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Computer Graphics (computer Science)
Computer graphics is a sub-field of computer science which studies methods for digitally synthesizing and manipulating visual content. Although the term often refers to the study of three-dimensional computer graphics, it also encompasses two-dimensional graphics and image processing. The individuals who serve as professional designers for computers graphics are known as "Graphics Programmers", who often are computer programmers with skills in computer graphics design. Overview Computer graphics studies the aesthetic manipulation of visual and geometric information using computational techniques. It focuses on the ''mathematical'' and ''computational'' foundations of image generation and processing rather than purely aesthetic issues. Computer graphics is often differentiated from the field of visualization, although the two fields have many similarities. Connected studies include: * Applied mathematics * Computational geometry * Computational topology * Computer vision ...
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Utah Teapot Simple 2
Utah ( , ) is a state in the Mountain West subregion of the Western United States. Utah is a landlocked U.S. state bordered to its east by Colorado, to its northeast by Wyoming, to its north by Idaho, to its south by Arizona, and to its west by Nevada. Utah also touches a corner of New Mexico in the southeast. Of the fifty U.S. states, Utah is the 13th-largest by area; with a population over three million, it is the 30th-most-populous and 11th-least-densely populated. Urban development is mostly concentrated in two areas: the Wasatch Front in the north-central part of the state, which is home to roughly two-thirds of the population and includes the capital city, Salt Lake City; and Washington County in the southwest, with more than 180,000 residents. Most of the western half of Utah lies in the Great Basin. Utah has been inhabited for thousands of years by various indigenous groups such as the ancient Puebloans, Navajo and Ute. The Spanish were the first Europeans t ...
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Association For Computing Machinery
The Association for Computing Machinery (ACM) is a US-based international learned society for computing. It was founded in 1947 and is the world's largest scientific and educational computing society. The ACM is a non-profit professional membership group, claiming nearly 110,000 student and professional members . Its headquarters are in New York City. The ACM is an umbrella organization for academic and scholarly interests in computer science ( informatics). Its motto is "Advancing Computing as a Science & Profession". History In 1947, a notice was sent to various people: On January 10, 1947, at the Symposium on Large-Scale Digital Calculating Machinery at the Harvard computation Laboratory, Professor Samuel H. Caldwell of Massachusetts Institute of Technology spoke of the need for an association of those interested in computing machinery, and of the need for communication between them. ..After making some inquiries during May and June, we believe there is ample interest to ...
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Level Set
In mathematics, a level set of a real-valued function of real variables is a set where the function takes on a given constant value , that is: : L_c(f) = \left\~, When the number of independent variables is two, a level set is called a level curve, also known as ''contour line'' or ''isoline''; so a level curve is the set of all real-valued solutions of an equation in two variables and . When , a level set is called a level surface (or ''isosurface''); so a level surface is the set of all real-valued roots of an equation in three variables , and . For higher values of , the level set is a level hypersurface, the set of all real-valued roots of an equation in variables. A level set is a special case of a fiber. Alternative names Level sets show up in many applications, often under different names. For example, an implicit curve is a level curve, which is considered independently of its neighbor curves, emphasizing that such a curve is defined by an implicit e ...
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Subdivision Surfaces
In the field of 3D computer graphics, a subdivision surface (commonly shortened to SubD surface) is a curved surface represented by the specification of a coarser polygon mesh and produced by a recursive algorithmic method. The curved surface, the underlying ''inner mesh'', can be calculated from the coarse mesh, known as the ''control cage'' or ''outer mesh'', as the functional limit of an iterative process of subdividing each polygonal face into smaller faces that better approximate the final underlying curved surface. Less commonly, a simple algorithm is used to add geometry to a mesh by subdividing the faces into smaller ones without changing the overall shape or volume. Overview A subdivision surface algorithm is recursive in nature. The process starts with a base level polygonal mesh. A refinement scheme is then applied to this mesh. This process takes that mesh and subdivides it, creating new vertices and new faces. The positions of the new vertices in the mesh are comput ...
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Polygon Mesh
In 3D computer graphics and solid modeling, a polygon mesh is a collection of , s and s that defines the shape of a polyhedral object. The faces usually consist of triangles (triangle mesh), quadrilaterals (quads), or other simple convex polygons ( n-gons), since this simplifies rendering, but may also be more generally composed of concave polygons, or even polygons with holes. The study of polygon meshes is a large sub-field of computer graphics (specifically 3D computer graphics) and geometric modeling. Different representations of polygon meshes are used for different applications and goals. The variety of operations performed on meshes may include: Boolean logic ( Constructive solid geometry), smoothing, simplification, and many others. Algorithms also exist for ray tracing, collision detection, and rigid-body dynamics with polygon meshes. If the mesh's edges are rendered instead of the faces, then the model becomes a wireframe model. Volumetric meshes are distinct f ...
