The Light Cycle is a type of fictional motorcycle featured in the Tron franchise. First introduced in the film Tron , they are used as part of a deadly virtual game conducted by the villainous Master Control Program . In it, players must ride around an arena without crashing into each other, the outer walls, or the light trails left behind by the vehicles. Subsequent generations of Light Cycles appeared in later works of media.
128-612: Following its appearance in Tron , the Light Cycle became a fixture of popular culture. The first Light Cycle sequence was also seen as a pioneering moment in computer graphics that inspired later works. Light Cycles are virtual and futuristic motorcycles that materialize from thin air, starting with the handlebars. They are neon-colored and move at extreme levels of speed. They are only able to turn at right angles , creating blocky trails of color. The arena in which they are used features
256-520: A geodesic is a generalization of the notion of a line to curved spaces . In Euclidean geometry a plane is a flat, two-dimensional surface that extends infinitely; the definitions for other types of geometries are generalizations of that. Planes are used in many areas of geometry. For instance, planes can be studied as a topological surface without reference to distances or angles; it can be studied as an affine space , where collinearity and ratios can be studied but not distances; it can be studied as
384-418: A parabola with the summation of an infinite series , and gave remarkably accurate approximations of pi . He also studied the spiral bearing his name and obtained formulas for the volumes of surfaces of revolution . Indian mathematicians also made many important contributions in geometry. The Shatapatha Brahmana (3rd century BC) contains rules for ritual geometric constructions that are similar to
512-425: A vector space and its dual space . Euclidean geometry is geometry in its classical sense. As it models the space of the physical world, it is used in many scientific areas, such as mechanics , astronomy , crystallography , and many technical fields, such as engineering , architecture , geodesy , aerodynamics , and navigation . The mandatory educational curriculum of the majority of nations includes
640-406: A broad sense to describe "almost everything on computers that is not text or sound". Typically, the term computer graphics refers to several different things: Today, computer graphics is widespread. Such imagery is found in and on television, newspapers, weather reports, and in a variety of medical investigations and surgical procedures. A well-constructed graph can present complex statistics in
768-405: A common endpoint, called the vertex of the angle. The size of an angle is formalized as an angular measure . In Euclidean geometry , angles are used to study polygons and triangles , as well as forming an object of study in their own right. The study of the angles of a triangle or of angles in a unit circle forms the basis of trigonometry . In differential geometry and calculus ,
896-519: A critical and commercial success of nine-figure magnitude. The studio to invent the programmable shader would go on to have many animated hits, and its work on prerendered video animation is still considered an industry leader and research trail breaker. In video games, in 1992, Virtua Racing , running on the Sega Model 1 arcade system board , laid the foundations for fully 3D racing games and popularized real-time 3D polygonal graphics among
1024-523: A decimal place value system with a dot for zero." Aryabhata 's Aryabhatiya (499) includes the computation of areas and volumes. Brahmagupta wrote his astronomical work Brāhmasphuṭasiddhānta in 628. Chapter 12, containing 66 Sanskrit verses, was divided into two sections: "basic operations" (including cube roots, fractions, ratio and proportion, and barter) and "practical mathematics" (including mixture, mathematical series, plane figures, stacking bricks, sawing of timber, and piling of grain). In
1152-527: A discipline until the 1950s and the post- World War II period – during which time the discipline emerged from a combination of both pure university and laboratory academic research into more advanced computers and the United States military 's further development of technologies like radar , aviation , and rocketry developed during the war. New kinds of displays were needed to process the wealth of information resulting from such projects, leading to
1280-463: A display scope image of a Disney cartoon character. Electronics pioneer Hewlett-Packard went public in 1957 after incorporating the decade prior, and established strong ties with Stanford University through its founders, who were alumni . This began the decades-long transformation of the southern San Francisco Bay Area into the world's leading computer technology hub – now known as Silicon Valley . The field of computer graphics developed with
1408-423: A display scope. One of the first interactive video games to feature recognizable, interactive graphics – Tennis for Two – was created for an oscilloscope by William Higinbotham to entertain visitors in 1958 at Brookhaven National Laboratory and simulated a tennis match. In 1959, Douglas T. Ross , while working at MIT on transforming mathematic statements into computer generated 3D machine tool vectors, created
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#17327801890511536-555: A feature-length motion picture using computer graphics – a goal he would achieve two decades later after his founding role in Pixar . In the same class, Fred Parke created an animation of his wife's face. The two animations were included in the 1976 feature film Futureworld . As the UU computer graphics laboratory was attracting people from all over, John Warnock was another of those early pioneers; he later founded Adobe Systems and created
1664-515: A form that is easier to understand and interpret. In the media "such graphs are used to illustrate papers, reports, theses", and other presentation material. Many tools have been developed to visualize data. Computer-generated imagery can be categorized into several different types: two dimensional (2D), three dimensional (3D), and animated graphics. As technology has improved, 3D computer graphics have become more common, but 2D computer graphics are still widely used. Computer graphics has emerged as
1792-598: A great deal of founding research to the field and taught several students who would grow to found several of the industry's most important companies – namely Pixar , Silicon Graphics , and Adobe Systems . Tom Stockham led the image processing group at UU which worked closely with the computer graphics lab. One of these students was Edwin Catmull . Catmull had just come from The Boeing Company and had been working on his degree in physics. Growing up on Disney , Catmull loved animation yet quickly discovered that he did not have
1920-447: A high-water mark for the field during the decade. The 1980s is also called the golden era of videogames ; millions-selling systems from Atari , Nintendo and Sega , among other companies, exposed computer graphics for the first time to a new, young, and impressionable audience – as did MS-DOS -based personal computers, Apple IIs , Macs , and Amigas , all of which also allowed users to program their own games if skilled enough. For
