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[Lycaon]

For the record, I'm using Unity and C#.

So, apologies if I don't explain this well. I have an object (an enemy), and I need to be able to tell when the player is in one of eight directions (front, back, left, right, but also the diagonals).

Basically, I'm doing a DOOM-style sprite-based 3D effect, so I need to change what animations the monsters are using depending on how the player is looking at them.

How should I go about this?

[jgrams]

Something like:

Code:

(atan2(x, y) + PI/8) % (PI/4)

This should give you an octant (0 through 7, or -3 through 4? it's late and I don't remember the range of atan2). atan2 gives you the angle in radians, given x, y (or x, z? whichever way your floor goes). Take the remainder from dividing by PI/4 (45 degrees, one-eighth of a circle) to get the octant, except you want to shift it by half that (PI/8 radians or 22.5 degrees) first so that it rounds properly.

Hope that helps...

[JakobProgsch]

Urgh, why use angles (for anything really, they are evil).

If you take the difference of the positions then you can just "look at the components". The sign of the x and y differences instantly tell you left, right, up and down. To tell if something is on a diagonal you can look at something like abs(min/max) > tan(pi/8). And since that tan is of a constant you don't actually have to compute it in code...

[jgrams]

Because I think what the OP is looking for is an angle (an integer-valued angle in a system of units where 8 units is a full turn)?

I thought about mentioning the "look at the components" approach, but it's messy and I think it expresses the intent poorly. I could definitely see taking a vector approach if you wanted the unit vector in the nearest of the eight directions, to avoid converting from a vector to an angle and then immediately back. But in this case I don't think it makes sense.

Both approaches are discussed a bit in this SE question:
http://gamedev.stackexchange.com/questions/49290/whats-the-best-way-of-translating-a-2d-vector-into-the-closest-8-way-compass-di

[BorisTheBrave]

atan2 works fine, but for the hell of it I tried doing it as neatly as possible without angles.

Code:

s = 0.3826834324
c = 0.9238795325
t1 = c*x+s*y
t2 = -s*x+c*y
q1 = t1 > 0
q2 = t2 > 0
d = (q1 ? 4 : 0) + (q1 ^ q2 ? 2 : 0) + (q1 ^ q2 ^ (abs(t1) > abs(t2)) ? 1 : 0)

[Lycaon]

Something like:

Code:

(atan2(x, y) + PI/8) % (PI/4)

This should give you an octant (0 through 7, or -3 through 4? it's late and I don't remember the range of atan2). atan2 gives you the angle in radians, given x, y (or x, z? whichever way your floor goes). Take the remainder from dividing by PI/4 (45 degrees, one-eighth of a circle) to get the octant, except you want to shift it by half that (PI/8 radians or 22.5 degrees) first so that it rounds properly.

Hope that helps...

Thanks. I've never used atan2 before, but it's only returning numbers less than one and greater than negative one. I'm feeding it the player's x and z coordinates converted to the enemy's local spaaaaaace. Is this supposed to happen?

Code:

		relativePoint = transform.parent.InverseTransformPoint(player.position);

		octant = (Mathf.Atan2(relativePoint.x, relativePoint.z) + Mathf.PI/8) % (Mathf.PI/4);

[jgrams]

@BorisTheBrave: Sweeeet!

@Lycaon: gah, I'm sorry, I did totally screw that up. Should be divide and round, not mod. Try the math from the stackexchange post:

Code:

octant = round(8 * atan2(x, z) / (2*PI) + 8) % 8

[Lycaon]

@BorisTheBrave: Sweeeet!

@Lycaon: gah, I'm sorry, I did totally screw that up. Should be divide and round, not mod. Try the math from the stackexchange post:

Code:

octant = round(8 * atan2(x, z) / (2*PI) + 8) % 8

Thanks much! That works perfectly.

[gimymblert]

another way, since it's unity is to do teh dot product of the transform.forward with the forward and right vector of the target vector.