]) / interval) - 1e-4
+		elseif maxp[c] == minp[c] then
+			d[c] = 1 -- Any value larger than 0 to avoid division by zero
+		else -- maxp[c] < minp[c], print error and treat as protection intersected
+			minetest.log("error", "maxp < minp in 'default.intersects_protection()'")
+			return true
+		end
+	end
+
+	for zf = minp.z, maxp.z, d.z do
+		local z = math.floor(zf + 0.5)
+		for yf = minp.y, maxp.y, d.y do
+			local y = math.floor(yf + 0.5)
+			for xf = minp.x, maxp.x, d.x do
+				local x = math.floor(xf + 0.5)
+				if minetest.is_protected({x = x, y = y, z = z}, player_name) then
+					return true
+				end
+			end
+		end
+	end
+
+	return false
+end