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.