angle math question

[aseminov]

Hello,

I have a principle angle system that looks like this:

                             0
                             |
                             |
                    -90 ----------- 90
                             |
                             |
                           +-180

given 2 angles angle1 and angle2, I need to write code that will determine if angle2 falls between 135 degrees and -135 degrees away from angle1. Here are some sample values:

angle1    range of angle2 values     
------------------------------------
  0              135 to -135           
90             -135 to -45
180             -45 to 45
-90               45 to 135

Does the following algorithm work in all cases?

int angleDistance = abs(angle1-angle2);
if(angleDistance >= 135)
    return true;
else
   return false;

Thanks!

[OReubens]

it depends on whether or not you account for wrapparound.

angle1 = 10
angle2 = 350

that looks like 20° (actually -20°) but if you only count the progressive angle then it's 340°

[treuss]

Does the following algorithm work in all cases?

int angleDistance = abs(angle1-angle2);
if(angleDistance >= 135)
    return true;
else
   return false;

Your algorithm returns true for angle1 = 170 and angle2 = -170 (distance 20°) but false for angle1 = 10 and angle2 = -10 (also distance 20°). So I would say, your algorithm is flawed.

[aseminov]

how can I fix the algorithm then?

Thanks!

[nuzzle]

how can I fix the algorithm then?

Lets say the two angles are within their defined range to start with. If not you need a transformation to bring that about.

Then you make sure both angles start at the positive y-axis going in the clockwise direction. This means you add 360 to a negative angle. It will come in between 180 and 360 and thus lie outside the defined range but that doesn't matter because you use it as part of a calculation only.

If you now subtract the two angles and the absolute is less than 135 or greater than 360-135 (in case it's a reflex angle) the angles are between -135 and 135 away from each other, like,

if (angle1 < 0) angle1 += 360;
if (angle2 < 0) angle2 += 360;
fi = abs(angle1-angle2);
if (fi < 135 || fi > (360-135)) {
   // angles are less than +-135 away from each other
}

This will also work in a standard 2D cartesian coordinate system where angles start at the positive x-axis and go in the counter-clockwise direction. I recommend you use such a system because everything becomes so much easier.