A Quaternion Sign Can Change a Naive Midpoint Without Changing Either Endpoint Pose

Authors

  • Cameron Porter Author
  • Jack Brooks Author
  • James Harrison Author

Abstract

Two quaternions with opposite signs encode the same rotation, yet their component average can behave very differently. We examined 615,364 short-interval pose pairs in 52 TUM RGB-D files. Native endpoint signs caused 778 naive normalized midpoints to be undefined or more than one degree from the shortest-path midpoint. The equal-file failure fraction was 0.1732%. Aligning endpoint hemispheres before averaging reduced the maximum observed midpoint discrepancy to numerical precision. This is a representation-consistency result for two-pose midpoints, not a test of physical intermediate orientation or a learned motion model.

Representation audit of native camera quaternions. The deliberately naive midpoint is our comparison rule; native sign choices are valid rotation representations and are not labelled dataset errors.

Original publication: October 28, 2026.

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Published

2026-10-28

Issue

Vol. 1 No. 1 (2026): Inaugural Issue

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Articles

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Copyright (c) 2026 Cameron Porter, Jack Brooks, James Harrison

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