 among these and other mirror array display features explained elsewhere herein.
Though low-resolution versions of the technique of the present invention have been possible for centuries, high resolution versions, quickly designed and fabricated, have only become recently possible, as the design and construction process involves precise and highly iterated measurements and calculations, digital imaging, 3D modeling and raytracing systems, and computer driven manufacturing systems.
In a photograph of a colorful city scene with cars, pedestrians, store fronts and window displays, to a certain rough accuracy all colors and shades are present, in greater or smaller abundance. If copies of this photograph are cut into tiny pieces, any image to a certain rough accuracy can be constructed with these pieces, mosaic style. Depending upon the size of the mosaic pieces this image can be crude, or photorealistic.
Picture such a mosaic, a colorful abstract image of a fish, constructed of tiles cut from this city scene photograph. Picture this fish image hanging opposite the original city scene photograph. This fish is mostly yellow, though there are only a few small patches of yellow in the city scene. Many copies of the city scene photo were cut up to obtain enough yellow pieces to build the fish image mosaic. Assume that all mosaic pieces are cut in an accurate square grid pattern, and are numbered with their row and column location in the city scene photograph.
Now, assume that we replace each tiny paper fleck of the diced photograph, used as a mosaic piece to form the fish, with a mirrored tile. We now have a faceted mirror, but no more fish. Assume that we stand at a certain position from which we can see the city scene reflected in the faceted mirror, as they hang opposite each other. We look in the faceted mirror and we see a slightly, randomly distorted cityscape.
Now, and this is the key step, assume that we very precisely angle each tile in the mirror mosaic so that it (each tile) reflects, from where we are standing, the exact position in the photograph from where that tile's tiny photo section was cut. The mosaic image of the fish is now recovered, this time as an array of tiny reflections. From our particular viewing location, the cityscape is “reflectively translated” into the fish image.
Let's now follow the same procedure again, this time constructing a mosaic image of a car on a desert highway, from flecks of the same cityscape photograph, and hang that mosaic next to the mirror fish. Let's again convert each photo fleck into a mirror tile, angle-targeting each mirror tile to the correct position in the reflective reference photo, the cityscape, as before. At the same position from which we see the fish reflection, the second mosaic reflects an entirely different image from the same original. The first mirror grid reflectively translates the cityscape into a fish, and the second mirror grid reflectively translates it into a desert highway scene.
Additional images can similarly be derived from the city scene from additional mirror arrays. Instead of adding more arrays, we can also use these two existing mirror arrays to present different images, from alternate viewing positions. From only one position do these mirror arrays reflect the city scene photograph, and thus display a fish and a desert scene. From other positions these two arrays simply reflect blank spaces on the wall. If we hang further copies of the city scene at these blank wall locations they will not exactly reflect as a fish or a desert scene, because the geometry will be distorted, and most mirror tiles will reflect a slightly offset position in the city photograph. To retain faithful reflections of the fish and the desert scene the city scene reflection source image would need to be distorted to compensate for the changed geometry. However, more interesting than providing additional fish and desert scene images from the two mirror arrays, might be to derive entirely new images from these arrays, to be presented at the additional viewing positions. How is this done? Take for example a photograph of Abraham Lincoln. To display Abraham Lincoln to a new viewing position in one of the existing mirror arrays a specifically derived graphic pattern must be placed at the blank area of the wall that is reflected by the array from that given viewing position. That graphic pattern is derived, specifically, by projecting the image of Abraham Lincoln backwards through the given mirror array. This results in an entirely abstract image, unrecognizable except when viewed in the mirror array. The translation pattern that changes the city scene into a fish is a very specific pattern, a very specific arrangement of mirror tile angles. If we want to change the output image from a fish we must change the input image from a city scene, and that input image will not be recognizable, since that image is the function of a given output image (Abraham Lincoln, a satellite image of a river delta, a colorful glass marble) multiplied, in a sense, by the existing mirror array. The mirror array was originally a function of the color arrangement in the fish as compared to the color arrangement of the city scene. Though this resulting array may not be random in a perfect mathematical sense, for current purposes it is essentially random, and when used as an encode pattern for new images to be viewed in that array, the resulting encoded reference images are, to the eye, random patterns.
