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HyperFun
HyperFun (from Hyperdimensional Functions) is a programming language{{cite web , work = HyperFun language specification, version 2.0 , title = HyperFun: Language for FRep Volume Modeling , url = http://hyperfun.org/wiki/doku.php?id=hyperfun:language , accessdate = 5 August 2012 and software used to create, visualize, and fabricate volumetric 3D and higher-dimensional models. The team maintaining the HyperFun project is a freely associated group of researchers and students from different countries from all over the world (UK, Russia, France, Japan, Norway, USA, and others) called the Digital Materialization Group (digitalmaterial.org). Overview HyperFun allows users to easily model objects of the quality found in reality and nature. The system is based on a new mathematical framework for geometry, function representation (FRep), which provides a uniform method to model both surface geometry and internal composition simultaneously. It is also a compact and precise framewo ...
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Function Representation
Function Representation (FRep or F-Rep) is used in solid modeling, volume modeling and computer graphics. FRep was introduced in "Function representation in geometric modeling: concepts, implementation and applications" as a uniform representation of multidimensional geometric objects (shapes). An object as a point set in multidimensional space is defined by a single continuous real-valued function f(X) of point coordinates X _1,x_2, ..., x_n/math> which is evaluated at the given point by a procedure traversing a tree structure with primitives in the leaves and operations in the nodes of the tree. The points with f(x_1,x_2, ..., x_n) \ge 0 belong to the object, and the points with f(x_1,x_2, ..., x_n) < 0 are outside of the object. The point set with f(x_1,x_2, ..., x_n)=0 is called an .


Geometric domain

The geometri ...
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Function Representation
Function Representation (FRep or F-Rep) is used in solid modeling, volume modeling and computer graphics. FRep was introduced in "Function representation in geometric modeling: concepts, implementation and applications" as a uniform representation of multidimensional geometric objects (shapes). An object as a point set in multidimensional space is defined by a single continuous real-valued function f(X) of point coordinates X _1,x_2, ..., x_n/math> which is evaluated at the given point by a procedure traversing a tree structure with primitives in the leaves and operations in the nodes of the tree. The points with f(x_1,x_2, ..., x_n) \ge 0 belong to the object, and the points with f(x_1,x_2, ..., x_n) < 0 are outside of the object. The point set with f(x_1,x_2, ..., x_n)=0 is called an .