2048-405: A highly popular tool for computer graphics among graphic design studios and businesses. Modern computers, dating from the 1980s, often use graphical user interfaces (GUI) to present data and information with symbols, icons and pictures, rather than text. Graphics are one of the five key elements of multimedia technology. In the field of realistic rendering, Japan 's Osaka University developed
2176-406: A leading developer of graphics boards in this decade, creating a "duopoly" in the field which exists this day. CGI became ubiquitous in earnest during this era. Video games and CGI cinema had spread the reach of computer graphics to the mainstream by the late 1990s and continued to do so at an accelerated pace in the 2000s. CGI was also adopted en masse for television advertisements widely in
2304-417: A light pen, Sketchpad allowed one to draw simple shapes on the computer screen, save them and even recall them later. The light pen itself had a small photoelectric cell in its tip. This cell emitted an electronic pulse whenever it was placed in front of a computer screen and the screen's electron gun fired directly at it. By simply timing the electronic pulse with the current location of the electron gun, it
2432-420: A model of a car, one could change the size of the tires without affecting the rest of the car. It could stretch the body of car without deforming the tires. The phrase "computer graphics" has been credited to William Fetter , a graphic designer for Boeing in 1960. Fetter in turn attributed it to Verne Hudson, also at Boeing. In 1961 another student at MIT, Steve Russell , created another important title in
2560-440: A more rigorous foundation for geometry, treated congruence as an undefined term whose properties are defined by axioms . Congruence and similarity are generalized in transformation geometry , which studies the properties of geometric objects that are preserved by different kinds of transformations. Classical geometers paid special attention to constructing geometric objects that had been described in some other way. Classically,
2688-428: A multitude of forms, including the graphics of Leonardo da Vinci , M. C. Escher , and others. In the second half of the 19th century, the relationship between symmetry and geometry came under intense scrutiny. Felix Klein 's Erlangen program proclaimed that, in a very precise sense, symmetry, expressed via the notion of a transformation group , determines what geometry is . Symmetry in classical Euclidean geometry
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#17327801890512816-407: A necessity for advanced work in the field, providing considerable complexity in manipulating pixels , vertices , and textures on a per-element basis, and countless possible effects. Their shader languages HLSL and GLSL are active fields of research and development. Physically based rendering or PBR, which implements many maps and performs advanced calculation to simulate real optic light flow,
2944-451: A number of apparently different definitions, which are all equivalent in the most common cases. The theme of symmetry in geometry is nearly as old as the science of geometry itself. Symmetric shapes such as the circle , regular polygons and platonic solids held deep significance for many ancient philosophers and were investigated in detail before the time of Euclid. Symmetric patterns occur in nature and were artistically rendered in
3072-444: A physical system, which has a dimension equal to the system's degrees of freedom . For instance, the configuration of a screw can be described by five coordinates. In general topology , the concept of dimension has been extended from natural numbers , to infinite dimension ( Hilbert spaces , for example) and positive real numbers (in fractal geometry ). In algebraic geometry , the dimension of an algebraic variety has received
3200-528: A plane or 3-dimensional space. Mathematicians have found many explicit formulas for area and formulas for volume of various geometric objects. In calculus , area and volume can be defined in terms of integrals , such as the Riemann integral or the Lebesgue integral . Other geometrical measures include the curvature and compactness . The concept of length or distance can be generalized, leading to
3328-602: A purely algebraic context. Scheme theory allowed to solve many difficult problems not only in geometry, but also in number theory . Wiles' proof of Fermat's Last Theorem is a famous example of a long-standing problem of number theory whose solution uses scheme theory and its extensions such as stack theory . One of seven Millennium Prize problems , the Hodge conjecture , is a question in algebraic geometry. Algebraic geometry has applications in many areas, including cryptography and string theory . Complex geometry studies
3456-568: A revolution in the publishing world with his PostScript page description language. Adobe would go on later to create the industry standard photo editing software in Adobe Photoshop and a prominent movie industry special effects program in Adobe After Effects . James Clark was also there; he later founded Silicon Graphics , a maker of advanced rendering systems that would dominate the field of high-end graphics until
3584-571: A screen. It was the first consumer computer graphics product. David C. Evans was director of engineering at Bendix Corporation 's computer division from 1953 to 1962, after which he worked for the next five years as a visiting professor at Berkeley. There he continued his interest in computers and how they interfaced with people. In 1966, the University of Utah recruited Evans to form a computer science program, and computer graphics quickly became his primary interest. This new department would become
3712-462: A separate and very powerful chip is used in parallel processing with a CPU to optimize graphics. The decade also saw computer graphics applied to many additional professional markets, including location-based entertainment and education with the E&;S Digistar, vehicle design, vehicle simulation, and chemistry. The 1990s' highlight was the emergence of 3D modeling on a mass scale and an rise in
3840-427: A size or measure to sets , where the measures follow rules similar to those of classical area and volume. Congruence and similarity are concepts that describe when two shapes have similar characteristics. In Euclidean geometry, similarity is used to describe objects that have the same shape, while congruence is used to describe objects that are the same in both size and shape. Hilbert , in his work on creating
3968-432: A specialized barrel shifter circuit made from discrete chips to help their Intel 8080 microprocessor animate their framebuffer graphics. The 1980s began to see the commercialization of computer graphics. As the home computer proliferated, a subject which had previously been an academics-only discipline was adopted by a much larger audience, and the number of computer graphics developers increased significantly. In
