A virtual ophthalmotrope illustrating oculomotor coordinate systems and retinal projection geometry.

Eye movements are kinematically complex. Even when only the rotational component is considered, the noncommutativity of 3D rotations makes it hard to develop good intuitive understanding of the geometric properties of eye movements and their influence on monocular and binocular vision. The use of at least three major mathematical systems for describing eye positions adds to these difficulties. Traditionally, ophthalmotropes have been used to visualize oculomotor kinematics. Here, we present a virtual ophthalmotrope that is designed to illustrate Helmholtz, Fick, and rotation vector coordinates, as well as Listing's extended law (L2), which is generalized to account for torsion with free changing vergence. The virtual ophthalmotrope shows the influence of these oculomotor patterns on retinal projection geometry.

[1]  A. Smit,et al.  Synapse Formation between Central Neurons Requires Postsynaptic Expression of the MEN1 Tumor Suppressor Gene , 2001, The Journal of Neuroscience.

[2]  Kai M Schreiber,et al.  The extended horopter: quantifying retinal correspondence across changes of 3D eye position. , 2006, Journal of vision.

[3]  J. Douglas Crawford,et al.  The motor side of depth vision , 2001, Nature.

[4]  A. V. van den Berg,et al.  Binocular eye orientation during fixations: Listing's law extended to include eye vergence. , 1993, Vision research.

[5]  Werner Haustein,et al.  Considerations on Listing's Law and the primary position by means of a matrix description of eye position control , 1989, Biological Cybernetics.

[6]  G A FRY,et al.  The center of rotation of the eye. , 1962, American journal of optometry and archives of American Academy of Optometry.

[7]  Harris Kern,et al.  About the Center , 2019, After Promontory.

[8]  D. Tweed,et al.  Stereopsis Outweighs Gravity in the Control of the Eyes , 2001, The Journal of Neuroscience.

[9]  T. Vilis,et al.  Rotation of Listing's plane during vergence , 1992, Vision Research.

[10]  Douglas Tweed,et al.  PII: S0042-6989(97)00002-3 , 2003 .

[11]  P. Cz..  Handbuch der physiologischen Optik , 1896 .

[12]  Andrew J. Hanson,et al.  Visualizing quaternions , 2005, SIGGRAPH Courses.

[13]  M. J. Allen.  The dependence of cyclophoria on convergence, elevation and the system of axes. , 1954, American journal of optometry and archives of American Academy of Optometry.

[14]  Raymond van Ee,et al.  The influence of cyclovergence on unconstrained stereoscopic matching , 2003, Vision Research.

[15]  D Tweed,et al.  Implications of rotational kinematics for the oculomotor system in three dimensions. , 1987, Journal of neurophysiology.

[16]  T. Haslwanter.  Mathematics of three-dimensional eye rotations , 1995, Vision Research.

[17]  A. V. D. Berg,et al.  Binocular eye orientation during fixations: Listing's law extended to include eye vergence , 1993, Vision Research.

[18]  H. Simonsz,et al.  19th century mechanical models of eye movements, Donders' law, Listing's law and Helmholtz' direction circles. , 1990 .

[19]  G A FRY,et al.  THE MECHANICS OF ELEVATING THE EYE. , 1963, American journal of optometry and archives of American Academy of Optometry.

[20]  S. Judge,et al.  Reflection makes sense of rotation of the eyes , 2006, Vision Research.