Maximum Escape Angle
When firing, the Maximum Escape Angle (MEA) is the largest angle offset from zero (i.e., Head-On Targeting) that could possibly hit an enemy bot, given the Game Physics of Robocode.
Calculation
Let's assume a triangle with sides a
, b
and c
and angles (vertices) A
, B
, and C
. A
is the angle opposite to a
, B
is opposite to b, and C
is opposite to c
. The Law of sines says that:
Now let's say that your bot is in the vertex A
and the enemy bot is in the vertex C
. We will fire a bullet with angle A
to hit the bot in vertex B
. We know the value of b
(it is the distance D
from your bot to the enemy).
We don't know c
, but we know that it will be the distance traveled by the bullet. Also, we know that a
will be the distance traveled by the enemy bot. If we put a
, b
, and c
as a function of time, we have:
b = D c = Vb * t (Vb is the bullet speed) a = Vr * t (Vr is the enemy bot velocity)
Now, using the Law of sines:
a/sin(A) = c/sin(C) -> Vr*t / sin(A) = Vb*t / sin(C) -> sin(A) = Vr/Vb * sin(C) -> A = asin(Vr/Vb * sin(C))
We don't know the value of C
, but we can take the worst scenario where
C = PI/2
(sin(C) = 1
) to get a Maximum Escape Angle of
A = asin(Vr/Vb * 1) = asin (Vr/Vb)
.
With a maximum Robot velocity of 8.0, a theoretical Maximum Escape Angle would be asin(8.0/Vb)
. Note that the actual maximum depends on the enemy's current heading, speed, and Wall Distance.
See Also
- Maximum Escape Angle/Precise Positional - A more precise method of calculating Maximum Escape Angle, that doesn't require movement simulation.
- Maximum Escape Angle/Precise - A sophisticated calculation for Maximum Escape Angle, using Precise Prediction.
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