Yeah, alas, that's unfortunately a thing.Ĭlick to expand.I totally agree. I stand by my my recommendation: A-Z and 0-9 only for filenames and paths. Is 100% of all Posix software going to correctly escape it with quotes? What about once it passes it to the NEXT piece of software? the entire default Posix command line relies on spaces to split data apart. space means so much to so many pieces of middleware. PS: underscore (_) you might get away with. Most of that software, probably the vast majority of it, especially the low-level driver stuff, was written by either an intern or a junior guy, or some guy who nobody liked and the tech lead just said "Hey, just have so-and-so finish the driver software, I don't wanna be bothered with it."Īnd besides, most developers, regardless of locale, never test outside of their own locale. That is unfortunately just not going to be the case. Every browser plugin and extension, every toolbar and antivirus solution, everything.Įvery single piece of software, every step of every operation must be coded to handle non-ascii characters. The finite groups generated in this way are examples of Coxeter groups.Click to expand.Yeah, alas, that's unfortunately a thing.Īnytime you use characters outside of A-Z and 0-9 in a filename or a path name, you are now an unpaid test pilot for every single piece of software from the operating system down through the video drivers and Unity and every piece of the toolchain and every piece of middleware and software ever installed on your system. In general, a group generated by reflections in affine hyperplanes is known as a reflection group. Similarly the Euclidean group, which consists of all isometries of Euclidean space, is generated by reflections in affine hyperplanes. Thus reflections generate the orthogonal group, and this result is known as the Cartan–Dieudonné theorem. Every rotation is the result of reflecting in an even number of reflections in hyperplanes through the origin, and every improper rotation is the result of reflecting in an odd number. The product of two such matrices is a special orthogonal matrix that represents a rotation. The matrix for a reflection is orthogonal with determinant −1 and eigenvalues −1, 1, 1. Construction Ī reflection across an axis followed by a reflection in a second axis not parallel to the first one results in a total motion that is a rotation around the point of intersection of the axes, by an angle twice the angle between the axes. Some mathematicians use " flip" as a synonym for "reflection". Typically, however, unqualified use of the term "reflection" means reflection in a hyperplane. Other examples include reflections in a line in three-dimensional space. In a Euclidean vector space, the reflection in the point situated at the origin is the same as vector negation. This operation is also known as a central inversion ( Coxeter 1969, §7.2), and exhibits Euclidean space as a symmetric space. For instance a reflection through a point is an involutive isometry with just one fixed point the image of the letter p under it Such isometries have a set of fixed points (the "mirror") that is an affine subspace, but is possibly smaller than a hyperplane. The term reflection is sometimes used for a larger class of mappings from a Euclidean space to itself, namely the non-identity isometries that are involutions. ![]() A reflection is an involution: when applied twice in succession, every point returns to its original location, and every geometrical object is restored to its original state. ![]() Its image by reflection in a horizontal axis would look like b. ![]() For example the mirror image of the small Latin letter p for a reflection with respect to a vertical axis would look like q. The image of a figure by a reflection is its mirror image in the axis or plane of reflection. In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection. A reflection through an axis (from the red object to the green one) followed by a reflection (green to blue) across a second axis parallel to the first one results in a total motion that is a translation - by an amount equal to twice the distance between the two axes.
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