The Retro Engine , also known as the Retro Software Development Kit , is a multiplatform game engine developed by Australian programmer Christian Whitehead , used in games from Sega 's Sonic the Hedgehog series.
74-576: The Retro Engine is primarily tailored for creating two-dimensional games like those released for 32-bit or below-era consoles, such as the Sega Saturn , Sega Genesis or the Super Nintendo Entertainment System . For this reason, the engine focuses more on raster graphics and palette manipulation , although it does feature support for widescreen graphics and online functionality. Australian programmer Christian Whitehead created
148-598: A rigid motion : other rigid motions include rotations and reflections. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system . A translation operator is an operator T δ {\displaystyle T_{\mathbf {\delta } }} such that T δ f ( v ) = f ( v + δ ) . {\displaystyle T_{\mathbf {\delta } }f(\mathbf {v} )=f(\mathbf {v} +\mathbf {\delta } ).} If v
222-562: A rotation in Euclidean space . rotates points in the xy - Cartesian plane counterclockwise through an angle θ about the origin of the Cartesian coordinate system . To perform the rotation using a rotation matrix R , the position of each point must be represented by a column vector v , containing the coordinates of the point. A rotated vector is obtained by using the matrix multiplication R v . Since matrix multiplication has no effect on
296-413: A scale factor that is the same in all directions. The result of uniform scaling is similar (in the geometric sense) to the original. A scale factor of 1 is normally allowed, so that congruent shapes are also classed as similar. (Some school text books specifically exclude this possibility, just as some exclude squares from being rectangles or circles from being ellipses.) More general is scaling with
370-614: A vector v = ( v x , v y , v z ), each homogeneous coordinate vector p = ( p x , p y , p z , 1) would need to be multiplied with this projective transformation matrix: As shown below, the multiplication will give the expected result: Since the last component of a homogeneous coordinate can be viewed as the denominator of the other three components, a uniform scaling by a common factor s (uniform scaling) can be accomplished by using this scaling matrix: For each vector p = ( p x , p y , p z , 1) we would have which would be homogenized to A convenient way to create
444-418: A "data pipeline" in which the raw data is managed and filtered to a form that makes it suitable for rendering. This is often called the "visualization data" . The visualization data is then mapped to a "visualization representation" that can be fed to a rendering system. This is usually called a "renderable representation" . This representation is then rendered as a displayable image. As the user interacts with
518-427: A common virtual geospatial model, these animated visualizations constitute the first true application of CGI to TV. CGI has become common in sports telecasting. Sports and entertainment venues are provided with see-through and overlay content through tracked camera feeds for enhanced viewing by the audience. Examples include the yellow " first down " line seen in television broadcasts of American football games showing
592-430: A complex image is to start with a blank "canvas" raster map (an array of pixels , also known as a bitmap ) filled with some uniform background color and then "draw", "paint" or "paste" simple patches of color onto it, in an appropriate order. In particular the canvas may be the frame buffer for a computer display . Some programs will set the pixel colors directly, but most will rely on some 2D graphics library or
666-681: A computer-generated reconstruction of the monastery at Georgenthal in Germany was derived from the ruins of the monastery, yet provides the viewer with a "look and feel" of what the building would have looked like in its day. Computer generated models used in skeletal animation are not always anatomically correct. However, organizations such as the Scientific Computing and Imaging Institute have developed anatomically correct computer-based models. Computer generated anatomical models can be used both for instructional and operational purposes. To date,
740-438: A description of a document based on 2D computer graphics techniques can be much smaller than the corresponding digital image—often by a factor of 1/1000 or more. This representation is also more flexible since it can be rendered at different resolutions to suit different output devices . For these reasons, documents and illustrations are often stored or transmitted as 2D graphic files . 2D computer graphics started in
814-473: A game to port to iOS . As a response, Whitehead produced a proof-of-concept video showing Sega's 1993 Sega CD game Sonic CD running on an iPhone . Sega later officially released the port in 2011 for various platforms, such as the Xbox 360 , PlayStation 3 , Windows , iOS and Android . Whitehead, along with fellow Sonic scene member Simon "Stealth" Thomley, were later commissioned to create remakes of Sonic
