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Geometry Processing
Geometry processing, or mesh processing, is an area of research that uses concepts from applied mathematics, computer science and engineering to design efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulation and transmission of complex 3D models. As the name implies, many of the concepts, data structures, and algorithms are directly analogous to signal processing and image processing. For example, where image smoothing might convolve an intensity signal with a blur kernel formed using the Laplace operator, geometric smoothing might be achieved by convolving a surface geometry with a blur kernel formed using the Laplace-Beltrami operator. Applications of geometry processing algorithms already cover a wide range of areas from multimedia, entertainment and classical computer-aided design, to biomedical computing, reverse engineering, and scientific computing. Geometry processing is a common research topic at SIGGRAPH, the premier comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polygon Mesh Processing Book Cover
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] |
Reverse Engineering
Reverse engineering (also known as backwards engineering or back engineering) is a process or method through which one attempts to understand through deductive reasoning how a previously made device, process, system, or piece of software accomplishes a task with very little (if any) insight into exactly how it does so. It is essentially the process of opening up or dissecting a system to see how it works, in order to duplicate or enhance it. Depending on the system under consideration and the technologies employed, the knowledge gained during reverse engineering can help with repurposing obsolete objects, doing security analysis, or learning how something works. Although the process is specific to the object on which it is being performed, all reverse engineering processes consist of three basic steps: Information extraction, Modeling, and Review. Information extraction refers to the practice of gathering all relevant information for performing the operation. Modeling refers to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Modeling And Fabrication
Digital modeling and fabrication is a design and production process that combines 3D modeling or computing-aided design (CAD) with additive and subtractive manufacturing. Additive manufacturing is also known as 3D printing, while subtractive manufacturing may also be referred to as machining, and many other technologies can be exploited to physically produce the designed objects. Modeling Digitally fabricated objects are created with a variety of CAD software packages, using both 2D vector drawing, and 3D modeling. Types of 3D models include wireframe, solid, surface and mesh. A design has one or more of these model types. Machines for fabrication Three machines are popular for fabrication: 1. CNC router 2. Laser cutter 3. 3D Printer CNC milling machine CNC stands for "computer numerical control". CNC mills or routers include proprietary software which interprets 2D vector drawings or 3D models and converts this information to a G-code, which represents specific CNC funct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rigid Transformation
In mathematics, a rigid transformation (also called Euclidean transformation or Euclidean isometry) is a geometric transformation of a Euclidean space that preserves the Euclidean distance between every pair of points. The rigid transformations include rotations, translations, reflections, or any sequence of these. Reflections are sometimes excluded from the definition of a rigid transformation by requiring that the transformation also preserve the handedness of objects in the Euclidean space. (A reflection would not preserve handedness; for instance, it would transform a left hand into a right hand.) To avoid ambiguity, a transformation that preserves handedness is known as a proper rigid transformation, or rototranslation. Any proper rigid transformation can be decomposed into a rotation followed by a translation, while any improper rigid transformation can be decomposed into an improper rotation followed by a translation, or into a sequence of reflections. Any object wil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler Characteristic
In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent. It is commonly denoted by \chi ( Greek lower-case letter chi). The Euler characteristic was originally defined for polyhedra and used to prove various theorems about them, including the classification of the Platonic solids. It was stated for Platonic solids in 1537 in an unpublished manuscript by Francesco Maurolico. Leonhard Euler, for whom the concept is named, introduced it for convex polyhedra more generally but failed to rigorously prove that it is an invariant. In modern mathematics, the Euler characteristic arises from homology and, more abstractly, homological algebra. Polyhedra The Euler characteristic \chi was classically defined for the surfaces of polyhedra, acc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
3D Scanner