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4096-508: A sports bike , and have been called symbols of futurism and posthumanism . In an analysis, author Esperanza Miyake interpreted the Light Cycles of the original Tron as representations of male power: only men get the chance to ride them, while the sole female character, Lora, does not. Their speed showed male dominance and control over technology, representing the means to "escape". The Light Cycle sequence inspired John Lasseter , who
4224-433: A square for example, they do not have to worry about drawing four lines perfectly to form the edges of the box. One can simply specify that they want to draw a box, and then specify the location and size of the box. The software will then construct a perfect box, with the right dimensions and at the right location. Another example is that Sutherland's software modeled objects – not just a picture of objects. In other words, with
4352-400: A sub-field of computer science which studies methods for digitally synthesizing and manipulating visual content. Over the past decade, other specialized fields have been developed like information visualization , and scientific visualization more concerned with "the visualization of three dimensional phenomena (architectural, meteorological, medical, biological , etc.), where the emphasis
4480-463: A suitably high-end system may simulate photorealism to the untrained eye. Texture mapping has matured into a multistage process with many layers; generally, it is not uncommon to implement texture mapping, bump mapping or isosurfaces or normal mapping , lighting maps including specular highlights and reflection techniques, and shadow volumes into one rendering engine using shaders , which are maturing considerably. Shaders are now very nearly
4608-600: A technical sense a type of transformation geometry , in which transformations are homeomorphisms . This has often been expressed in the form of the saying 'topology is rubber-sheet geometry'. Subfields of topology include geometric topology , differential topology , algebraic topology and general topology . Algebraic geometry is fundamentally the study by means of algebraic methods of some geometrical shapes, called algebraic sets , and defined as common zeros of multivariate polynomials . Algebraic geometry became an autonomous subfield of geometry c. 1900 , with
4736-518: A theorem called Hilbert's Nullstellensatz that establishes a strong correspondence between algebraic sets and ideals of polynomial rings . This led to a parallel development of algebraic geometry, and its algebraic counterpart, called commutative algebra . From the late 1950s through the mid-1970s algebraic geometry had undergone major foundational development, with the introduction by Alexander Grothendieck of scheme theory , which allows using topological methods , including cohomology theories in
4864-494: A theory of ratios that avoided the problem of incommensurable magnitudes , which enabled subsequent geometers to make significant advances. Around 300 BC, geometry was revolutionized by Euclid, whose Elements , widely considered the most successful and influential textbook of all time, introduced mathematical rigor through the axiomatic method and is the earliest example of the format still used in mathematics today, that of definition, axiom, theorem, and proof. Although most of
4992-467: A white grid on black ground, marking the distance the Light Cycles travel. Light Cycles were designed by artist Syd Mead . They were initially rendered digitally. The Light Cycle sequence in Tron was developed by MAGi in Westchester County, New York . It takes place over a length of about three minutes, which is interspersed with one minute of live-action footage. For Tron: Legacy ,
5120-587: A wider audience in the video game industry . The Sega Model 2 in 1993 and Sega Model 3 in 1996 subsequently pushed the boundaries of commercial, real-time 3D graphics. Back on the PC, Wolfenstein 3D , Doom and Quake , three of the first massively popular 3D first-person shooter games, were released by id Software to critical and popular acclaim during this decade using a rendering engine innovated primarily by John Carmack . The Sony PlayStation , Sega Saturn , and Nintendo 64 , among other consoles, sold in
5248-411: Is diffeomorphic to Euclidean space. Manifolds are used extensively in physics, including in general relativity and string theory . Euclid defines a plane angle as the inclination to each other, in a plane, of two lines which meet each other, and do not lie straight with respect to each other. In modern terms, an angle is the figure formed by two rays , called the sides of the angle, sharing
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5376-540: Is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic , one of the oldest branches of mathematics. 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. Originally developed to model
5504-400: Is a part of some ambient flat Euclidean space). Topology is the field concerned with the properties of continuous mappings , and can be considered a generalization of Euclidean geometry. In practice, topology often means dealing with large-scale properties of spaces, such as connectedness and compactness . The field of topology, which saw massive development in the 20th century, is in
5632-413: Is a three-dimensional object bounded by a closed surface; for example, a ball is the volume bounded by a sphere. A manifold is a generalization of the concepts of curve and surface. In topology , a manifold is a topological space where every point has a neighborhood that is homeomorphic to Euclidean space. In differential geometry , a differentiable manifold is a space where each neighborhood
5760-539: Is an active research area as well, along with advanced areas like ambient occlusion , subsurface scattering , Rayleigh scattering , photon mapping , ray-tracing and many others. Experiments into the processing power required to provide graphics in real time at ultra-high-resolution modes like 4K Ultra HD begun, though beyond reach of all but the highest-end hardware. In cinema, most animated movies are CGI now; many animated CGI films are made per year , but few, if any, attempt photorealism due to continuing fears of
5888-409: Is defined. The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia and Egypt in the 2nd millennium BC. Early geometry was a collection of empirically discovered principles concerning lengths, angles, areas, and volumes, which were developed to meet some practical need in surveying , construction , astronomy , and various crafts. The earliest known texts on geometry are
6016-437: Is not viewed as the set of the points through which it passes. However, there are modern geometries in which points are not primitive objects, or even without points. One of the oldest such geometries is Whitehead's point-free geometry , formulated by Alfred North Whitehead in 1919–1920. Euclid described a line as "breadthless length" which "lies equally with respect to the points on itself". In modern mathematics, given
