[p5.js 2.0+ Bug Report]: Vector angleBetween() doesn't work for vectors with 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 four dimensional vectors
2. Use angleBetween to compute the angle between them
3. Note that it is incorrect (although no errors were reported)

Snippet:

function setup() {
  let v1 = createVector(1, 0, 0, 0);
  let v2 = createVector(0, 0, 0, 1);
  let theta = v1.angleBetween(v2);
  
  // The correct angle between v1 and v2 is PI/2, but theta is 0
  print(theta);
}

Discussion

The angleBetween() method currently uses cross() to compute the angle. This was fine in p5.js version 1 since vectors were always 3D. But version 2 vectors can have any number of dimensions, so angleBetween() needs to use a more general method. I recommend using the dot product divided by the product of the vector lengths:

angleBetween(v1, v2) = acos(v1.dot(v2) / (v1.mag() * v2.mag()))

This will work for vectors of any dimension (including 2D and 3D vectors).

This issue applies to both the instance and static methods.

Locate the Vector angleBetween() instance and static methods in the p5.js math implementation, then inspect how they use cross() for angle calculation. Verify the behavior with the four-dimensional example and confirm that both methods return PI/2 for perpendicular vectors while continuing to work for 2D and 3D vectors.