Digital intermediate (DI) is a motion picture finishing process which classically involves digitizing a motion picture and manipulating the color and other image characteristics. == Definition and overview == A digital intermediate often replaces or augments the photochemical timing process and is usually the final creative adjustment to a movie before distribution in theaters. It is distinguished from the telecine process in which film is scanned and color is manipulated early in the process to facilitate editing. However the lines between telecine and DI are continually blurred and are often executed on the same hardware by colorists of the same background. These two steps are typically part of the overall color management process in a motion picture at different points in time. A digital intermediate is also customarily done at higher resolution and with greater color fidelity than telecine transfers. Although originally used to describe a process that started with film scanning and ended with film recording, digital intermediate is also used to describe color correction and color grading and even final mastering when a digital camera is used as the image source and/or when the final movie is not output to film. This is due to recent advances in digital cinematography and digital projection technologies that strive to match film origination and film projection. In traditional photochemical film finishing, an intermediate is produced by exposing film to the original camera negative. The intermediate is then used to mass-produce the films that get distributed to theaters. Color grading is done by varying the amount of red, green, and blue light used to expose the intermediate. The digital intermediate process uses digital tools to color grade, which allows for much finer control of individual colors and areas of the image, and allows for the adjustment of image structure (grain, sharpness, etc.). The intermediate for film reproduction can then be produced by means of a film recorder. The physical intermediate film that is a result of the recording process is sometimes also called a digital intermediate, and is usually recorded to internegative (IN) stock, which is inherently finer-grain than original camera negative (OCN). One of the key technical achievements that made the transition to DI possible was the use of 3D look-up tables, which could be used to mimic how the digital image would look once it was printed onto release print stock. This removed a large amount of guesswork from the film-making process, and allowed greater freedom in the colour grading process while reducing risk. The digital master is often used as a source for a DCI-compliant distribution of the motion picture for digital projection. For archival purposes, the digital master created during the digital intermediate process can be recorded to very stable high dynamic range yellow-cyan-magenta (YCM) separations on black-and-white film with an expected 100-year or longer life. While still subject to the natural degradation of any analog chemical master, this archival format, long used in the industry prior to the invention of DI, was considered valuable for providing an archival medium that is independent of changes in digital data recording technologies and file formats that might otherwise render digitally archived material unreadable in the long term. A "film intermediate" is an analog variation of a digital intermediate, where a project shot on digital video is printed onto film stock and transferred back to digital video to emulate film. The term was coined after it was used on the Oscar-winning 2012 short film "Curfew". The process was also used on the films Dune (2021) and The Batman (2022). == History == Telecine tools to electronically capture film images are nearly as old as broadcast television, but the resulting images were widely considered unsuitable for exposing back onto film for theatrical distribution. Film scanners and recorders with quality sufficient to produce images that could be inter-cut with regular film began appearing in the 1970s, with significant improvements in the late 1980s and early 1990s. During this time, digitally processing an entire feature-length film was impractical because the scanners and recorders were extremely slow and the image files were too large compared to computing power available. Instead, individual shots or short sequences were processed for visual effects. In 1992, Visual Effects Supervisor/Producer Chris F. Woods broke through several "techno-barriers" in creating a digital studio to produce the visual effects for the 1993 release Super Mario Bros. It was the first feature film project to digitally scan a large number of VFX plates (over 700) at 2K resolution. It was also the first film scanned and recorded at Kodak's just launched Cinesite facility in Hollywood. This project based studio was the first feature film to use Discreet Logic's (now Autodesk) Flame and Inferno systems, which enjoyed early dominance as high resolution / high performance digital compositing systems. Digital film compositing for visual effects was immediately embraced, while optical printer use for VFX declined just as quickly. Chris Watts further revolutionized the process on the 1998 feature film Pleasantville, becoming the first visual effects supervisor for New Line Cinema to scan, process, and record the majority of a feature-length, live-action, Hollywood film digitally. The first Hollywood film to utilize a digital intermediate process from beginning to end was O Brother, Where Art Thou? in 2000 and in Europe it was Chicken Run released that same year. The process rapidly caught on in the mid-2000s. Around 50% of Hollywood films went through a digital intermediate in 2005, increasing to around 70% by mid-2007. This is due not only to the extra creative options the process affords film makers but also the need for high-quality scanning and color adjustments to produce movies for digital cinema. == Milestones == 1990: The Rescuers Down Under – First feature-length film to be entirely recorded to film from digital files; in this case animation assembled on computers using Walt Disney Feature Animation and Pixar's CAPS system. 