6144-415: Is of importance to mathematical physics due to Albert Einstein 's general relativity postulation that the universe is curved . Differential geometry can either be intrinsic (meaning that the spaces it considers are smooth manifolds whose geometric structure is governed by a Riemannian metric , which determines how distances are measured near each point) or extrinsic (where the object under study
6272-498: Is on realistic renderings of volumes, surfaces, illumination sources, and so forth, perhaps with a dynamic (time) component". The precursor sciences to the development of modern computer graphics were the advances in electrical engineering , electronics , and television that took place during the first half of the twentieth century. Screens could display art since the Lumiere brothers ' use of mattes to create special effects for
6400-482: Is represented by congruences and rigid motions, whereas in projective geometry an analogous role is played by collineations , geometric transformations that take straight lines into straight lines. However it was in the new geometries of Bolyai and Lobachevsky, Riemann, Clifford and Klein, and Sophus Lie that Klein's idea to 'define a geometry via its symmetry group ' found its inspiration. Both discrete and continuous symmetries play prominent roles in geometry,
6528-753: The Sulba Sutras . According to ( Hayashi 2005 , p. 363), the Śulba Sūtras contain "the earliest extant verbal expression of the Pythagorean Theorem in the world, although it had already been known to the Old Babylonians. They contain lists of Pythagorean triples , which are particular cases of Diophantine equations . In the Bakhshali manuscript , there are a handful of geometric problems (including problems about volumes of irregular solids). The Bakhshali manuscript also "employs
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#17327801890516656-690: The Egyptian Rhind Papyrus (2000–1800 BC) and Moscow Papyrus ( c. 1890 BC ), and the Babylonian clay tablets , such as Plimpton 322 (1900 BC). For example, the Moscow Papyrus gives a formula for calculating the volume of a truncated pyramid, or frustum . Later clay tablets (350–50 BC) demonstrate that Babylonian astronomers implemented trapezoid procedures for computing Jupiter's position and motion within time-velocity space. These geometric procedures anticipated
6784-492: The GPGPU technique to pass large amounts of data bidirectionally between a GPU and CPU was invented; speeding up analysis on many kinds of bioinformatics and molecular biology experiments. The technique has also been used for Bitcoin mining and has applications in computer vision . In the 2010s, CGI has been nearly ubiquitous in video, pre-rendered graphics are nearly scientifically photorealistic , and real-time graphics on
6912-598: The LINKS-1 Computer Graphics System , a supercomputer that used up to 257 Zilog Z8001 microprocessors , in 1982, for the purpose of rendering realistic 3D computer graphics . According to the Information Processing Society of Japan: "The core of 3D image rendering is calculating the luminance of each pixel making up a rendered surface from the given viewpoint, light source , and object position. The LINKS-1 system
7040-523: The Lambert quadrilateral and Saccheri quadrilateral , were part of a line of research on the parallel postulate continued by later European geometers, including Vitello ( c. 1230 – c. 1314 ), Gersonides (1288–1344), Alfonso, John Wallis , and Giovanni Girolamo Saccheri , that by the 19th century led to the discovery of hyperbolic geometry . In the early 17th century, there were two important developments in geometry. The first
7168-518: The Oxford Calculators , including the mean speed theorem , by 14 centuries. South of Egypt the ancient Nubians established a system of geometry including early versions of sun clocks. In the 7th century BC, the Greek mathematician Thales of Miletus used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. He is credited with
7296-509: The Riemann surface , and Henri Poincaré , the founder of algebraic topology and the geometric theory of dynamical systems . As a consequence of these major changes in the conception of geometry, the concept of " space " became something rich and varied, and the natural background for theories as different as complex analysis and classical mechanics . The following are some of the most important concepts in geometry. Euclid took an abstract approach to geometry in his Elements , one of
7424-472: The arcades , advances were made in commercial, real-time 3D graphics. In 1988, the first dedicated real-time 3D graphics boards were introduced for arcades, with the Namco System 21 and Taito Air System. On the professional side, Evans & Sutherland and SGI developed 3D raster graphics hardware that directly influenced the later single-chip graphics processing unit (GPU), a technology where
7552-399: The complex plane using techniques of complex analysis ; and so on. A curve is a 1-dimensional object that may be straight (like a line) or not; curves in 2-dimensional space are called plane curves and those in 3-dimensional space are called space curves . In topology, a curve is defined by a function from an interval of the real numbers to another space. In differential geometry,
7680-731: The uncanny valley . Most are 3D cartoons . In videogames, the Microsoft Xbox One , Sony PlayStation 4 , and Nintendo Switch dominated the home space and were all capable of advanced 3D graphics; Windows was still one of the most active gaming platforms as well. In the 2020s', advances in ray-tracing technology allowed it to be used for real-time rendering, as well as AI-powered graphics for generating or upscaling Geometry Geometry (from Ancient Greek γεωμετρία ( geōmetría ) 'land measurement'; from γῆ ( gê ) 'earth, land' and μέτρον ( métron ) 'a measure')
7808-631: The 19th century changed the way it had been studied previously. These were the discovery of non-Euclidean geometries by Nikolai Ivanovich Lobachevsky, János Bolyai and Carl Friedrich Gauss and of the formulation of symmetry as the central consideration in the Erlangen programme of Felix Klein (which generalized the Euclidean and non-Euclidean geometries). Two of the master geometers of the time were Bernhard Riemann (1826–1866), working primarily with tools from mathematical analysis , and introducing
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#17327801890517936-496: The 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss 's Theorema Egregium ("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
8064-474: The 19th century, the discovery of non-Euclidean geometries by Nikolai Ivanovich Lobachevsky (1792–1856), János Bolyai (1802–1860), Carl Friedrich Gauss (1777–1855) and others led to a revival of interest in this discipline, and in the 20th century, David Hilbert (1862–1943) employed axiomatic reasoning in an attempt to provide a modern foundation of geometry. Points are generally considered fundamental objects for building geometry. They may be defined by
8192-459: The Light Cycle was redesigned by Daniel Simon . Five prop Light Cycles were built in real life, with four of them being destroyed post-production. The final one was purchased by Xiao Yu, a collector based in Nanjing, China ; however, he was told by the authorities that it was not street-legal. Light Cycles became well-known in popular culture as one of the first mainstream cinematic appearances of
