Types of vection

Figure 8.15: Six different types of optical flows, based on six degrees of freedom for motion of a rigid body. Each of these is a contributing component of vection.
...(e) vertical & & (f) forward/backward \\

Vection can be caused by any combination of angular and linear velocities of the viewpoint in the virtual world. To characterize the effects of different kinds of motions effectively, it is convenient to decompose the viewpoint velocities into the three linear components, $ v_x$, $ v_y$, and $ v_z$, and three angular components, $ \omega_x$, $ \omega_y$, and $ \omega_z$. Therefore, we consider the optical flow for each of these six cases (see Figure 8.15):

  1. Yaw vection: If the viewpoint is rotated counterclockwise about the $ y$ axis (positive $ \omega_y$), then all visual features move from right to left at the same velocity, as shown in Figure 8.15(a). Equivalently, the virtual world is rotating clockwise around the user; however, self motion in the opposite direction is perceived. This causes the user to feel as if she is riding a merry-go-round (recall Figure 8.2).
  2. Pitch vection: By rotating the viewpoint counterclockwise about the $ x$ axis (positive $ \omega_x$), all features move downward at the same velocity, as shown in Figure 8.15(b).
  3. Roll vection: Rotating the viewpoint counterclockwise about $ z$, the optical axis (positive $ \omega_z$), causes the features to rotate clockwise around the center of the image, as shown in Figure 8.15(c). The velocity of each feature is tangent to the circle that contains it, and the speed is proportional to the distance from the feature to the image center.
  4. Lateral vection: In this case, the viewpoint is translated to the right, corresponding to positive $ v_x$. As a result, the features move horizontally; however, there is an important distinction with respect to yaw vection: Features that correspond to closer objects move more quickly than those from distant objects. Figure 8.15(d) depicts the field by assuming vertical position of the feature corresponds to its depth (lower in the depth field is closer). This is a reappearance of parallax, which in this case gives the illusion of lateral motion and distinguishes it from yaw motion.
  5. Vertical vection: The viewpoint is translated upward, corresponding to positive $ v_x$, and resulting in downward flow as shown i Figure 8.15(e). Once again, parallax causes the speed of features to depend on the distance of the corresponding object. This enables vertical vection to be distinguished from pitch vection.
  6. Forward/backward vection: If the viewpoint is translated along the optical axis away from the scene (positive $ v_z$), then the features flow inward toward the image center, as shown in Figure 8.15(f). Their speed depends on both their distance from the image center and the distance of their corresponding objects in the virtual world. The resulting illusion is backward motion. Translation in the negative $ z$ direction results in perceived forward motion (as in the case of the Millennium Falcon spaceship after its jump to hyperspace in the Star Wars movies).
The first two are sometimes called circular vection, and the last three are known as linear vection. Since our eyes are drawn toward moving features, changing the viewpoint may trigger smooth pursuit eye movements (recall from Section 5.3). In this case, the optical flows shown in Figure 8.15 would not correspond to the motions of the features on the retina. Thus, our characterization so far ignores eye movements, which are often designed to counteract optical flow and provide stable images on the retina. Nevertheless, due the proprioception, the brain is aware of these eye rotations, which results in an equivalent perception of self motion.

All forms of vection cause perceived velocity, but the perception of acceleration is more complicated. First consider pure rotation of the viewpoint. Angular acceleration is perceived if the rotation rate of yaw, pitch, and roll vection are varied. Linear acceleration is also perceived, even in the case of yaw, pitch, or roll vection at constant angular velocity. This is due to the merry-go-round effect, which was shown in Figure 8.2(b).

Now consider pure linear vection (no rotation). Any linear acceleration of the viewpoint will be perceived as an acceleration. However, if the viewpoint moves at constant velocity, then this is the only form of vection in which there is no perceived acceleration. In a VR headset, the user may nevertheless perceive accelerations due to optical distortions or other imperfections in the rendering and display.

Steven M LaValle 2020-01-06