3D scanning is the process of analyzing a real-world object or environment to collect data on its shape and possibly its appearance (e.g. color). The collected data can then be used to construct digital 3D modelling, 3D models. A 3D scanner can be based on many different technologies, each with its own limitations, advantages and costs. Many limitations in the kind of objects that can be digitization, digitised are still present. For example, optical technology may encounter many difficulties with dark, shiny, reflective or transparent objects. For example, industrial computed tomography scanning, structured-light 3D scanners, Lidar, LiDAR and Time-of-flight camera, Time Of Flight 3D Scanners can be used to construct digital 3D modeling, 3D models, without non-destructive testing, destructive testing. Collected 3D data is useful for a wide variety of applications. These devices are used extensively by the entertainment industry in the production of movies and video games, includ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the function and the set is called the codomain of the function.Codomain ''Encyclopedia of Mathematics'Codomain. ''Encyclopedia of Mathematics''/ref> The earliest known approach to the notion of function can be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
3D Modeling
In 3D computer graphics, 3D modeling is the process of developing a mathematical coordinate-based representation of any surface of an object (inanimate or living) in three dimensions via specialized software by manipulating edges, vertices, and polygons in a simulated 3D space. Three-dimensional (3D) models represent a physical body using a collection of points in 3D space, connected by various geometric entities such as triangles, lines, curved surfaces, etc. Being a collection of data ( points and other information), 3D models can be created manually, algorithmically (procedural modeling), or by scanning. Their surfaces may be further defined with texture mapping. Outline The product is called a 3D model. Someone who works with 3D models may be referred to as a 3D artist or a 3D modeler. A 3D Model can also be displayed as a two-dimensional image through a process called 3D rendering or used in a computer simulation of physical phenomena. 3D Models may be created au ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shape
A shape or figure is a graphics, graphical representation of an object or its external boundary, outline, or external Surface (mathematics), surface, as opposed to other properties such as color, Surface texture, texture, or material type. A plane shape or plane figure is constrained to lie on a ''plane (geometry), plane'', in contrast to ''solid figure, solid'' 3D shapes. A two-dimensional shape or two-dimensional figure (also: 2D shape or 2D figure) may lie on a more general curved ''surface (mathematics), surface'' (a non-Euclidean two-dimensional space). Classification of simple shapes Some simple shapes can be put into broad categories. For instance, polygons are classified according to their number of edges as triangles, quadrilaterals, pentagons, etc. Each of these is divided into smaller categories; triangles can be equilateral, isosceles, obtuse triangle, obtuse, Triangle#By internal angles, acute, Triangle, scalene, etc. while quadrilaterals can be rectangles, rho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cactus Gaussian Curvature
A cactus (, or less commonly, cactus) is a member of the plant family Cactaceae, a family comprising about 127 genera with some 1750 known species of the order Caryophyllales. The word ''cactus'' derives, through Latin, from the Ancient Greek word (''káktos''), a name originally used by Theophrastus for a spiny plant whose identity is now not certain. Cacti occur in a wide range of shapes and sizes. Although some species live in quite humid environments, most cacti live in habitats subject to at least some drought. Many live in extremely dry environments, even being found in the Atacama Desert, one of the driest places on Earth. Because of this, cacti show many adaptations to conserve water. For example, almost all cacti are succulents, meaning they have thickened, fleshy parts adapted to store water. Unlike many other succulents, the stem is the only part of most cacti where this vital process takes place. Most species of cacti have lost true leaves, retaining only spines, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symposium On Geometry Processing
Symposium on Geometry Processing (SGP) is an annual symposium hosted by the European Association For Computer Graphics (Eurographics). The goal of the symposium is to present and discuss new research ideas and results in geometry processing. The conference is geared toward the discussion of mathematical foundations and practical algorithms for the processing of complex geometric data sets, ranging from acquisition and editing all the way to animation, transmission and display. As such, it draws on many disciplines spanning pure and applied mathematics, computer science, and engineering. The proceedings of SGP appear as a special issue of the ''Computer Graphics Forum A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations ( computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These pro ...'', the International Journal of the Eurographics Association. Si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Graphics
Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great deal of specialized hardware and software has been developed, with the displays of most devices being driven by computer graphics hardware. It is a vast and recently developed area of computer science. The phrase was coined in 1960 by computer graphics researchers Verne Hudson and William Fetter of Boeing. It is often abbreviated as CG, or typically in the context of film as computer generated imagery (CGI). The non-artistic aspects of computer graphics are the subject of computer science research. Some topics in computer graphics include user interface design, sprite graphics, rendering, ray tracing, geometry processing, computer animation, vector graphics, 3D modeling, shaders, GPU design, implicit surfaces, visualization, scientific c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
