Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Mathematics of three-dimensional eye rotations

T Haslwanter1

  • 1Department of Psychology, University of Sydney, NSW, Australia.

Vision Research
|June 1, 1995
PubMed
Summary

This paper reviews the mathematics for representing 3D eye movements, covering rotation matrices, vectors, and quaternions. It explains how these mathematical tools connect to eye tracking methods and velocity analysis for oculomotor research.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Non invasive assessment of the human tear film dynamics.

Annals of anatomy = Anatomischer Anzeiger : official organ of the Anatomische Gesellschaft·2015
Same author

The distribution of otolith polarization vectors in mammals: comparison between model predictions and single cell recordings.

Hearing research·2008
Same author

SEE++: a biomechanical model of the oculomotor plant.

Annals of the New York Academy of Sciences·2005
Same author

Reduction of ocular muscle power by splitting of the rectus muscle I: biomechanics.

The British journal of ophthalmology·2004
Same author

Reduction of ocular muscle torque by splitting of the rectus muscle II: technique and results.

The British journal of ophthalmology·2004
Same author

Otolith responses to dynamical stimuli: results of a numerical investigation.

Biological cybernetics·2004

Area of Science:

  • Oculomotor research
  • Biomechanics
  • Neuroscience

Background:

  • Three-dimensional eye position recording is standard in oculomotor research.
  • Understanding the mathematical representation of eye movements is crucial for accurate analysis.
  • Existing literature may not comprehensively cover the mathematical underpinnings of 3D eye movement representation.

Purpose of the Study:

  • To review and explain the mathematics underlying the representation of three-dimensional eye movements.
  • To describe the relationships between different mathematical models used for eye movement analysis.
  • To connect common eye tracking methodologies with these mathematical frameworks.

Main Methods:

  • Review of mathematical concepts including rotation matrices, rotation vectors, and quaternions.
  • Explanation of the mathematical relationships between these representations.
  • Description of the connection between search coil data and rotation matrices.
  • Analysis of the relationship between static eye position and dynamic eye velocity.

Main Results:

  • Rotation matrices, rotation vectors, and quaternions provide distinct yet related methods for representing 3D eye orientation.
  • The mathematical framework allows for the conversion between different representational methods.
  • Search coil data can be directly related to rotation matrices for quantitative eye movement analysis.
  • Formulas are presented for calculating eye velocity from positional data.

Conclusions:

  • The reviewed mathematical methods provide a robust foundation for analyzing 3D eye movements.
  • These mathematical tools are essential for advancing oculomotor research, particularly in areas like vestibulo-ocular reflex studies.
  • The principles discussed have broader applicability to the study of other biological motor systems.

Related Experiment Videos