[p5.js 2.0+ Bug Report]: Vector.slerp() does not work correctly for vectors of more than three dimensions

Most appropriate sub-area of p5.js?

• Accessibility
• Color
• Core/Environment/Rendering
• Data
• DOM
• Events
• Image
• IO
• Math
• Typography
• Utilities
• WebGL
• WebGPU
• p5.strands
• Build process
• Unit testing
• Internationalization
• Friendly errors
• Other (specify if possible)

p5.js version

2.3.0

Web browser and version

Brave 1.90.122

Operating system

Linux Mint 22.1

Steps to reproduce this

Steps:

1. Create two 4D vectors
2. Use slerp() to interpolate between the two
3. Note the result is incorrect

Snippet:

function setup() {
  let c = 0.5;
  let v1 = createVector(0, 1, 0, 1);
  let v2 = createVector(1, 0, 1, 0);
  v1.slerp(v2, 0.5);
  
  // v1 should be vector[0.707, 0.707, 0.707, 0.707] but is actually vector[0.5, 0.707, 0.5, 1]
  print(v1.toString());
}

Discussion

slerp() currently uses cross() for its computation, which is only defined for 3D vectors. It needs to use a more general formula, which is readily available on the web; search for "slerp formula".

Feel free to adapt the following (to both the instance and static methods). In my brief testing, it gives the same result as the current slerp() for 2D and 3D vectors, and also seems to work correctly for 4D vectors. It can certainly be optimized.

function slerp(v0, v1, t) {
  let m = v0.mag() + (v1.mag() - v0.mag()) * t;
  let r0 = p5.Vector.normalize(v0);
  let r1 = p5.Vector.normalize(v1);
  let a = acos(r0.dot(r1));
  if (a === 0) {
    return p5.Vector.add(v0, p5.Vector.sub(v1, v0).mult(t));
  } else {
    r0.mult(sin((1 - t) * a) / sin(a));
    r1.mult(sin(t * a) / sin(a));
    return r0.add(r1).mult(m);
  }
}

Start with the instance and static p5.Vector.slerp() entry points described in the issue, then reproduce the provided 4D example. Compare the current cross()-based behavior with the proposed general slerp formula, while checking that 2D and 3D results remain unchanged. Done means 4D interpolation produces the expected vector and the existing lower-dimensional behavior is preserved.