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#1733084675684888-543: A large body of artist produced medical images continue to be used by medical students, such as images by Frank H. Netter , e.g. Cardiac images . However, a number of online anatomical models are becoming available. A single patient X-ray is not a computer generated image, even if digitized. However, in applications which involve CT scans a three-dimensional model is automatically produced from many single-slice x-rays, producing "computer generated image". Applications involving magnetic resonance imaging also bring together
962-426: A number of "snapshots" (in this case via magnetic pulses) to produce a composite, internal image. In modern medical applications, patient-specific models are constructed in 'computer assisted surgery'. For instance, in total knee replacement , the construction of a detailed patient-specific model can be used to carefully plan the surgery. These three-dimensional models are usually extracted from multiple CT scans of
1036-407: A race proceeds to allow viewers to compare the current race to the best performance. Other examples include hockey puck tracking and annotations of racing car performance and snooker ball trajectories. Sometimes CGI on TV with correct alignment to the real world has been referred to as augmented reality . Computer-generated imagery is often used in conjunction with motion capture to better cover
1110-454: A rate of 24 or 30 frames/second). This technique is identical to how the illusion of movement is achieved with television and motion pictures . A text-to-image model is a machine learning model which takes an input natural language description and produces an image matching that description. Text-to-image models began to be developed in the mid-2010s during the beginnings of the AI boom , as
1184-631: A representation of one potential sequence of events. Weather visualizations were the first application of CGI in television. One of the first companies to offer computer systems for generating weather graphics was ColorGraphics Weather Systems in 1979 with the "LiveLine", based around an Apple II computer, with later models from ColorGraphics using Cromemco computers fitted with their Dazzler video graphics card. It has now become common in weather casting to display full motion video of images captured in real-time from multiple cameras and other imaging devices. Coupled with 3D graphics symbols and mapped to
1258-500: A result of advances in deep neural networks . In 2022, the output of state-of-the-art text-to-image models—such as OpenAI's DALL-E 2 , Google Brain 's Imagen , Stability AI's Stable Diffusion , and Midjourney —began to be considered to approach the quality of real photographs and human-drawn art . A virtual world is an agent-based and simulated environment allowing users to interact with artificially animated characters (e.g software agent ) or with other physical users, through
1332-406: A separate scale factor for each axis direction. Non-uniform scaling ( anisotropic scaling , inhomogeneous dilation ) is obtained when at least one of the scaling factors is different from the others; a special case is directional scaling or stretching (in one direction). Non-uniform scaling changes the shape of the object; e.g. a square may change into a rectangle, or into a parallelogram if
1406-474: A sound model for certain techniques such as mitered joints and the even–odd rule . Layered models are also used to allow the user to suppress unwanted information when viewing or printing a document, e.g. roads or railways from a map , certain process layers from an integrated circuit diagram, or hand annotations from a business letter. In a layer-based model, the target image is produced by "painting" or "pasting" each layer, in order of decreasing depth, on
1480-546: A specific order. The ordering is usually defined by a single number (the layer's depth , or distance from the viewer). Layered models are sometimes called "2 1 ⁄ 2 -D computer graphics". They make it possible to mimic traditional drafting and printing techniques based on film and paper, such as cutting and pasting; and allow the user to edit any layer without affecting the others. For these reasons, they are used in most graphics editors . Layered models also allow better spatial anti-aliasing of complex drawings and provide
1554-406: A translation matrix can be obtained by reversing the direction of the vector: Similarly, the product of translation matrices is given by adding the vectors: Because addition of vectors is commutative , multiplication of translation matrices is therefore also commutative (unlike multiplication of arbitrary matrices). In linear algebra , a rotation matrix is a matrix that is used to perform