8320-410: 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 computer graphics hardware . It is a vast and recently developed area of computer science. The phrase
8448-590: The angles between plane curves or space curves or surfaces can be calculated using the derivative . Length , area , and volume describe the size or extent of an object in one dimension, two dimension, and three dimensions respectively. In Euclidean geometry and analytic geometry , the length of a line segment can often be calculated by the Pythagorean theorem . Area and volume can be defined as fundamental quantities separate from length, or they can be described and calculated in terms of lengths in
8576-573: The attitude of a satellite could be altered as it orbits the Earth. He created the animation on an IBM 7090 mainframe computer. Also at BTL, Ken Knowlton , Frank Sinden, Ruth A. Weiss and Michael Noll started working in the computer graphics field. Sinden created a film called Force, Mass and Motion illustrating Newton's laws of motion in operation. Around the same time, other scientists were creating computer graphics to illustrate their research. At Lawrence Radiation Laboratory , Nelson Max created
8704-557: The box office in this field. The Final Fantasy: The Spirits Within , released in 2001, was the first fully computer-generated feature film to use photorealistic CGI characters and be fully made with motion capture. The film was not a box-office success, however. Some commentators have suggested this may be partly because the lead CGI characters had facial features which fell into the " uncanny valley ". Other animated films like The Polar Express drew attention at this time as well. Star Wars also resurfaced with its prequel trilogy and
8832-412: The concept of angle and distance, finite geometry that omits continuity , and others. This enlargement of the scope of geometry led to a change of meaning of the word "space", which originally referred to the three-dimensional space of the physical world and its model provided by Euclidean geometry; presently a geometric space , or simply a space is a mathematical structure on which some geometry
8960-513: The contents of the Elements were already known, Euclid arranged them into a single, coherent logical framework. The Elements was known to all educated people in the West until the middle of the 20th century and its contents are still taught in geometry classes today. Archimedes ( c. 287–212 BC ) of Syracuse, Italy used the method of exhaustion to calculate the area under the arc of
9088-602: The development of computer graphics as a discipline. Early projects like the Whirlwind and SAGE Projects introduced the CRT as a viable display and interaction interface and introduced the light pen as an input device . Douglas T. Ross of the Whirlwind SAGE system performed a personal experiment in which he wrote a small program that captured the movement of his finger and displayed its vector (his traced name) on
9216-458: The development of the Gouraud shading and Blinn–Phong shading models, allowing graphics to move beyond a "flat" look to a look more accurately portraying depth. Jim Blinn also innovated further in 1978 by introducing bump mapping , a technique for simulating uneven surfaces, and the predecessor to many more advanced kinds of mapping used today. The modern videogame arcade as is known today
9344-501: The earliest films dating from 1895, but such displays were limited and not interactive. The first cathode ray tube , the Braun tube , was invented in 1897 – it in turn would permit the oscilloscope and the military control panel – the more direct precursors of the field, as they provided the first two-dimensional electronic displays that responded to programmatic or user input. Nevertheless, computer graphics remained relatively unknown as
9472-417: The early 1980s, metal–oxide–semiconductor (MOS) very-large-scale integration (VLSI) technology led to the availability of 16-bit central processing unit (CPU) microprocessors and the first graphics processing unit (GPU) chips, which began to revolutionize computer graphics, enabling high-resolution graphics for computer graphics terminals as well as personal computer (PC) systems. NEC 's μPD7220
9600-416: The early 1990s. A major advance in 3D computer graphics was created at UU by these early pioneers – hidden surface determination . In order to draw a representation of a 3D object on the screen, the computer must determine which surfaces are "behind" the object from the viewer's perspective, and thus should be "hidden" when the computer creates (or renders) the image. The 3D Core Graphics System (or Core )
9728-603: The early decade with occasional significant competing presence from ATI . As the decade progressed, even low-end machines usually contained a 3D-capable GPU of some kind as Nvidia and AMD both introduced low-priced chipsets and continued to dominate the market. Shaders which had been introduced in the 1980s to perform specialized processing on the GPU would by the end of the decade become supported on most consumer hardware, speeding up graphics considerably and allowing for greatly improved texture and shading in computer graphics via
9856-706: The effects continued to set a bar for CGI in film. In videogames , the Sony PlayStation 2 and 3 , the Microsoft Xbox line of consoles, and offerings from Nintendo such as the GameCube maintained a large following, as did the Windows PC . Marquee CGI-heavy titles like the series of Grand Theft Auto , Assassin's Creed , Final Fantasy , BioShock , Kingdom Hearts , Mirror's Edge and dozens of others continued to approach photorealism , grow
9984-454: The emergence of computer graphics hardware. Further advances in computing led to greater advancements in interactive computer graphics . In 1959, the TX-2 computer was developed at MIT's Lincoln Laboratory . The TX-2 integrated a number of new man-machine interfaces. A light pen could be used to draw sketches on the computer using Ivan Sutherland 's revolutionary Sketchpad software . Using
10112-449: The end of the decade, the GPU would begin its rise to the prominence it still enjoys today. The field began to see the first rendered graphics that could truly pass as photorealistic to the untrained eye (though they could not yet do so with a trained CGI artist) and 3D graphics became far more popular in gaming , multimedia , and animation . At the end of the 1980s and the beginning of
10240-428: The field has been split in many subfields that depend on the underlying methods— differential geometry , algebraic geometry , computational geometry , algebraic topology , discrete geometry (also known as combinatorial geometry ), etc.—or on the properties of Euclidean spaces that are disregarded— projective geometry that consider only alignment of points but not distance and parallelism, affine geometry that omits