1992: Visual effects supervisor and producer Chris F. Woods creates a VFX studio to produce the visual effects for the 1993 film Super Mario Bros. It was the first 35mm feature film to digitally scan a large number of VFX plates (over 700) at 2K resolution, as well as to output the finished VFX to 35mm negative at 2K. 1993: Snow White and the Seven Dwarfs – First film to be entirely scanned to digital files, manipulated, and recorded back to film at 4K resolution. The restoration project was done entirely at 4K resolution and 10-bit color depth using the Cineon system to digitally remove dirt and scratches and restore faded colors. 1998: Pleasantville – The first time the majority of a new feature film was scanned, processed, and recorded digitally. The black-and-white meets color world portrayed in the movie was filmed entirely in color and selectively desaturated and contrast adjusted digitally. The work was done in Los Angeles by Cinesite utilizing a Spirit DataCine for scanning at 2K resolution and a MegaDef color correction system from UK Company Pandora International 1998: Zingo - The first feature film to use digital color correction via digital intermediate in its entirety. The work was performed at the Digital Film Lab in Copenhagen, using a Spirit Datacine to transfer the entire film to digital files at 2K resolution. The digital intermediate process was also used to perform a digital blowup of the film's original Super 16 source format to a 35mm output. 1999: Pacific Ocean Post Film, a team led by John McCunn and Greg Kimble used Kodak film scanners & laser film printer, Cineon software as well as proprietary tools to rebuild and repair the first two reels of the 1968 Beatles' film Yellow Submarine for re-release. 1999: Star Wars: Episode I – The Phantom Menace - Industrial Light & Magic (ILM) scanned the entirety of the visual effects-laden film for the purposes of digital enhancement and the integration of thousands of separately filmed elements with computer generated characters and environments. Outside of the approximately 2000 effects shots that were digitally manipulated, the remaining 170 non-effects shots were also scanned for continuity. However, after the digital shots were manipulated at ILM, they were filmed out individually and sent to Deluxe Labs where they were processed and color timed photochemically. 2000: Sorted - The first feature-length, color 35mm motion picture to fully utilize the digital intermediate process in its entirety from inception to completion. The film was produced at Wave Pictures' digital intermediate film facility in London, England. It was scanned at 2K resolution with 8 bits color depth per color / per pixel using a pin registered, liquid gate Oxberry
Python (programming language)
Python is a high-level, general-purpose programming language that emphasizes code readability, simplicity, and ease-of-writing with the use of significant indentation, "plain English" naming, an extensive ("batteries-included") standard library, and garbage collection. Python supports multiple programming paradigms but with an emphasis on object-oriented programming and dynamic typing. Guido van Rossum began working on Python in the late 1980s as a successor to the ABC programming language. Python 3.0, released in 2008, was a major revision and not completely backward-compatible with earlier versions. Beginning with Python 3.5, capabilities and keywords for typing were added to the language, allowing optional static typing. As of 2026, the Python Software Foundation supports Python 3.10, 3.11, 3.12, 3.13, and 3.14, following the project's annual release cycle and five-year support policy. Python 3.15 is currently in the alpha development phase, and the stable release is expected to launch in October 2026. Earlier versions in the 3.x series have reached end-of-life and no longer receive security updates. Python has gained extensive use in the machine learning community. It is widely taught as an introductory programming language. Since 2003, Python has consistently ranked among the top ten most popular programming languages in the TIOBE Programming Community Index, which ranks programming languages based on searches across 24 platforms. == History == Python was conceived in the late 1980s by Guido van Rossum at Centrum Wiskunde & Informatica (CWI) in the Netherlands. It was designed as a successor to the ABC programming language, which was inspired by SETL, capable of exception handling and interfacing with the Amoeba operating system. Python implementation began in December 1989. Van Rossum first released it in 1991 as Python 0.9.0. Van Rossum assumed sole responsibility for the project, as the lead developer, until 12 July 2018, when he announced his "permanent vacation" from responsibilities as Python's "benevolent dictator for life" (BDFL); this title was bestowed on him by the Python community to reflect his long-term commitment as the project's chief decision-maker. (He has since come out of retirement and is self-titled "BDFL-emeritus".) In January 2019, active Python core developers elected a five-member Steering Council to lead the project. The name Python derives from the British comedy series Monty Python's Flying Circus. (See § Naming.) Python 2.0 was released on 16 October 