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#17330846756841628-405: Is a fixed vector, then the translation T v will work as T v ( p ) = p + v . If T is a translation, then the image of a subset A under the function T is the translation of A by T . The translation of A by T v is often written A + v . In a Euclidean space , any translation is an isometry . The set of all translations forms the translation group T , which
1702-407: Is isomorphic to the space itself, and a normal subgroup of Euclidean group E ( n ). The quotient group of E ( n ) by T is isomorphic to the orthogonal group O ( n ): Since a translation is an affine transformation but not a linear transformation , homogeneous coordinates are normally used to represent the translation operator by a matrix and thus to make it linear. Thus we write
1776-610: Is known as inverting color or color inversion , and is often used in graphical user interfaces for highlighting, rubber-band drawing, and other volatile painting—since re-painting the same shapes with the same color will restore the original pixel values. The models used in 2D computer graphics usually do not provide for three-dimensional shapes, or three-dimensional optical phenomena such as lighting, shadows , reflection , refraction , etc. However, they usually can model multiple layers (conceptually of ink, paper, or film; opaque, translucent , or transparent —stacked in
1850-415: Is not commonly used in dimensions higher than 3; there is a notion of a rotational displacement , which can be represented by a matrix, but no associated single axis or angle. Rotation matrices are square matrices , with real entries. More specifically they can be characterized as orthogonal matrices with determinant 1: The set of all such matrices of size n forms a group , known as
1924-528: Is to use an extension of the triangular mesh method, relying on the construction of some special case of a de Rham curve , e.g., midpoint displacement . For instance, the algorithm may start with a large triangle, then recursively zoom in by dividing it into four smaller Sierpinski triangles , then interpolate the height of each point from its nearest neighbors. The creation of a Brownian surface may be achieved not only by adding noise as new nodes are created but by adding additional noise at multiple levels of
1998-406: Is used, with the x axis to the right and the y axis up, the rotation R( θ ) is counterclockwise. If a left-handed Cartesian coordinate system is used, with x directed to the right but y directed down, R( θ ) is clockwise. Such non-standard orientations are rarely used in mathematics but are common in 2D computer graphics, which often have the origin in the top left corner and the y -axis down
2072-446: The special orthogonal group SO( n ) . In two dimensions every rotation matrix has the following form: This rotates column vectors by means of the following matrix multiplication : So the coordinates (x',y') of the point (x,y) after rotation are: The direction of vector rotation is counterclockwise if θ is positive (e.g. 90°), and clockwise if θ is negative (e.g. -90°). If a standard right-handed Cartesian coordinate system
2146-693: The 1950s, based on vector graphics devices . These were largely supplanted by raster-based devices in the following decades. The PostScript language and the X Window System protocol were landmark developments in the field. 2D graphics models may combine geometric models (also called vector graphics ), digital images (also called raster graphics ), text to be typeset (defined by content, font style and size, color, position, and orientation), mathematical functions and equations , and more. These components can be modified and manipulated by two-dimensional geometric transformations such as translation , rotation , and scaling . In object-oriented graphics ,
2220-402: The 3-dimensional vector w = ( w x , w y , w z ) using 4 homogeneous coordinates as w = ( w x , w y , w z , 1). To translate an object by a vector v , each homogeneous vector p (written in homogeneous coordinates) would need to be multiplied by this translation matrix : As shown below, the multiplication will give the expected result: The inverse of
2294-426: The 4 entries of a rotation matrix with 2 rows and 2 columns. In 3-dimensional space, every rotation can be interpreted as a rotation by a given angle about a single fixed axis of rotation (see Euler's rotation theorem ), and hence it can be simply described by an angle and a vector with 3 entries. However, it can also be represented by the 9 entries of a rotation matrix with 3 rows and 3 columns. The notion of rotation
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2368-542: The B-52. Link's Digital Image Generator had architecture to provide a visual system that realistically corresponded with the view of the pilot. The basic archictecture of the DIG and subsequent improvements contained a scene manager followed by geometric processor, video processor and into the display with the end goal of a visual system that processed realistic texture, shading, translucency capabilties, and free of aliasing. Combined with
