Beware the "Natural" Quaternion
The article discusses the complexities and confusions surrounding the use of quaternions in 3D rotation mathematics. It highlights the existence of two different quaternion conventions, one of which is referred to as the 'natural' quaternion. The author argues that this alternative is not inherently preferable and emphasizes the importance of clear documentation in coding practices.
- ▪There are two different quaternion conventions used in 3D rotations.
- ▪The 'natural' quaternion is presented as an alternative but is argued to be unnecessary.
- ▪Clear communication and documentation are essential to avoid confusion in rotation mathematics.
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Record
| Original publisher | Possibly Wrong |
| Canonical URL | https://possiblywrong.wordpress.com/2021/05/10/beware-the-natural-quaternion/ |
| Publication time | Sun, 24 May 2026 10:11:48 +0000 |
| Retrieval time | 2026-05-24T10:37:32.389Z |
| Last seen | 2026-05-24T10:37:32.389Z |
| Headline source | Publisher (no WeSearch rewrite) |
| Excerpt source | publisher body |
| Excerpt method | First ~120 words (~800 chars) of extracted publisher body, fair-use limited. |
| Summary | WeSearch · cerebras-chat (WeSearch summarizer) |
| Summary source text | contentText |
| Citation coverage | Summary is a WeSearch-generated derivative; primary citation is the original publisher URL. |
| Cluster | 8RSXhvSgxMZl |
| Cluster logic | Grouped by semantic title/content similarity across sources within a rolling window. Same-publisher template collisions are excluded from coverage comparison. |
| Ranking reason | Story pages are not engagement-ranked. Hub feeds use recency, with optional source-diversified chronological ordering (cap consecutive stories per source). No personalized ranking. |
| Publisher visit | Yes — open original |
| Substitutes article? | No — link-out required for full text |
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| Indexing | May the item be indexed (stored, ranked, made findable)? | Allowed |
| Snippet | May a short excerpt of the publisher's text be shown? | Allowed |
| AI summary | May WeSearch generate its own short summary of the article? | Limited |
| Retrieval / RAG | May the content be exposed for third-party retrieval-augmented generation? | Not asserted |
| Model training | May the content be used to train AI models? | Not asserted |
| Commercial reuse | May the content be reused commercially? | Not permitted |
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Opening excerpt (first ~120 words) tap to expand
Beware the “natural” quaternion Posted on May 10, 2021 by possiblywrong Introduction Rotation math can be confusing. But it didn’t need to be this confusing. I think the reason that 3D rotations can be tricky to work with is that there are so many choices of convention– in interpretation, notation, and implementation– and we often do not communicate or document all of those choices clearly and completely. Are we “actively” rotating vectors, or “passively” rotating frames? If the latter, are we rotating from the “body” to “world” frame, or from world to body? Are rotations applied as we write them left to right, or right to left? Are the rotations right-handed or left-handed? Etc.
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Excerpt limited to ~120 words for fair-use compliance. The full article is at Possibly Wrong.
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