I hope i can ask this question. Its cleary related to some field of math, where as i dont know how its called..In fact, i cant even describe the problems in terms that a professional would understand in a few words (topic).
The green and red dot represent a starship each.
Based upon the angle between both starships (they are shooting each) other, i want to calculate a a chance to hit that specific target from that angle.
Starships have fixed hit chances for the 4 major locations, front/aft/port/board or 0/180/90/270 respectivly. However, if the firing angle is between those arcs, i want to calculate a mixed hitchances based on the two nearest profile values.
In the example below, a angle of 45 degree would certainly result in 77.5% (70 + 85/2). However, for 44 or 46 degree im already unsure.
However, for any hit angle between 0 and 90, excluding 45, i dont know i would calculate the...average ? for that specific angle. Can anyone advice ?
You could probably use something that mathematicians call "linear interpolation". It's really just a more general version of the technique you used to get a value for 45 degrees.
Suppose you know the probabilities $P_A$ and $P_B$ for two angles $A$ and $B$. Now we want to calculate the probability $P_C$ for some other angle $C$, where $A \le C \le B$.
The linear interpolation formula is: $$ P_C = \frac{(B-C)P_A + (C-A)P_B }{B - A} $$ Note that:
Example 1:
Suppose $A = 0$ and $B=90$, and the corresponding probabilities are $P_A = 70$ and $P_B = 85$. If $C=45$, then $$ P_C = \frac{(90-45)*(70) + (45-0)*(85) }{90 - 0} = 77.5 $$ Example 2:
Suppose $A = 0$ and $B=90$, and the corresponding probabilities are $P_A = 70$ and $P_B = 85$. If $C=30$, then $$ P_C = \frac{(90-30)*(70) + (30-0)*(85) }{90 - 0} = 75 $$