2442-469: The Hedgehog and Sonic the Hedgehog 2 using the engine, released for mobile platforms in 2013. In 2014, to celebrate the twentieth anniversary of the release of Sonic 3 & Knuckles , Whitehead and Thomley produced a proof-of-concept showing the game using the engine on an iPhone. Despite fan support, Sega did not approve of the project. Thomley speculated that this was due to legal problems regarding
2516-529: The Retro Engine for its performance, which has been called superior to simply emulating the original games. TouchArcade has referred to the remasters of Sonic the Hedgehog and Sonic the Hedgehog 2 as "spectacular". Whitehead has named games such as Ristar , Knuckles' Chaotix , and Dynamite Headdy , as well as non-Sega games like the Castlevania series, as others that would be possible to port to
2590-516: The Retro Engine for use with a 2007 fangame entitled Retro Sonic , which is based upon the original Sonic games released for the Sega Genesis . The game became notable after its release for its accuracy to the games, despite not being a ROM hack or modification to an existing Sonic game. Retro Sonic later merged with two other Sonic fangames, Sonic XG and Sonic Nexus , to form Retro Sonic Nexus . In 2009, Sega asked fans for ideas on
2664-538: The Retro Engine initially had been renamed the Star Engine. In October 2021, Evening Star announced development was underway for a game using the Star Engine, which was later revealed as Penny's Big Breakaway in June 2023. In conjunction with this, it was announced that the Star Engine had been turned into a separate engine with a focus on 3D rendering, with the Retro Engine remaining as their 2D game engine. Reviewers praised
2738-730: The ability to superimpose texture over the surfaces as well as transition imagery from one level of detail to the next one in a smooth manner. The evolution of CGI led to the emergence of virtual cinematography in the 1990s, where the vision of the simulated camera is not constrained by the laws of physics. Availability of CGI software and increased computer speeds have allowed individual artists and small companies to produce professional-grade films, games, and fine art from their home computers. Not only do animated images form part of computer-generated imagery; natural looking landscapes (such as fractal landscapes ) are also generated via computer algorithms . A simple way to generate fractal surfaces
2812-426: The appropriate parts of the patient's own anatomy. Such models can also be used for planning aortic valve implantations, one of the common procedures for treating heart disease . Given that the shape, diameter, and position of the coronary openings can vary greatly from patient to patient, the extraction (from CT scans ) of a model that closely resembles a patient's valve anatomy can be highly beneficial in planning
2886-475: The case of one or more negative scale factors. The latter corresponds to a combination of scaling proper and a kind of reflection: along lines in a particular direction we take the reflection in the point of intersection with a plane that need not be perpendicular; therefore it is more general than ordinary reflection in the plane. In projective geometry , often used in computer graphics , points are represented using homogeneous coordinates . To scale an object by
2960-468: The case where v x = v y = v z = k , the scaling is also called an enlargement or dilation by a factor k, increasing the area by a factor of k and the volume by a factor of k . Scaling in the most general sense is any affine transformation with a diagonalizable matrix . It includes the case that the three directions of scaling are not perpendicular. It includes also the case that one or more scale factors are equal to zero ( projection ), and
3034-450: The chemical weathering of stones to model erosion and produce an "aged appearance" for a given stone-based surface. Modern architects use services from computer graphic firms to create 3-dimensional models for both customers and builders. These computer generated models can be more accurate than traditional drawings. Architectural animation (which provides animated movies of buildings, rather than interactive images) can also be used to see
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3108-440: The complex anatomy of the human body, can often fail to replicate it perfectly. Artists can use motion capture to get footage of a human performing an action and then replicate it perfectly with computer-generated imagery so that it looks normal. The lack of anatomically correct digital models contributes to the necessity of motion capture as it is used with computer-generated imagery. Because computer-generated imagery reflects only