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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to an open subset of n-dimensional Euclidean space. One-dimensional manifolds include lines and circles, but not lemniscates. Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, and also the Klein bottle and real projective plane. The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows complicated structures to be described in terms of well-understood topological properties of simpler spaces. Manifolds naturally arise as solution sets of systems of equations and as graphs of functions. The concept has applications in computer-graphics given the need to associate pictures with coordinates (e.g ...
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Surface (topology)
In the part of mathematics referred to as topology, a surface is a two-dimensional manifold. Some surfaces arise as the boundaries of three-dimensional solids; for example, the sphere is the boundary of the solid ball. Other surfaces arise as graphs of functions of two variables; see the figure at right. However, surfaces can also be defined abstractly, without reference to any ambient space. For example, the Klein bottle is a surface that cannot be embedded in three-dimensional Euclidean space. Topological surfaces are sometimes equipped with additional information, such as a Riemannian metric or a complex structure, that connects them to other disciplines within mathematics, such as differential geometry and complex analysis. The various mathematical notions of surface can be used to model surfaces in the physical world. In general In mathematics, a surface is a geometrical shape that resembles a deformed plane. The most familiar examples arise as boundaries of solid ob ...
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Boundary Representation
In solid modeling and computer-aided design, boundary representation (often abbreviated B-rep or BREP) is a method for representing a 3D shape by defining the limits of its volume. A solid is represented as a collection of connected surface elements, which define the boundary between interior and exterior points. Overview A boundary representation of a model comprises topological components (faces, edges and vertices) and the connections between them, along with geometric definitions for those components (surfaces, curves and points, respectively). A face is a bounded portion of a surface; an edge is a bounded piece of a curve and a vertex lies at a point. Other elements are the ''shell'' (a set of connected faces), the ''loop'' (a circuit of edges bounding a face) and ''loop-edge links'' (also known as ''winged edge links'' or ''half-edges'') which are used to create the edge circuits. Vs Constructive Solid Geometry Compared to the constructive solid geometry (CSG) repr ...
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Stanford Bunny Qem
Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is considered among the most prestigious universities in the world. Stanford was founded in 1885 by Leland and Jane Stanford in memory of their only child, Leland Stanford Jr., who had died of typhoid fever at age 15 the previous year. Leland Stanford was a U.S. senator and former governor of California who made his fortune as a railroad tycoon. The school admitted its first students on October 1, 1891, as a coeducational and non-denominational institution. Stanford University struggled financially after the death of Leland Stanford in 1893 and again after much of the campus was damaged by the 1906 San Francisco earthquake. Following World War II, provost of Stanford Frederick Terman inspired and supported faculty and graduates' entrepreneurialism ...
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Digital Imaging
Digital imaging or digital image acquisition is the creation of a digital representation of the visual characteristics of an object, such as a physical scene or the interior structure of an object. The term is often assumed to imply or include the processing, compression, storage, printing and display of such images. A key advantage of a digital image, versus an analog image such as a film photograph, is the ability to digitally propagate copies of the original subject indefinitely without any loss of image quality. Digital imaging can be classified by the type of electromagnetic radiation or other waves whose variable attenuation, as they pass through or reflect off objects, conveys the information that constitutes the image. In all classes of digital imaging, the information is converted by image sensors into digital signals that are processed by a computer and made output as a visible-light image. For example, the medium of visible light allows digital photography (in ...
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Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a Heuristic (computer science), heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm ca ...
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Rendering (computer Graphics)
Rendering or image synthesis is the process of generating a photorealistic or non-photorealistic image from a 2D or 3D model by means of a computer program. The resulting image is referred to as the render. Multiple models can be defined in a ''scene file'' containing objects in a strictly defined language or data structure. The scene file contains geometry, viewpoint, texture, lighting, and shading information describing the virtual scene. The data contained in the scene file is then passed to a rendering program to be processed and output to a digital image or raster graphics image file. The term "rendering" is analogous to the concept of an artist's impression of a scene. The term "rendering" is also used to describe the process of calculating effects in a video editing program to produce the final video output. Rendering is one of the major sub-topics of 3D computer graphics, and in practice it is always connected to the others. It is the last major step in the gr ...
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