Iterating toward a specific angle on a circle - math

Question

I'm building a robot vehicle that has an on-board compass. Starting from the current orientation of the vehicle in degrees, I would like to rotate it 90 degrees in either direction, using the compass.
I'm supposing that the best way to do this is to rotate the vehicle in increments within a "while" loop and test after each rotational increment if it has moved 90 degrees.
However, while dealing with transitions between two positive points is simple, it becomes challenging with transitions that involve the transition from 0 to 360.
In other words, this code for left rotation fails for obvious reasons:
let startingPoint = 30 // in degrees
let endPoint = startingPoint - 90
while currentPoint > endPoint {
rotateLeft()
}
Is there an equation that will enable this comparison when crossing the 360/0 boundary?

Answer 1

You can check difference, not absolute value.
To find whether difference is outside 90 range, you can use formula that accounts for arbitrary angles including transitions through 0 (don't forget angles should be in radians)
if Cos(startingangle - currentangle) <=0 then
absolute difference is equal or more than Pi/2 (90 degrees)
Here thick arrow shows (ignore axis labels or divide them by 4) Cos of difference of zero start angle with +-30 degrees angles (works for any start angle)
Python demo:
import math
def AngleInRange(value, central, arange):
value = math.radians(value)
central = math.radians(central)
arange = math.radians(arange)
return (math.cos(value - central) >= math.cos(arange))
for a in range (100, 220, 15): #through 180
print(a, AngleInRange(a, 150, 45))
for a in range (-40, 40, 10): #through 0
print(a, AngleInRange(a, -10, 20))
100 False
115 True
130 True
145 True
160 True
175 True
190 True
205 False
-40 False
-30 True
-20 True
-10 True
0 True
10 True
20 False
30 False