3182-419: The creation of images that would not be feasible using any other technology. It can also allow a single graphic artist to produce such content without the use of actors, expensive set pieces, or props. To create the illusion of movement, an image is displayed on the computer screen and repeatedly replaced by a new image which is similar to the previous image, but advanced slightly in the time domain (usually at
3256-417: The early 2000s. However, some experts have argued that it is prejudicial. They are used to help judges or the jury to better visualize the sequence of events, evidence or hypothesis. However, a 1997 study showed that people are poor intuitive physicists and easily influenced by computer generated images. Thus it is important that jurors and other legal decision-makers be made aware that such exhibits are merely
3330-610: The engine. 2D computer graphics 2D computer graphics is the computer-based generation of digital images —mostly from two-dimensional models (such as 2D geometric models , text, and digital images) and by techniques specific to them. It may refer to the branch of computer science that comprises such techniques or to the models themselves. 2D computer graphics are mainly used in applications that were originally developed upon traditional printing and drawing technologies, such as typography , cartography , technical drawing , advertising , etc. In those applications,
3404-439: The expected result: Such a scaling changes the diameter of an object by a factor between the scale factors, the area by a factor between the smallest and the largest product of two scale factors, and the volume by the product of all three. The scaling is uniform if and only if the scaling factors are equal ( v x = v y = v z ). If all except one of the scale factors are equal to 1, we have directional scaling. In
3478-406: The fabled checker paint which used to be available only in cartoons ). Painting a pixel with a given color usually replaces its previous color. However, many systems support painting with transparent and translucent colors, which only modify the previous pixel values. The two colors may also be combined in more complex ways, e.g. by computing their bitwise exclusive or . This technique
3552-432: The faults that come with CGI and animation. Computer-generated imagery is limited in its practical application by how realistic it can look. Unrealistic, or badly managed computer-generated imagery can result in the uncanny valley effect. This effect refers to the human ability to recognize things that look eerily like humans, but are slightly off. Such ability is a fault with normal computer-generated imagery which, due to
3626-442: The image is described indirectly by an object endowed with a self- rendering method —a procedure that assigns colors to the image pixels by an arbitrary algorithm. Complex models can be built by combining simpler objects, in the paradigms of object-oriented programming . In Euclidean geometry , a translation (geometry) moves every point a constant distance in a specified direction. A translation can be described as
3700-415: The latter two games to be run natively on PC platforms. The Retro Engine was also used for the compilation Sonic Origins in 2022, which includes remakes of Sonic the Hedgehog , Sonic the Hedgehog 2 , Sonic CD , and Sonic 3 & Knuckles . In 2019, Whitehead, in collaboration with other members behind Sonic Mania , founded a new video game studio named Evening Star . In reference to the studio name,
3774-403: The line the offensive team must cross to receive a first down. CGI is also used in association with football and other sporting events to show commercial advertisements overlaid onto the view of the playing area. Sections of rugby fields and cricket pitches also display sponsored images. Swimming telecasts often add a line across the lanes to indicate the position of the current record holder as
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#17330846756843848-436: The machine's graphics card , which usually implement the following operations: Text, shapes and lines are rendered with a client-specified color. Many libraries and cards provide color gradients , which are handy for the generation of smoothly-varying backgrounds, shadow effects, etc. (See also Gouraud shading ). The pixel colors can also be taken from a texture, e.g. a digital image (thus emulating rub-on screentones and
3922-460: The mesh. Thus a topographical map with varying levels of height can be created using relatively straightforward fractal algorithms. Some typical, easy-to-program fractals used in CGI are the plasma fractal and the more dramatic fault fractal . Many specific techniques have been researched and developed to produce highly focused computer-generated effects — e.g., the use of specific models to represent
