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Geometry Processing
Geometry processing is an area of research that uses concepts from applied mathematics, computer science and engineering to design efficient algorithms for the acquisition, 3D reconstruction, 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, Laplacian smoothing, geometric smoothing might be achieved by convolving a Surface (mathematics), 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 topi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Polygon Mesh Processing Book Cover
In geometry, a polygon () is a plane (mathematics), plane Shape, figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its ''edge (geometry), edges'' or ''sides''. The points where two edges meet are the polygon's ''Vertex (geometry), vertices'' or ''corners''. 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. More precisely, the only allowed intersections among the line segments that make up the polygon are the shared endpoints of consecutive segments in the polygonal chain. A simple polygon is the boundary of a region of the plane that is called a ''solid polygon''. The interior of a solid polygon is its ''body'', also known as a ''polygonal region'' or ''polygonal area''. In contexts where one is concerned only with simple and solid polygons, a ''polygon'' may refer only to a simple polygon or to a solid polygon. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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. 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 is the practice of gathering all relevant information for performing the operation. Modeling is the practice of combining the gathered information into an abstract model, which can be used as a guide for designing the new object or syst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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 used 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 functions i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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 rigid motion, a Euclidean motion, or a proper rigid transformation. In dimension two, a rigid motion is either a translation or a rotation. In dimension three, every rigid motion can be decomposed as the composition of a rotation and a translation, and is thus sometimes called a rototranslation. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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 alphabet, Greek lower-case letter chi (letter), chi). The Euler characteristic was originally defined for polyhedron, 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 (mathematics), homology and, more abstractly, homological algebra. Polyhedra The Euler characteristic was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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3D Scanner
3D scanning is the process of analyzing a real-world object or environment to collect three dimensional data of its shape and possibly its appearance (e.g. color). The collected data can then be used to construct digital 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 digitized are still present. For example, optical technology may encounter difficulties with dark, shiny, reflective or transparent objects while industrial computed tomography scanning, structured-light 3D scanners, LiDAR and Time Of Flight 3D Scanners can be used to construct digital 3D models, without 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, including virtual reality. Other common applications of this technology include augmented rea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Function (mathematics)
In mathematics, a function from a set (mathematics), set to a set assigns to each element of exactly one element of .; the words ''map'', ''mapping'', ''transformation'', ''correspondence'', and ''operator'' are sometimes used synonymously. The set is called the Domain of a function, domain of the function and the set is called the codomain of the function. 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. History of the function concept, 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 function, differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the 19th century in terms of set theory, and this greatly increased the possible applications of the concept. A f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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3D Modeling
In 3D computer graphics, 3D modeling is the process of developing a mathematical coordinate-based Computer representation of surfaces, representation of a surface of an object (inanimate or living) in Three-dimensional space, three dimensions via 3D computer graphics software, 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 (Point (geometry), points and other information), 3D models can be created manually, algorithmically (procedural modeling), or by 3D scanning, scanning. Their surfaces may be further defined with texture mapping. Outline The product is called a 3D model, while 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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Shape
A shape is a graphics, graphical representation of an object's form or its external boundary, outline, or external Surface (mathematics), surface. It is distinct from other object properties, such as color, Surface texture, texture, or material type. In geometry, ''shape'' excludes information about the object's Position (geometry), position, size, Orientation (geometry), orientation and chirality. A ''figure'' is a representation including both shape and size (as in, e.g., figure of the Earth). 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 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, qua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Cactus Gaussian Curvature
A cactus (: cacti, cactuses, or less commonly, cactus) is a member of the plant family Cactaceae (), a family of the order Caryophyllales comprising about 127 genera with some 1,750 known species. 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. They are native to the Americas, ranging from Patagonia in the south to parts of western Canada in the north, with the exception of ''Rhipsalis baccifera'', which is also found in Africa and Sri Lanka. Cacti are adapted to live in very dry environments, including 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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 Engineering is the practice of using natural science, mathematics, and the engineering design process to Problem solving#Engineering, solve problems within technology, increase efficiency and productivity, and improve Systems engineering, s .... The proceedings of SGP appear as a special issue of the '' Computer Graphics Forum'', the International Journal of the Eurographics Association. S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Computer Graphics
Computer graphics deals with generating images and art with the aid of computers. Computer graphics is a core technology in digital photography, film, video games, digital art, 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 graphics hardware, 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, computer generated imagery (CGI). The non-artistic aspects of computer graphics are the subject of Computer graphics (computer science), computer science research. Some topics in computer graphics include user interface design, Sprite (computer graphics), sprite graphics, raster graphics, Rendering (computer graph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |