Mathematics of three-dimensional eye rotations

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334 Citations (Scopus)


The recording of three-dimensional eye position has become the accepted standard in oculomotor research. In this paper we review the mathematics underlying the representation of three-dimensional eye movements. Rotation matrices, rotation vectors and quaternions are presented, and their relations described. The connection between search coils and rotation matrices is explained, as well as the connection between eye position and eye velocity. While examples of applications of the formulas to vestibulo-ocular research are given, the methods and mathematical analyses are also useful for studying other motor systems.

Original languageEnglish
Pages (from-to)1727-1739
Number of pages13
JournalVision Research
Issue number12
Publication statusPublished - Jun 1995


  • Eye movements
  • Listing'slaw
  • Rotations
  • Search coils
  • Three-dimensional
  • Eye Movements/physiology
  • Time Factors
  • Humans
  • Mathematics
  • Rotation

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