3996-474: The music. In 2015, Whitehead, Thomley's studio Headcannon, and PagodaWest Games collaborated on an original Sonic game using the Retro Engine titled Sonic Mania , which released August 2017, with DLC titled Sonic Mania Plus being released in July 2018. In January 2021, an open-source decompilation of the Retro Engine versions of Sonic CD , Sonic the Hedgehog , and Sonic the Hedgehog 2 were released, allowing
4070-474: The need to pair virtual synthesis with military level training requirements, CGI technologies applied in flight simulation were often years ahead of what would have been available in commercial computing or even in high budget film. Early CGI systems could depict only objects consisting of planar polygons. Advances in algorithms and electronics in flight simulator visual systems and CGI in the 1970s and 1980s influenced many technologies still used in modern CGI adding
4144-504: The object of flight simulation was to reproduce on the ground the behavior of an aircraft in flight. Much of this reproduction had to do with believable visual synthesis that mimicked reality. The Link Digital Image Generator (DIG) by the Singer Company (Singer-Link), was considered one of the worlds first generation CGI systems. It was a real-time, 3D capable, day/dusk/night system that was used by NASA shuttles, for F-111s, Black Hawk and
4218-556: The opening credits of the film. The first feature film to make use of CGI with live action in the storyline of the film was the 1973 film Westworld . Other early films that incorporated CGI include Star Wars: Episode IV (1977), Tron (1982), Star Trek II: The Wrath of Khan (1982), Golgo 13: The Professional (1983), The Last Starfighter (1984), Young Sherlock Holmes (1985), The Abyss (1989), Terminator 2: Judgement Day (1991), Jurassic Park (1993) and Toy Story (1995). The first music video to use CGI
4292-401: The outside, or skin, of the object being rendered, it fails to capture the infinitesimally small interactions between interlocking muscle groups used in fine motor skills like speaking. The constant motion of the face as it makes sounds with shaped lips and tongue movement, along with the facial expressions that go along with speaking are difficult to replicate by hand. Motion capture can catch
4366-464: The possible relationship a building will have in relation to the environment and its surrounding buildings. The processing of architectural spaces without the use of paper and pencil tools is now a widely accepted practice with a number of computer-assisted architectural design systems. Architectural modeling tools allow an architect to visualize a space and perform "walk-throughs" in an interactive manner, thus providing "interactive environments" both at
4440-532: The procedure. Models of cloth generally fall into three groups: To date, making the clothing of a digital character automatically fold in a natural way remains a challenge for many animators. In addition to their use in film, advertising and other modes of public display, computer generated images of clothing are now routinely used by top fashion design firms. The challenge in rendering human skin images involves three levels of realism: The finest visible features such as fine wrinkles and skin pores are
4514-420: The purpose of designing characters, virtual worlds , or scenes and special effects (in films , television programs, commercials, etc.). The application of CGI for creating/improving animations is called computer animation , or CGI animation . The first feature film to use CGI as well as the composition of live-action film with CGI was Vertigo , which used abstract computer graphics by John Whitney in
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#17330846756844588-469: The same pixel. See also Portable Document Format#Layers . Computer-generated imagery Computer-generated imagery ( CGI ) is a specific-technology or application of computer graphics for creating or improving images in art , printed media , simulators , videos and video games. These images are either static (i.e. still images ) or dynamic (i.e. moving images). CGI both refers to 2D computer graphics and (more frequently) 3D computer graphics with
4662-408: The screen or page. See below for other alternative conventions which may change the sense of the rotation produced by a rotation matrix . Particularly useful are the matrices for 90° and 180° rotations: In Euclidean geometry , uniform scaling ( isotropic scaling , homogeneous dilation , homothety ) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by
4736-410: The sides of the square are not parallel to the scaling axes (the angles between lines parallel to the axes are preserved, but not all angles). A scaling can be represented by a scaling matrix. To scale an object by a vector v = ( v x , v y , v z ), each point p = ( p x , p y , p z ) would need to be multiplied with this scaling matrix : As shown below, the multiplication will give
4810-435: The size of about 100 μm or 0.1 millimetres . Skin can be modeled as a 7- dimensional bidirectional texture function (BTF) or a collection of bidirectional scattering distribution function (BSDF) over the target's surfaces. Interactive visualization is the rendering of data that may vary dynamically and allowing a user to view the data from multiple perspectives. The applications areas may vary significantly, ranging from
4884-420: The system (e.g. by using joystick controls to change their position within the virtual world) the raw data is fed through the pipeline to create a new rendered image, often making real-time computational efficiency a key consideration in such applications. While computer-generated images of landscapes may be static, computer animation only applies to dynamic images that resemble a movie. However, in general,
4958-532: The term computer animation refers to dynamic images that do not allow user interaction, and the term virtual world is used for the interactive animated environments. Computer animation is essentially a digital successor to the art of stop motion animation of 3D models and frame-by-frame animation of 2D illustrations. Computer generated animations are more controllable than other more physically based processes, such as constructing miniatures for effects shots or hiring extras for crowd scenes, and because it allows
5032-409: The two-dimensional image is not just a representation of a real-world object, but an independent artifact with added semantic value; two-dimensional models are therefore preferred, because they give more direct control of the image than 3D computer graphics (whose approach is more akin to photography than to typography). In many domains, such as desktop publishing , engineering , and business ,
5106-578: The urban and building levels. Specific applications in architecture not only include the specification of building structures (such as walls and windows) and walk-throughs but the effects of light and how sunlight will affect a specific design at different times of the day. Architectural modeling tools have now become increasingly internet-based. However, the quality of internet-based systems still lags behind sophisticated in-house modeling systems. In some applications, computer-generated images are used to "reverse engineer" historical buildings. For instance,
5180-585: The use of avatars . Virtual worlds are intended for its users to inhabit and interact, and the term today has become largely synonymous with interactive 3D virtual environments, where the users take the form of avatars visible to others graphically. These avatars are usually depicted as textual, two-dimensional, or three-dimensional graphical representations, although other forms are possible (auditory and touch sensations for example). Some, but not all, virtual worlds allow for multiple users. Computer-generated imagery has been used in courtrooms, primarily since
5254-743: The virtual canvas. Conceptually, each layer is first rendered on its own, yielding a digital image with the desired resolution which is then painted over the canvas, pixel by pixel. Fully transparent parts of a layer need not be rendered, of course. The rendering and painting may be done in parallel, i.e., each layer pixel may be painted on the canvas as soon as it is produced by the rendering procedure. Layers that consist of complex geometric objects (such as text or polylines ) may be broken down into simpler elements ( characters or line segments , respectively), which are then painted as separate layers, in some order. However, this solution may create undesirable aliasing artifacts wherever two elements overlap
5328-403: The visualization of the flow patterns in fluid dynamics to specific computer aided design applications. The data rendered may correspond to specific visual scenes that change as the user interacts with the system — e.g. simulators, such as flight simulators , make extensive use of CGI techniques for representing the world. At the abstract level, an interactive visualization process involves
5402-452: The zero vector (i.e., on the coordinates of the origin), rotation matrices can only be used to describe rotations about the origin of the coordinate system. Rotation matrices provide a simple algebraic description of such rotations, and are used extensively for computations in geometry , physics , and computer graphics . In 2-dimensional space, a rotation can be simply described by an angle θ of rotation , but it can be also represented by
5476-495: Was Will Powers ' Adventures in Success (1983). Prior to CGI being prevalent in film, virtual reality, personal computing and gaming, one of the early practical applications of CGI was for aviation and military training, namely the flight simulator . Visual systems developed in flight simulators were also an important precursor to three dimensional computer graphics and Computer Generated Imagery (CGI) systems today. Namely because
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