Geometric domain

The geometri ...
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Procedural Modeling
Procedural modeling is an umbrella term for a number of techniques in computer graphics to create 3D models and textures from sets of rules. L-Systems, fractals, and generative modeling are procedural modeling techniques since they apply algorithms for producing scenes. The set of rules may either be embedded into the algorithm, configurable by parameters, or the set of rules is separate from the evaluation engine. The output is called procedural content, which can be used in computer games, films, be uploaded to the internet, or the user may edit the content manually. Procedural models often exhibit database amplification, meaning that large scenes can be generated from a much smaller number of rules. If the employed algorithm produces the same output every time, the output need not be stored. Often, it suffices to start the algorithm with the same random seed to achieve this. Although all modeling techniques on a computer require algorithms to manage and store data at some p ...
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Cross-platform
In computing, cross-platform software (also called multi-platform software, platform-agnostic software, or platform-independent software) is computer software that is designed to work in several computing platforms. Some cross-platform software requires a separate build for each platform, but some can be directly run on any platform without special preparation, being written in an interpreted language or compiled to portable bytecode for which the interpreters or run-time packages are common or standard components of all supported platforms. For example, a cross-platform application may run on Microsoft Windows, Linux, and macOS. Cross-platform software may run on many platforms, or as few as two. Some frameworks for cross-platform development are Codename One, Kivy, Qt, Flutter, NativeScript, Xamarin, Phonegap, Ionic, and React Native. Platforms ''Platform'' can refer to the type of processor (CPU) or other hardware on which an operating system (OS) or application runs ...
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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 ...
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3D Printing
3D printing or additive manufacturing is the construction of a three-dimensional object from a CAD model or a digital 3D model. It can be done in a variety of processes in which material is deposited, joined or solidified under computer control, with material being added together (such as plastics, liquids or powder grains being fused), typically layer by layer. In the 1980s, 3D printing techniques were considered suitable only for the production of functional or aesthetic prototypes, and a more appropriate term for it at the time was rapid prototyping. , the precision, repeatability, and material range of 3D printing have increased to the point that some 3D printing processes are considered viable as an industrial-production technology, whereby the term ''additive manufacturing'' can be used synonymously with ''3D printing''. One of the key advantages of 3D printing is the ability to produce very complex shapes or geometries that would be otherwise impossible to construct ...
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3D Computer Graphics
3D computer graphics, or “3D graphics,” sometimes called CGI, 3D-CGI or three-dimensional computer graphics are graphics that use a three-dimensional representation of geometric data (often Cartesian) that is stored in the computer for the purposes of performing calculations and rendering digital images, usually 2D images but sometimes 3D images. The resulting images may be stored for viewing later (possibly as an animation) or displayed in real time. 3D computer graphics, contrary to what the name suggests, are most often displayed on two-dimensional displays. Unlike 3D film and similar techniques, the result is two-dimensional, without visual depth. More often, 3D graphics are being displayed on 3D displays, like in virtual reality systems. 3D graphics stand in contrast to 2D computer graphics which typically use completely different methods and formats for creation and rendering. 3D computer graphics rely on many of the same algorithms as 2D computer vector ...
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Geometric Primitive
In vector computer graphics, CAD systems, and geographic information systems, geometric primitive (or prim) is the simplest (i.e. 'atomic' or irreducible) geometric shape that the system can handle (draw, store). Sometimes the subroutines that draw the corresponding objects are called "geometric primitives" as well. The most "primitive" primitives are point and straight line segment, which were all that early vector graphics systems had. In constructive solid geometry, primitives are simple geometric shapes such as a cube, cylinder, sphere, cone, pyramid, torus. Modern 2D computer graphics systems may operate with primitives which are curves (segments of straight lines, circles and more complicated curves), as well as shapes (boxes, arbitrary polygons, circles). A common set of two-dimensional primitives includes lines, points, and polygons, although some people prefer to consider triangles primitives, because every polygon can be constructed from triangles. All other graphic ...
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Black Box
In science, computing, and engineering, a black box is a system which can be viewed in terms of its inputs and outputs (or transfer characteristics), without any knowledge of its internal workings. Its implementation is "opaque" (black). The term can be used to refer to many inner workings, such as those of a transistor, an engine, an algorithm, the human brain, or an institution or government. To analyse an open system with a typical "black box approach", only the behavior of the stimulus/response will be accounted for, to infer the (unknown) ''box''. The usual representation of this ''black box system'' is a data flow diagram centered in the box. The opposite of a black box is a system where the inner components or logic are available for inspection, which is most commonly referred to as a white box (sometimes also known as a "clear box" or a "glass box"). History The modern meaning of the term "black box" seems to have entered the English language around 1945. In electr ...
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National Centre For Computer Animation
The National Centre for Computer Animation (NCCA) is part of the Media School at Bournemouth University in the United Kingdom. Founded in 1989, it is often regarded as one of the best UK institutions available for study in the field of computer graphics, offering both undergraduate and postgraduate degree courses. Its first director was Peter Comninos. The interdisciplinary centre, operating under the motto 'Science in the service of the Arts', enjoys strong links with industry, with much of it consisting of NCCA graduates. In the 2001 national Research Assessment Exercise (RAE), the NCCA was awarded the maximum possible mark of 5 and performed similarly well in the 2008 RAE. NESTA's 'Livingstone-Hope Skills Review of Video Games and Visual Effects', launched in 2010, published its result in the ''Next Gen.'' report, which singles out the NCCA for 'excellence in visual effects education', placing it 'at the forefront of education for the visual effects and animation industries'. ...
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Geometric Algorithms
The following is a list of well-known algorithms along with one-line descriptions for each. Automated planning Combinatorial algorithms General combinatorial algorithms * Brent's algorithm: finds a cycle in function value iterations using only two iterators * Floyd's cycle-finding algorithm: finds a cycle in function value iterations * Gale–Shapley algorithm: solves the stable marriage problem * Pseudorandom number generators (uniformly distributed—see also List of pseudorandom number generators for other PRNGs with varying degrees of convergence and varying statistical quality): ** ACORN generator ** Blum Blum Shub ** Lagged Fibonacci generator ** Linear congruential generator ** Mersenne Twister Graph algorithms * Coloring algorithm: Graph coloring algorithm. * Hopcroft–Karp algorithm: convert a bipartite graph to a maximum cardinality matching * Hungarian algorithm: algorithm for finding a perfect matching * Prüfer coding: conversion between a labeled tree and ...
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3D Graphics Software
3D computer graphics, or “3D graphics,” sometimes called CGI, 3D-CGI or three-dimensional computer graphics are graphics that use a three-dimensional representation of geometric data (often Cartesian) that is stored in the computer for the purposes of performing calculations and rendering digital images, usually 2D images but sometimes 3D images. The resulting images may be stored for viewing later (possibly as an animation) or displayed in real time. 3D computer graphics, contrary to what the name suggests, are most often displayed on two-dimensional displays. Unlike 3D film and similar techniques, the result is two-dimensional, without visual depth. More often, 3D graphics are being displayed on 3D displays, like in virtual reality systems. 3D graphics stand in contrast to 2D computer graphics which typically use completely different methods and formats for creation and rendering. 3D computer graphics rely on many of the same algorithms as 2D computer vector graphic ...
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