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Type variable
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From Wikipedia, the free encyclopedia
In type theory and programming languages, a type variable is a mathematical variable ranging over types. Even in programming languages that allow mutable variables, a type variable remains an abstraction, in the sense that it does not correspond to some memory locations.
Programming languages that support parametric polymorphism make use of universally quantified type variables. Languages that support existential types make use of existentially quantified type variables. For example, the following OCaml code defines a polymorphic identity function that has a universally quantified type, which is printed by the interpreter on the second line.
A piece of amber imaged with this technique. Looking at such an image on a high resolution screen or printout allows studying fine details in a way not otherwise possible. Anaglyph, Red left.
A variation of macrophotography involves using the scanner to produce stereoscopic or “3D“ images of small objects. This is made possible because of the optical system of a typical scanner, which uses prisms to put the sensor at an optical distance from the glass of 3 to 4 feet, allowing a small sensor to cover the entire width of the bed, while keeping the bed physically shallow. This also gives better than expected depth of field, and introduces a certain amount of parallax when the same object appears at different positions on the bed. This allows the generation of stereo pairs, much like the “shift“ technique where a single camera is shifted to produce right and left views of a still life scene.
This technique probably goes back to the earliest days of flatbed scanners and was mentioned on the photo-3D mail list by Bob Wier on December 14, 1995, though he makes vague reference to earlier experiments by others.[20] Though it could be described as a trivial application of a centuries-old technique to a new device, the concept is not widely known, even among stereo photography enthusiasts. This may be due to the common misconception that the typical flatbed scanner uses an imager that spans the width of the bed, thus leading to the assumption that shifting objects would not produce parallax.
The most basic version of this technique involves simply placing the object upside down on the scanner and moving it by hand, but this leads to irregularities between the two images. Better results can be obtained by placing the object in a glass front display box and sliding the box against a straight edge. Smaller objects such as seeds can be placed on a microscope slide and secured using small adhesive labels. Another, more involved technique is to remove the lid and turn the scanner upside down, then move the scanner rather than the subject. This allows the imaging of extremely flexible objects as well as objects such as small plants which cannot be turned upside down. A variation of this method was used in a patented system which involved mechanically moving an inverted scanner to generate multiple views to produce 3D lenticular artwork. This was marketed briefly as a “lenticular starter kit.“ The product has since been discontinued but the inventor continues to use it to produce his own artwork.[21]
Images generated this way can be edited with stereo imaging software and viewed as traditional stereo pairs or can be converted to any of a number of formats, including anaglyphs, which are viewed using common bicolor 3D glasses, such as those often used with 3D TV and printed materials. Anaglyphs can be printed with normal printers and used as 3D posters.
The high resolution of consumer level flatbed scanners allows taking stereoscopic images of objects that would otherwise be possible only through a stereo microscope, with similar limitations involving depth of field. The scanner, of course, does not feature adjustable focus, so the sharpest focus will always be closest to the glass.
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