The smallest difference between 2 Angles

Question

Given 2 angles in the range -PI -  PI around a coordinate  what is the value of the smallest of the 2 angles between them   Taking into account that the difference between PI and -PI is not 2 PI but zero   Example   Imagine a circle  with 2 lines coming out from the center  there are 2 angles between those lines  the angle they make on the inside aka the smaller angle  and the angle they make on the outside  aka the bigger angle  Both angles when added up make a full circle  Given that each angle can fit within a certain range  what is the smaller angles value  taking into account the rollover

User · Answer

There is no need to compute trigonometric functions. The simple code in C language is:

#include <math.h>
#define PIV2 M_PI+M_PI
#define C360 360.0000000000000000000
double difangrad(double x, double y)
{
double arg;

arg = fmod(y-x, PIV2);
if (arg < 0 )  arg  = arg + PIV2;
if (arg > M_PI) arg  = arg - PIV2;

return (-arg);
}
double difangdeg(double x, double y)
{
double arg;
arg = fmod(y-x, C360);
if (arg < 0 )  arg  = arg + C360;
if (arg > 180) arg  = arg - C360;
return (-arg);
}

let dif = a - b , in radians

dif = difangrad(a,b);

let dif = a - b , in degrees

dif = difangdeg(a,b);

difangdeg(180.000000 , -180.000000) = 0.000000
difangdeg(-180.000000 , 180.000000) = -0.000000
difangdeg(359.000000 , 1.000000) = -2.000000
difangdeg(1.000000 , 359.000000) = 2.000000

No sin, no cos, no tan,.... only geometry!!!!

User · Answer

A simple method  which I use in C   is  double deltaOrientation   angle1 - angle2  double delta    remainder deltaOrientation  2 M PI

User · Answer

x is the target angle  y is the source or starting angle   atan2 sin x-y   cos x-y     It returns the signed delta angle  Note that depending on your API the order of the parameters for the atan2   function might be different

User · Answer

I rise to the challenge of providing the signed answer   def f x y     import math   return min y-x  y-x 2 math pi  y-x-2 math pi  key abs

User · Answer

If your two angles are x and y  then one of the angles between them is abs x - y   The other angle is  2   PI  - abs x - y   So the value of the smallest of the 2 angles is   min  2   PI  - abs x - y   abs x - y     This gives you the absolute value of the angle  and it assumes the inputs are normalized  ie  within the range  0  2p      If you want to preserve the sign  ie  direction  of the angle and also accept angles outside the range  0  2p  you can generalize the above  Here s Python code for the generalized version   PI   math pi TAU   2 PI def smallestSignedAngleBetween x  y       a    x - y    TAU     b    y - x    TAU     return -a if a  lt  b else b   Note that the   operator does not behave the same in all languages  particularly when negative values are involved  so if porting some sign adjustments may be necessary

User · Answer

For UnityEngine users  the easy way is just to use Mathf DeltaAngle

User · Answer

This gives a signed angle for any angles   a   targetA - sourceA a    a   180    360 - 180   Beware in many languages the modulo operation returns a value with the same sign as the dividend  like C  C    C   JavaScript  full list here   This requires a custom mod function like so   mod    a  n  - gt  a - floor a n    n   Or so   mod    a  n  - gt   a   n   n    n   If angles are within  -180  180  this also works   a   targetA - sourceA a     a gt 180    -360    a lt -180    360   0   In a more verbose way   a   targetA - sourceA a -  360 if a  gt  180 a    360 if a  lt  -180

User · Answer

An efficient code in C   that works for any angle and in both  radians and degrees is   inline double getAbsoluteDiff2Angles const double x  const double y  const double c           c can be PI  for radians  or 180 0  for degrees       return c - fabs fmod fabs x - y   2 c  - c

User · Answer

Arithmetical  as opposed to algorithmic  solution   angle   Pi - abs abs a1 - a2  - Pi

[language-agnostic] The smallest difference between 2 Angles

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