Quaternion.setFromUnitVectors lacks precision for close to opposite vectors

Describe the bug

A Quaternion calculated using setFromUnitVectors doesn’t align the two unit vectors precisely if it get’s applied.

To Reproduce

run the following code using node (I’ve tested with 14.7.0) or check the live example on JSFiddle.

Code

const three = require("three");

const zAxis = new three.Vector3(0, 0, 1);
// just 3 example Vectors that fail
const normals = [
  new three.Vector3(0.00001630279256671349, 0.00021101192465278993, -0.9999999776040931).normalize(),
  new three.Vector3(-0.00011854270500476976, 0.00027142141201982574, -0.9999999561390212).normalize(),
  new three.Vector3(0.000042675541323141565, -0.00040869364504498944, -0.9999999155741478).normalize(),
];

normals.forEach(normal => {
  const alignNormalsRotation = new three.Quaternion().setFromUnitVectors(normal, zAxis);
  console.log(normal.clone().applyQuaternion(alignNormalsRotation).angleTo(zAxis));
});

Live example

• jsfiddle-latest-release

Expected behavior I would expect the calculations to have higher precision. I’ve only encounterd this amount of error with Vectors that are close to being opposite.

Result of the code:

0.00021164076687348634
0.000296178929600093
0.00041091569275236077

Expected result:

0
0
0

Platform: Tested locally with:

• Device: Desktop
• OS: Windows 10
• NodeJS: v14.7.0
• Three.js version: three@0.110.0

and in the browser with:

• Device: Desktop
• OS: Windows 10
• Browser: Chromium, Firefox, Edge (via jsfiddle see link above)
• Three.js version: “https://threejs.org/build/three.module.js” (17.03.2021)

[WestLangley]

If you feel your testing is exhaustive, give it a go. 😃 I was just opting to be a bit more conservative.

[WestLangley]

@Mugen87 Thanks for working on it!

The links you are looking for are hidden in here: https://github.com/mrdoob/three.js/pull/4580/files.

You can also check out a glm implementation: https://github.com/g-truc/glm/blob/ace16e47780dcef815294715237f51e9129b6eb3/glm/gtx/quaternion.inl#L121-L158