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OFF (file Format)
OFF (Object File Format) is a geometry definition file format containing the description of the composing polygons of a geometric object. It can store 2D or 3D objects, and simple extensions allow it to represent higher-dimensional objects as well. Though originally developed for Geomview, a geometry visualization software, other software has adapted the simple standard. Composition The composition of a standard OFF file is as follows: * First line (optional): the letters OFF to mark the file type. *Second line: the number of vertices, number of faces, and number of edges, in order (the latter can be ignored by writing 0 instead). * List of vertices: X, Y and Z coordinates. * List of faces: number of vertices, followed by the indexes of the composing vertices, in order (indexed from zero). **Optionally, the RGB values for the face color can follow the elements of the faces. The four-dimensional OFF format, most notably used by Stella4D, which allows visualization of four-dime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
File Format
A file format is a standard way that information is encoded for storage in a computer file. It specifies how bits are used to encode information in a digital storage medium. File formats may be either proprietary or free. Some file formats are designed for very particular types of data: PNG files, for example, store bitmapped images using lossless data compression. Other file formats, however, are designed for storage of several different types of data: the Ogg format can act as a container for different types of multimedia including any combination of audio and video, with or without text (such as subtitles), and metadata. A text file can contain any stream of characters, including possible control characters, and is encoded in one of various character encoding schemes. Some file formats, such as HTML, scalable vector graphics, and the source code of computer software are text files with defined syntaxes that allow them to be used for specific purposes. Specifications ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polygons
In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed ''polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two together, may be called a polygon. The segments of a polygonal circuit are called its '' edges'' or ''sides''. The points where two edges meet are the polygon's '' vertices'' (singular: vertex) or ''corners''. The interior of a solid polygon is sometimes called its ''body''. An ''n''-gon is a polygon with ''n'' sides; for example, a triangle is a 3-gon. A simple polygon is one which does not intersect itself. Mathematicians are often concerned only with the bounding polygonal chains of simple polygons and they often define a polygon accordingly. A polygonal boundary may be allowed to cross over itself, creating star polygons and other self-intersecting polygons. A polygon is a 2-dimensional example of the more general polytope in any number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geomview
The Geometry Center was a mathematics research and education center at the University of Minnesota. It was established by the National Science Foundation in the late 1980s and closed in 1998. The focus of the center's work was the use of computer graphics and visualization for research and education in pure mathematics and geometry. The center's founding director was Al Marden. Richard McGehee directed the center during its final years. The center's governing board was chaired by David P. Dobkin. Geomview Much of the work done at the center was for the development of Geomview, a three-dimensional interactive geometry program. This focused on mathematical visualization with options to allow hyperbolic space to be visualised. It was originally written for Silicon Graphics workstations, and has been ported to run on Linux systems; it is available for installation in most Linux distributions through the package management system. ''Geomview'' can run under Windows using Cygwin and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RGB Color Model
The RGB color model is an additive color model in which the red, green and blue primary colors of light are added together in various ways to reproduce a broad array of colors. The name of the model comes from the initials of the three additive primary colors, red, green, and blue. The main purpose of the RGB color model is for the sensing, representation, and display of images in electronic systems, such as televisions and computers, though it has also been used in conventional photography. Before the electronic age, the RGB color model already had a solid theory behind it, based in human perception of colors. RGB is a ''device-dependent'' color model: different devices detect or reproduce a given RGB value differently, since the color elements (such as phosphors or dyes) and their response to the individual red, green, and blue levels vary from manufacturer to manufacturer, or even in the same device over time. Thus an RGB value does not define the same ''color'' across d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Four-dimensional Space
A four-dimensional space (4D) is a mathematical extension of the concept of three-dimensional or 3D space. Three-dimensional space is the simplest possible abstraction of the observation that one only needs three numbers, called ''dimensions'', to describe the sizes or locations of objects in the everyday world. For example, the volume of a rectangular box is found by measuring and multiplying its length, width, and height (often labeled ''x'', ''y'', and ''z''). The idea of adding a fourth dimension began with Jean le Rond d'Alembert's "Dimensions" being published in 1754, was followed by Joseph-Louis Lagrange in the mid-1700s, and culminated in a precise formalization of the concept in 1854 by Bernhard Riemann. In 1880, Charles Howard Hinton popularized these insights in an essay titled "What is the Fourth Dimension?", which explained the concept of a " four-dimensional cube" with a step-by-step generalization of the properties of lines, squares, and cubes. The simplest form ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stella (software)
