Abstract
A 3-dimensional object may contain tunnels passing through the object so that when the object rotates, if the object is viewed from a certain angle, the tunnel is only visible for the moment that the tunnel is pointed directly at the viewer's eye. This system of tunnels can be used to create an animated system of dots when the shape rotates, and the dots can be positioned so that they create the animated illusion of dots moving along the surface of the shape in the opposite of the true direction of rotation.
Claims
1. A system comprising: a solid 3-dimensional shape, containing a plurality of tunnels through which light can pass such that each of the plurality of tunnels is only visible as a dot when the shape is oriented so that that tunnel is pointed directly at the viewer's eye, and such that the dots visible at different times create an animated optical illusion as the shape rotates; and a device, causing the shape to rotate at a constant speed.
2. The system of claim 1 wherein the device creating rotating motion is physically part of the 3-dimensional shape.
3. The system of claim 1 wherein the device creating rotating motion is physically separate from the 3-dimensional shape but attached in a way to drive the rotating motion.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0008] FIG. 1 illustrates the geometry of a single tunnel passing through a cylinder, forming a 10-degree angle with the horizontal plane, seen from a top view.
[0009] FIG. 2 illustrates the same shape as FIG. 1 seen from a side view.
[0010] FIG. 3 illustrates the geometry of a system of tunnels positioned to create the illusion of a single dot moving in the opposite of the true direction of rotation.
[0011] FIG. 4 illustrates the geometry of multiple systems of tunnels (repeated instances of the system depicted in FIG. 3), positioned to create the illusion of multiple dots moving in the opposite of the true direction of rotation.
DETAILED DESCRIPTION
[0012] FIG. 1 shows a top view of a cylinder 110 with a single tunnel 120 passing through the cylinder at a 10-degree angle with the ground.
[0013] FIG. 2 shows the same cylinder 110 from a side view. If a viewer is viewing the cylinder 110 from above at an angle of 10 degrees, one can imagine that as the cylinder 110 rotates through a full rotation cycle, the tunnel is only visible for the single moment that the tunnel is pointed directly at the viewer's eye 210. The cylinder is shown connected to a device 220 driving the rotation of the cylinder.
[0014] FIG. 3 shows the top view of a system of tunnels passing through the cylinder 110, positioned so that as the cylinder 110 rotates clockwise, if the cylinder 110 is viewed from above at a 10-degree angle, the tunnels 120 create the illusion of a single dot moving in the opposite of the true direction of rotation. The point at which the tunnels converge is at the lower ends of the tunnels 310; the divergent ends of the tunnel are the higher ends of the tunnels 320. If one imagines the circular shape rotating clockwise, and imagines the point of view of a viewer who can only see each tunnel 120 when the “upper” end of the tunnel is pointed directly toward the viewer's eye, then even though the bottom edge of the shape is moving from right to left, the tunnels will create in the viewer's perception a series of dots with each one appearing to the right of the previous one, such that together they create the animated illusion of a single dot moving from left to right. As this shape rotates, during the period of rotation when all of the “higher” ends of the tunnels are on the opposite side of the shape from the viewer's eye, no dots will be visible to the viewer.
[0015] FIG. 4 depicts the geometry of a cylinder 110 containing multiple systems of tunnels, where each system of tunnels is identical to the system shown in FIG. 3, translated and rotated within the geometry of the shape. This ensures that, unlike the shape depicted in FIG. 3, as this shape rotates there are always multiple dots visible to the viewer's eye, each appearing to move in the opposite from the true direction of movement of the side of the shape facing the viewer. By ensuring that multiple dots are always visibly moving, this enhances the illusion of continuous rotation of the shape in the opposite of the direction of true rotation.
