[p5.js 2.0+ Bug Report]: Vector angleBetween() doesn't work for vectors with more than three dimensions

[sidwellr]

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.