Stella, a computer program available in three versions (Great Stella, Small Stella and Stella4D), was created by Robert Webb of Australia. The programs contain a large library of polyhedra which can be manipulated and altered in various ways. Polyhedra Polyhedra in Great Stella's library include the Platonic solids, the Archimedean solids, the Kepler-Poinsot solids, the Johnson solids, some Johnson Solid near-misses, numerous compounds including the uniform polyhedra, and other polyhedra. Operations which can be performed on these polyhedra include stellation, faceting, augmentation, dualization (also called "reciprocation"), creating convex hulls, and others. All versions of the program enable users to print nets for polyhedra. These nets may then be assembled into actual three-dimensional polyhedral models of great beauty and complexity. Stella4D In 2007, a Stella4D version was added, allowing the generation and display of four-dimensional polytopes ( polychora), i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavefront
In physics, the wavefront of a time-varying ''wave field'' is the set (locus) of all points having the same ''phase''. The term is generally meaningful only for fields that, at each point, vary sinusoidally in time with a single temporal frequency (otherwise the phase is not well defined). Wavefronts usually move with time. For waves propagating in a unidimensional medium, the wavefronts are usually single points; they are curves in a two dimensional medium, and surfaces in a three-dimensional one. For a sinusoidal plane wave, the wavefronts are planes perpendicular to the direction of propagation, that move in that direction together with the wave. For a sinusoidal spherical wave, the wavefronts are spherical surfaces that expand with it. If the speed of propagation is different at different points of a wavefront, the shape and/or orientation of the wavefronts may change by refraction. In particular, lenses can change the shape of optical wavefronts from planar to spher ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
STL (file Format)
STL is a file format native to the stereolithography CAD software created by 3D Systems. STL has several backronyms such as "Standard Triangle Language" and "Standard Tessellation Language". This file format is supported by many other software packages; it is widely used for rapid prototyping, 3D printing and computer-aided manufacturing. STL files describe only the surface geometry of a three-dimensional object without any representation of color, texture or other common CAD model attributes. The STL format specifies both ASCII and binary representations. Binary files are more common, since they are more compact. An STL file describes a raw, unstructured triangulated surface by the unit normal and vertices (ordered by the right-hand rule) of the triangles using a three-dimensional Cartesian coordinate system. In the original specification, all STL coordinates were required to be positive numbers, but this restriction is no longer enforced and negative coordinates are commonly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PLY (file Format)
PLY is a computer file format known as the Polygon File Format or the Stanford Triangle Format. It was principally designed to store three-dimensional data from 3D scanners. The data storage format supports a relatively simple description of a single object as a list of nominally flat polygons. A variety of properties can be stored, including color and transparency, surface normals, texture coordinates and data confidence values. The format permits one to have different properties for the front and back of a polygon. There are two versions of the file format, one in ASCII, the other in binary. The file format A Ply file starts with the "header" attribute, which specifies the elements of a mesh and their types, followed by the list of elements itself. The elements are usually vertices and faces, but may include other entities such as edges, samples of range maps, and triangle strips. The header of both ASCII and binary files is ASCII text. Only the numerical data that follows th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stereolithography
Stereolithography (SLA or SL; also known as vat photopolymerisation, optical fabrication, photo-solidification, or resin printing) is a form of 3D printing technology used for creating models, prototypes, patterns, and production parts in a layer by layer fashion using photochemical processes by which light causes chemical monomers and oligomers to cross-link together to form polymers.U.S. Patentbr>4,575,330(“Apparatus for Production of Three-Dimensional Objects by Stereolithography”) Those polymers then make up the body of a three-dimensional solid. Research in the area had been conducted during the 1970s, but the term was coined by Chuck Hull in 1984 when he applied for a patent on the process, which was granted in 1986. Stereolithography can be used to create prototypes for products in development, medical models, and computer hardware, as well as in many other applications. While stereolithography is fast and can produce almost any design, it can be expensive. History ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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