10368-485: The field of computer graphics. By 1973, the first annual SIGGRAPH conference was held, which has become one of the focuses of the organization. SIGGRAPH has grown in size and importance as the field of computer graphics has expanded over time. Subsequently, a number of breakthroughs in the field occurred at the University of Utah in the 1970s, which had hired Ivan Sutherland . He was paired with David C. Evans to teach an advanced computer graphics class, which contributed
10496-472: The films Flow of a Viscous Fluid and Propagation of Shock Waves in a Solid Form . Boeing Aircraft created a film called Vibration of an Aircraft . Also sometime in the early 1960s, automobiles would also provide a boost through the early work of Pierre Bézier at Renault , who used Paul de Casteljau 's curves – now called Bézier curves after Bézier's work in the field – to develop 3d modeling techniques for Renault car bodies. These curves would form
10624-492: The first ray casting algorithm, the first of a class of ray tracing -based rendering algorithms that have since become fundamental in achieving photorealism in graphics by modeling the paths that rays of light take from a light source, to surfaces in a scene, and into the camera. In 1969, the ACM initiated A Special Interest Group on Graphics ( SIGGRAPH ) which organizes conferences , graphics standards , and publications within
10752-498: The first shaders – small programs designed specifically to do shading as a separate algorithm – were developed by Pixar , which had already spun off from Industrial Light & Magic as a separate entity – though the public would not see the results of such technological progress until the next decade. In the late 1980s, Silicon Graphics (SGI) computers were used to create some of the first fully computer-generated short films at Pixar , and Silicon Graphics machines were considered
10880-520: The first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem . Pythagoras established the Pythagorean School , which is credited with the first proof of the Pythagorean theorem , though the statement of the theorem has a long history. Eudoxus (408– c. 355 BC ) developed the method of exhaustion , which allowed the calculation of areas and volumes of curvilinear figures, as well as
11008-526: The former in topology and geometric group theory , the latter in Lie theory and Riemannian geometry . A different type of symmetry is the principle of duality in projective geometry , among other fields. This meta-phenomenon can roughly be described as follows: in any theorem , exchange point with plane , join with meet , lies in with contains , and the result is an equally true theorem. A similar and closely related form of duality exists between
11136-402: The foundation for much curve-modeling work in the field, as curves – unlike polygons – are mathematically complex entities to draw and model well. It was not long before major corporations started taking an interest in computer graphics. TRW , Lockheed-Georgia , General Electric and Sperry Rand are among the many companies that were getting started in computer graphics by the mid-1960s. IBM
11264-570: The history of video games , Spacewar! Written for the DEC PDP-1, Spacewar was an instant success and copies started flowing to other PDP-1 owners and eventually DEC got a copy. The engineers at DEC used it as a diagnostic program on every new PDP-1 before shipping it. The sales force picked up on this quickly enough and when installing new units, would run the "world's first video game" for their new customers. (Higginbotham's Tennis For Two had beaten Spacewar by almost three years, but it
11392-598: The idea of metrics . For instance, the Euclidean metric measures the distance between points in the Euclidean plane , while the hyperbolic metric measures the distance in the hyperbolic plane . Other important examples of metrics include the Lorentz metric of special relativity and the semi- Riemannian metrics of general relativity . In a different direction, the concepts of length, area and volume are extended by measure theory , which studies methods of assigning
11520-537: The idea of reducing geometrical problems such as duplicating the cube to problems in algebra. Thābit ibn Qurra (known as Thebit in Latin ) (836–901) dealt with arithmetic operations applied to ratios of geometrical quantities, and contributed to the development of analytic geometry . Omar Khayyam (1048–1131) found geometric solutions to cubic equations . The theorems of Ibn al-Haytham (Alhazen), Omar Khayyam and Nasir al-Din al-Tusi on quadrilaterals , including
11648-484: The intelligence in the workstation, rather than continuing to rely on central mainframe and minicomputers . Typical of the early move to high-resolution computer graphics, intelligent workstations for the computer-aided engineering market were the Orca 1000, 2000 and 3000 workstations, developed by Orcatech of Ottawa, a spin-off from Bell-Northern Research , and led by David Pearson, an early workstation pioneer. The Orca 3000
11776-399: The late 1990s and 2000s, and so became familiar to a massive audience. The continued rise and increasing sophistication of the graphics processing unit were crucial to this decade, and 3D rendering capabilities became a standard feature as 3D-graphics GPUs became considered a necessity for desktop computer makers to offer. The Nvidia GeForce line of graphics cards dominated the market in
11904-423: The later films of the original trilogy. Two other pieces of video would also outlast the era as historically relevant: Dire Straits ' iconic, near-fully-CGI video for their song " Money for Nothing " in 1985, which popularized CGI among music fans of that era, and a scene from Young Sherlock Holmes the same year featuring the first fully CGI character in a feature movie (an animated stained-glass knight ). In 1988,
12032-552: The latter section, he stated his famous theorem on the diagonals of a cyclic quadrilateral . Chapter 12 also included a formula for the area of a cyclic quadrilateral (a generalization of Heron's formula ), as well as a complete description of rational triangles ( i.e. triangles with rational sides and rational areas). In the Middle Ages , mathematics in medieval Islam contributed to the development of geometry, especially algebraic geometry . Al-Mahani (b. 853) conceived
12160-696: The mid-1980s. In 1984, Hitachi released the ARTC HD63484, the first complementary MOS (CMOS) GPU. It was capable of displaying high-resolution in color mode and up to 4K resolution in monochrome mode, and it was used in a number of graphics cards and terminals during the late 1980s. In 1986, TI introduced the TMS34010 , the first fully programmable MOS graphics processor. Computer graphics terminals during this decade became increasingly intelligent, semi-standalone and standalone workstations. Graphics and application processing were increasingly migrated to
12288-572: The millions and popularized 3D graphics for home gamers. Certain late-1990s first-generation 3D titles became seen as influential in popularizing 3D graphics among console users, such as platform games Super Mario 64 and The Legend of Zelda: Ocarina of Time , and early 3D fighting games like Virtua Fighter , Battle Arena Toshinden , and Tekken . Technology and algorithms for rendering continued to improve greatly. In 1996, Krishnamurty and Levoy invented normal mapping – an improvement on Jim Blinn's bump mapping . 1999 saw Nvidia release
