The best way to interpolate 2D angles

angleLerp.js

/*
2D Angle Interpolation (shortest distance)

Parameters:
a0 = start angle
a1 = end angle
t = interpolation factor (0.0=start, 1.0=end)

Benefits:
1. Angles do NOT need to be normalized.
2. Implementation is portable, regardless of how the modulo "%" operator outputs sign (i.e. Python, Ruby, Javascript)
3. Very easy to remember.

Thanks to Trey Wilson for the closed-form solution for shortAngleDist!
*/

function shortAngleDist(a0,a1) {
    var max = Math.PI*2;
    var da = (a1 - a0) % max;
    return 2*da % max - da;
}

function angleLerp(a0,a1,t) {
    return a0 + shortAngleDist(a0,a1)*t;
}

Very usefull, thanks.

Angles do NOT need to be normalized.

Doesn't seem to be true or I'm doing something wrong...
Trying it here and it works only if I'm passing the previous angle as a1 argument and the new angle as a0 (which is really surprising as description says a0 is start a1 is end). If used as is (a0 as old angle and a1 as a new angle) it's accumulating a huge value in the result over time as the result is never normalized.

In shortAngleDist, why do you need this statement return 2*da % max - da; ?

Thank you for this, it's really useful!
It does appear to have a problem when a1 - a0 is a very small negative value. For example, if a1 - a0 = -1e-16, the result will be incorrect. A solution I found was to remove the sign from the modulo operation:
da = sign(a1 - a0)*(abs(a1 - a0) % max)
and then again on the return:
return sign(a1 - a0)*(2*abs(da) % max) - da

translated from Unity's source code (but with DEGREES), Mathf.LerpAngle

function repeat(t, m) {
  return clamp(t - floor(t / m) * m, 0, m);
}

function lerpTheta(a, b, t) {
  const dt = repeat(b - a, 360);
  return lerp(a, a + (dt > 180 ? dt - 360 : dt), t);
}

Very useful !

How is that better? I see a number of branches, less numerical stability/continuity (due to the clamp which presumably handles rounding errors from the divide)

It's important to note that % has the same operator precedence as * and / in JavaScript, when porting this to other languages. Maybe that's conventional, but in languages where you have to use a function for modulo (for floats), such as Go or GLSL, you have to be mindful of it.

Here's a Golang version:

func shortAngleDist(from float64, to float64) float64 {
	var turn = math.Pi * 2
	var deltaAngle = math.Mod(to-from, turn)
	return math.Mod(2*deltaAngle, turn) - deltaAngle
}

func angleLerp(from float64, to float64, fraction float64) float64 {
	return from + shortAngleDist(from, to)*fraction
}

I prefer the @earlin code
https://gist.github.com/shaunlebron/8832585?permalink_comment_id=3227412#gistcomment-3227412
because when testing godotengine/godot#30564 (the C++ version)

• lerp_angle(-90.0_deg, 90.0_deg, 0.0) returns 90.0_deg
• lerp_angle(-90.0_deg, 90.0_deg, 0.5) returns -180.0_deg instead of 0.0_deg
• lerp_angle(-90.0_deg, 90.0_deg, 1.0) returns -270.0_deg instead of -90.0_deg

Which is not the case with earlin's code.

My quick implementation in C++ using https://github.com/nholthaus/units:

#include "units.h"

using namespace units::literals;
using Radian = units::angle::radian_t;
using Degree = units::angle::degree_t;

template<typename T, typename U>
inline T lerp(T const from, T const to, U const weight)
{
   return from + (to - from) * weight;
}

template<typename T>
inline T constrain(T const value, T const lower, T const upper)
{
    if (value < lower) { return lower; }
    if (value > upper) { return upper; }
    return value;
}

inline Degree lerp_angle(Degree const from, Degree const to, double weight)
{
   auto repeat = [](Degree const t, Degree const m) -> Degree
   {
      return constrain(t - units::math::floor(t / m) * m, 0.0_deg, m);
   };
   const Degree dt = repeat(to - from, 360.0_deg);
   return lerp(from, from + (dt > 180.0_deg ? dt - 360.0_deg : dt), weight);
}

@codergautam nice !