We now have a gallery with two mirror arrays on one wall and, on the opposite wall, one photo of a city scene, and several abstract images, the reverse encoded source images for a photo of Abraham Lincoln and several other images. Viewers stepping from one position to the next first see in the reflection grid the fish and the desert scene. Then they see the additional images from the additional viewing positions. The additional images are entirely distinct and different, none are visible from any position other than their assigned viewing position.
We've seen two illustrations of the general principle that any image can be reflectively translated into any other image, provided the original image is a palette super-set of the reflectively constructed image (the fish and the desert scene). We've also seen several examples of how any arbitrary reflection grid can be used to construct any given image, provided that this new graphic is produced with a reference graphic that was backward calculated, through that reflection grid, from this desired display image.
Let's look now at some image effects that can be generated when the reflection reference colors are freely configurable at the same time that the reflection grid mirror angles are also freely configurable, both taking their form from the needs of the desired image effect. Removing the constraints on the design of both the reflection reference and the mirror grid allows a wealth of display effects otherwise not possible. To explore one of these new effects, let's work with just the original cityscape and the fish.
Assume that we remove all parts of the reference image (the cityscape photo) that are not reflectively referenced to construct the image of the fish—those sections of the photographs not targeted by any mirror tiles—leaving just a few patches of the original photograph. Though most parts of the photographs are missing, leaving just a skeleton of patches, the reflected fish image remains completely intact.
Note that although there are only a few small patches of yellow in the city scene photograph, the fish is mostly yellow. When cutting up the cityscape it took many copies of the photograph to make enough yellow mosaic pieces to construct the fish. When extracting the same amount of yellow using mirrors, however, there is no shortage, since any number of the mirror tiles can simultaneously reflect the same small yellow sections of the original image.
The correlation between each mirror tile and its assigned color reference, and the reflection of that color back toward the viewing position, are reflection vectors. This elementary discussion treats the reflection vector simply, omitting certain complications like the fact that there are really two vectors, one for each eye when dealing with narrow-field reference color sources and we gloss over several other geometric subtleties. What is introduced here is the general notion that the reflection vectors from viewer to mirror tile and mirror tile to reference color are based on easily computed geometry and this simple geometry is at the center of this system and simple adjustments of this geometry are the basis for various image effects. Three elements in this system—viewer, mirror, source color pattern—form a single reflection, a single V shape, at the individual mirror tile level, and a flock of variously angled Vs, at the image level.
For our next example we'll stretch both ends of all reflection vectors from points into lines. The reference graphic swatches become lines or stripes and the viewing positions become paths. These paths can be vertical, lateral or any shape. If each reflection reference is extended into a lateral line then the viewing position is thus extended laterally. The viewing area shape and the reference graphic shape are, simply, reciprocal mirrors of each other.
If we change the color of each mirror's reflection source as it moves along its path, that color change can be seen by the viewer of the image as he or she moves in either direction along the viewing path. For example, the reference image stripes can be darkened gradually to black, and this darkening will be seen in the reflection as the viewer moves along the viewing path. With this in mind, we can start to explore time-based image effects. In order to do so, we'll first need to change the geometry of our color reference graphics, to allow all tile color reference sources to be extended into lines, but without those lines crossing and obscuring each other.
After all portions of the cityscape that are not reflectively referenced as source colors from which to construct the fish are removed from the cityscape image, all that remains is the fish image palette, though possibly with duplicate colors. If we remove all duplicate colors, we'll need to re-aim all mirror tiles that referenced the duplicates, to now reference the single instances of those colors. If we then stack these colors in a vertical column, in a series of spectra, sorted by brightness, and then again re-aim all the tiles so that they still retain their reflective reference target colors, the reflectively constructed image