12416-439: The most important research centers in graphics for nearly a decade thereafter, eventually producing some of the most important pioneers in the field. There Sutherland perfected his HMD; twenty years later, NASA would re-discover his techniques in their virtual reality research. At Utah, Sutherland and Evans were highly sought after consultants by large companies, but they were frustrated at the lack of graphics hardware available at
12544-411: The most influential books ever written. Euclid introduced certain axioms , or postulates , expressing primary or self-evident properties of points, lines, and planes. He proceeded to rigorously deduce other properties by mathematical reasoning. The characteristic feature of Euclid's approach to geometry was its rigor, and it has come to be known as axiomatic or synthetic geometry. At the start of
12672-429: The multitude of geometries, the concept of a line is closely tied to the way the geometry is described. For instance, in analytic geometry , a line in the plane is often defined as the set of points whose coordinates satisfy a given linear equation , but in a more abstract setting, such as incidence geometry , a line may be an independent object, distinct from the set of points which lie on it. In differential geometry,
12800-528: The nineties were created, in France, the very first computer graphics TV series: La Vie des bêtes by studio Mac Guff Ligne (1988), Les Fables Géométriques (1989–1991) by studio Fantôme, and Quarxs , the first HDTV computer graphics series by Maurice Benayoun and François Schuiten (studio Z-A production, 1990–1993). In film, Pixar began its serious commercial rise in this era under Edwin Catmull , with its first major film release, in 1995 – Toy Story –
12928-441: The only instruments used in most geometric constructions are the compass and straightedge . Also, every construction had to be complete in a finite number of steps. However, some problems turned out to be difficult or impossible to solve by these means alone, and ingenious constructions using neusis , parabolas and other curves, or mechanical devices, were found. The geometrical concepts of rotation and orientation define part of
13056-514: The physical world, geometry has applications in almost all sciences, and also in art, architecture , and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem , a problem that was stated in terms of elementary arithmetic , and remained unsolved for several centuries. During
13184-407: The placement of objects embedded in the plane or in space. Traditional geometry allowed dimensions 1 (a line or curve), 2 (a plane or surface), and 3 (our ambient world conceived of as three-dimensional space ). Furthermore, mathematicians and physicists have used higher dimensions for nearly two centuries. One example of a mathematical use for higher dimensions is the configuration space of
13312-482: The properties that they must have, as in Euclid's definition as "that which has no part", or in synthetic geometry . In modern mathematics, they are generally defined as elements of a set called space , which is itself axiomatically defined. With these modern definitions, every geometric shape is defined as a set of points; this is not the case in synthetic geometry, where a line is another fundamental object that
13440-442: The quality of CGI generally. Home computers became able to take on rendering tasks that previously had been limited to workstations costing thousands of dollars; as 3D modelers became available for home systems, the popularity of Silicon Graphics workstations declined and powerful Microsoft Windows and Apple Macintosh machines running Autodesk products like 3D Studio or other home rendering software ascended in importance. By
13568-554: The same definition is used, but the defining function is required to be differentiable. Algebraic geometry studies algebraic curves , which are defined as algebraic varieties of dimension one. A surface is a two-dimensional object, such as a sphere or paraboloid. In differential geometry and topology , surfaces are described by two-dimensional 'patches' (or neighborhoods ) that are assembled by diffeomorphisms or homeomorphisms , respectively. In algebraic geometry, surfaces are described by polynomial equations . A solid
13696-507: The seminal GeForce 256 , the first home video card billed as a graphics processing unit or GPU, which in its own words contained "integrated transform , lighting , triangle setup / clipping , and rendering engines". By the end of the decade, computers adopted common frameworks for graphics processing such as DirectX and OpenGL . Since then, computer graphics have only become more detailed and realistic, due to more powerful graphics hardware and 3D modeling software . AMD also became
13824-589: The study of Euclidean concepts such as points , lines , planes , angles , triangles , congruence , similarity , solid figures , circles , and analytic geometry . Euclidean vectors are used for a myriad of applications in physics and engineering, such as position , displacement , deformation , velocity , acceleration , force , etc. Differential geometry uses techniques of calculus and linear algebra to study problems in geometry. It has applications in physics , econometrics , and bioinformatics , among others. In particular, differential geometry
13952-474: The talent for drawing. Now Catmull (along with many others) saw computers as the natural progression of animation and they wanted to be part of the revolution. The first computer animation that Catmull saw was his own. He created an animation of his hand opening and closing. He also pioneered texture mapping to paint textures on three-dimensional models in 1974, now considered one of the fundamental techniques in 3D modeling . It became one of his goals to produce
14080-409: The theory of manifolds and Riemannian geometry . Later in the 19th century, it appeared that geometries without the parallel postulate ( non-Euclidean geometries ) can be developed without introducing any contradiction. The geometry that underlies general relativity is a famous application of non-Euclidean geometry. Since the late 19th century, the scope of geometry has been greatly expanded, and
14208-554: The time, so they started formulating a plan to start their own company. In 1968, Dave Evans and Ivan Sutherland founded the first computer graphics hardware company, Evans & Sutherland . While Sutherland originally wanted the company to be located in Cambridge, Massachusetts, Salt Lake City was instead chosen due to its proximity to the professors' research group at the University of Utah. Also in 1968 Arthur Appel described
14336-521: The underlying sciences of geometry , optics , physics , and perception . Computer graphics is responsible for displaying art and image data effectively and meaningfully to the consumer. It is also used for processing image data received from the physical world, such as photo and video content. Computer graphics development has had a significant impact on many types of media and has revolutionized animation , movies , advertising , and video games , in general. The term computer graphics has been used in
