Test for approximate rotation

So lets say you have an entity which happens to be of type=Player.
Such that a command block, when powered

testfor @e[r=15,type=Player] {}

will output true.

Now, lets teleport this player

tp @e[r=15,type=Player] ~ ~ ~ -90 45

They should now be facing due east and at the ground.

Now if I test for this:

testfor @e[r=15,type=Player] {Rotation:[0:-90f,1:45f]}

I'll output true as well.

Now the player turns around. the same command block will now output false (Proving that the command block has successfully tested for a players rotation)

but the rotation is a floating point number, having many decimals of accuracy, and the only way to have it tested and it be true (unless you get realllllly lucky and land on exactly -90.000000000) is to tp the player to have that rotation.

I'd like to be able to test for a player's rotation, but in a natural state.

So the fundamental question is... Can i test for a data tag which is Close to a given value?

Ideally it would look like this:

testfor @e[type=Player,r=15] {Rotation:[0:{min:-45,max:-125}]}

but I know this is wrong. So anyone, has anyone found a solution to testing for approximate data tags?

Solution 1:

Here's a video by MNSweet demonstrating rotational direction detection:

Rather than checking the NBT data (i.e. using {}), rotation can be tested for using the target selector arguments ry, rym, rx, and rxm, denoting the maximum and minimum view angle in the horizontal (east, south, etc.) and vertical (up, down) direction, respectively.

For example, to test for someone looking South (=0±22), use

testfor @a[ry=22,rym=-22]

To test for someone looking 45° upwards (±10) and to the northeast (=135±22)

testfor @a[ry=-113,rym=-157,rx=55,rxm=35]

See Commands wiki page for more information.

Solution 2:

I like a function which returns one of the 8 directions. As a standard keypad has 8 directions from the 5 in the middle, and as maps usually show North at the top, I assign 8 to North, 2 to South, 3 to Southeast, etc. BUT, I also like to know if I am looking up or down. If I am looking up, that is a 5 and looking down is 0. That makes it easy to place a block right where I am looking (of course if it is UP you'd want to place it up 2 blocks so you won't clunk your head. /testfor will return a list of targets matching the condition, so check if what returns is the target you are interested in (your player name).

First I check for up/down:
UP /testfor @a[rxm=-90,rx=-66] if true return 5
DN /testfor @a[rxm=66,rx=90] if true return 0

Now do a general check to find out a quadrant using two tests:
/testfor @a[rym=-22.5,ry=157.5]
/testfor @a[rym=-112.5,ry=67.5]
Depending on whether the target was found for both tests:
0 0 89 /testfor @a[rym=-157.5,ry=-112.5] if true return 9 else return 8
0 1 63 /testfor @a[rym=-67.5,ry=-22.5] if true return 3 else return 6
1 0 74 /testfor @a[rym=112.5,ry=157.5] if true return 7 else return 4
1 1 12 /testfor @a[rym=22.5,ry=67.5] if true return 1 else return 2

/testfor with a username and parameters didn't seem to work for me.