14464-552: The video game industry and impress, until that industry's revenues became comparable to those of movies. Microsoft made a decision to expose DirectX more easily to the independent developer world with the XNA program, but it was not a success. DirectX itself remained a commercial success, however. OpenGL continued to mature as well, and it and DirectX improved greatly; the second-generation shader languages HLSL and GLSL began to be popular in this decade. In scientific computing ,
14592-448: The widespread adoption of normal mapping , bump mapping , and a variety of other techniques allowing the simulation of a great amount of detail. Computer graphics used in films and video games gradually began to be realistic to the point of entering the uncanny valley . CGI movies proliferated, with traditional animated cartoon films like Ice Age and Madagascar as well as numerous Pixar offerings like Finding Nemo dominating
14720-418: The world's primary research center for computer graphics through the 1970s. Also, in 1966, Ivan Sutherland continued to innovate at MIT when he invented the first computer-controlled head-mounted display (HMD). It displayed two separate wireframe images, one for each eye. This allowed the viewer to see the computer scene in stereoscopic 3D . The heavy hardware required for supporting the display and tracker
14848-423: Was almost unknown outside of a research or academic setting.) At around the same time (1961–1962) in the University of Cambridge, Elizabeth Waldram wrote code to display radio-astronomy maps on a cathode ray tube. E. E. Zajac, a scientist at Bell Telephone Laboratory (BTL), created a film called "Simulation of a two-giro gravity attitude control system" in 1963. In this computer-generated film, Zajac showed how
14976-488: Was based on the 16-bit Motorola 68000 microprocessor and AMD bit-slice processors, and had Unix as its operating system. It was targeted squarely at the sophisticated end of the design engineering sector. Artists and graphic designers began to see the personal computer, particularly the Amiga and Macintosh , as a serious design tool, one that could save time and draw more accurately than other methods. The Macintosh remains
15104-409: Was birthed in the 1970s, with the first arcade games using real-time 2D sprite graphics. Pong in 1972 was one of the first hit arcade cabinet games. Speed Race in 1974 featured sprites moving along a vertically scrolling road. Gun Fight in 1975 featured human-looking animated characters, while Space Invaders in 1978 featured a large number of animated figures on screen; both used
15232-497: Was called the Sword of Damocles because of the potential danger if it were to fall upon the wearer. After receiving his Ph.D. from MIT, Sutherland became Director of Information Processing at ARPA (Advanced Research Projects Agency), and later became a professor at Harvard. In 1967 Sutherland was recruited by Evans to join the computer science program at the University of Utah – a development which would turn that department into one of
15360-760: 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 computing , image processing , computational photography , scientific visualization , computational geometry and computer vision , among others. The overall methodology depends heavily on
15488-500: Was developed in 1986 – an important step towards implementing global illumination , which is necessary to pursue photorealism in computer graphics. The continuing popularity of Star Wars and other science fiction franchises were relevant in cinematic CGI at this time, as Lucasfilm and Industrial Light & Magic became known as the "go-to" house by many other studios for topnotch computer graphics in film. Important advances in chroma keying ("bluescreening", etc.) were made for
15616-463: Was developed to realize an image rendering methodology in which each pixel could be parallel processed independently using ray tracing . By developing a new software methodology specifically for high-speed image rendering, LINKS-1 was able to rapidly render highly realistic images." The LINKS-1 was the world's most powerful computer , as of 1984. Also in the field of realistic rendering, the general rendering equation of David Immel and James Kajiya
15744-432: Was easy to pinpoint exactly where the pen was on the screen at any given moment. Once that was determined, the computer could then draw a cursor at that location. Sutherland seemed to find the perfect solution for many of the graphics problems he faced. Even today, many standards of computer graphics interfaces got their start with this early Sketchpad program. One example of this is in drawing constraints. If one wants to draw
15872-535: Was quick to respond to this interest by releasing the IBM 2250 graphics terminal, the first commercially available graphics computer. Ralph Baer , a supervising engineer at Sanders Associates , came up with a home video game in 1966 that was later licensed to Magnavox and called the Odyssey . While very simplistic, and requiring fairly inexpensive electronic parts, it allowed the player to move points of light around on
16000-596: Was the creation of analytic geometry, or geometry with coordinates and equations , by René Descartes (1596–1650) and Pierre de Fermat (1601–1665). This was a necessary precursor to the development of calculus and a precise quantitative science of physics . The second geometric development of this period was the systematic study of projective geometry by Girard Desargues (1591–1661). Projective geometry studies properties of shapes which are unchanged under projections and sections , especially as they relate to artistic perspective . Two developments in geometry in
16128-564: Was the first GPU, fabricated on a fully integrated NMOS VLSI chip . It supported up to 1024x1024 resolution , and laid the foundations for the emerging PC graphics market. It was used in a number of graphics cards , and was licensed for clones such as the Intel 82720, the first of Intel's graphics processing units . MOS memory also became cheaper in the early 1980s, enabling the development of affordable framebuffer memory, notably video RAM (VRAM) introduced by Texas Instruments (TI) in
16256-539: Was the first graphical standard to be developed. A group of 25 experts of the ACM Special Interest Group SIGGRAPH developed this "conceptual framework". The specifications were published in 1977, and it became a foundation for many future developments in the field. Also in the 1970s, Henri Gouraud , Jim Blinn and Bui Tuong Phong contributed to the foundations of shading in CGI via
16384-531: Was then working at Disney , to enter computer animation; he went on to direct Toy Story , crediting its creation to Tron . The Light Cycle design served as the basis for a roller coaster called Tron Lightcycle Power Run , which opened in Shanghai Disneyland in 2016 and Magic Kingdom in 2023, the latter in which it is known as Tron Lightcycle / Run. Computer graphics Computer graphics deals with generating images and art with
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