2000, featuring many new features such as list comprehensions, cycle-detecting garbage collection, reference counting, and Unicode support. Python 2.7's end-of-life was initially set for 2015, and then postponed to 2020 out of concern that a large body of existing code could not easily be forward-ported to Python 3. It no longer receives security patches or updates. While Python 2.7 and older versions are officially unsupported, a different unofficial Python implementation, PyPy, continues to support Python 2, i.e., "2.7.18+" (plus 3.11), with the plus signifying (at least some) "backported security updates". Python 3.0 was released on 3 December 2008, and was a major revision and not completely backward-compatible with earlier versions, with some new semantics and changed syntax. Python 2.7.18, released in 2020, was the last release of Python 2. Several releases in the Python 3.x series have added new syntax to the language, and made a few (considered very minor) backward-incompatible changes. As of May 2026, Python 3.14.5 is the latest stable release. All older 3.x versions had a security update down to Python 3.9.24 then again with 3.9.25, the final version in 3.9 series. Python 3.10 is, since November 2025, the oldest supported branch. Python 3.15 has an alpha released, and Android has an official downloadable executable available for Python 3.14. Releases receive two years of full support followed by three years of security support. == Design philosophy and features == Python is a multi-paradigm programming language. Object-oriented programming and structured programming are fully supported, and many of their features support functional programming and aspect-oriented programming – including metaprogramming and metaobjects. Many other paradigms are supported via extensions, including design by contract and logic programming. Python is often referred to as a 'glue language' because it is purposely designed to be able to integrate components written in other languages. Python uses dynamic typing and a combination of reference counting and a cycle-detecting garbage collector for memory management. It uses dynamic name resolution (late binding), which binds method and variable names during program execution. Python's design offers some support for functional programming in the "Lisp tradition". It has filter, map, and reduce functions; list comprehensions, dictionaries, sets, and generator expressions. The standard library has two modules (itertools and functools) that implement functional tools borrowed from Haskell and Standard ML. Python's core philosophy is summarized in the Zen of Python (PEP 20) written by Tim Peters, which includes aphorisms such as these: Explicit is better than implicit. Simple is better than complex. Readability counts. Special cases aren't special enough to break the rules. Although practicality beats purity, errors should never pass silently, unless explicitly silenced. There should be one-- and preferably only one --obvious way to do it. However, Python has received criticism for violating these principles and adding unnecessary language bloat. Responses to these criticisms note that the Zen of Python is a guideline rather than a rule. The addition of some new features had been controversial: Guido van Rossum resigned as Benevolent Dictator for Life after conflict about adding the assignment expression operator in Python 3.8. Nevertheless, rather than building all functionality into its core, Python was designed to be highly extensible through modules. This compact modularity has made it particularly popular as a means of adding programmable interfaces to existing applications. Van Rossum's vision of a small core language with a large standard library and an easily extensible interpreter stemmed from his frustrations with ABC, which represented the opposite approach. Python claims to strive for a simpler, less-cluttered syntax and grammar, while giving developers a choice in their coding methodology. Python lacks do .. while loops, which Rossum considered harmful. In contrast to Perl's motto "there is more than one way to do it", Python advocates an approach where "there should be one – and preferably only one – obvious way to do it". In practice, however, Python provides many ways to achieve a given goal. There are at least three ways to format a string literal, with no certainty as to which one a programmer should use. Alex Martelli is a Fellow at the Python Software Foundation and Python book author; he wrote that "To describe something as 'clever' is not considered a compliment in the Python culture." Python's developers typically prioritize readability over performance. For example, they reject patches to non-critical parts of the CPython reference implementation that would offer increases in speed that do not justify the cost of clarity and readability. Execution speed can be improved by moving speed-critical functions to extension modules written in languages such as C, or by using a just-in-time compiler like PyPy. Also, it is possible to transpile to other languages. However, this approach either fails to achieve the expected speed-up, since Python is a very dynamic language, or only a restricted subset of Python is compiled (with potential minor semantic changes). Python is meant to be a fun language to use. This goal is reflected in the name – a tribute to the British comedy group Monty Python – and in playful approaches to some tutorials and reference materials. For instance, some code examples use the terms "spam" and "eggs" (in reference to a Monty Python sketch), rather than the typical terms "foo" and "bar". A common neologism in the Python community is pythonic, which has a broad range of meanings related to program style: Pythonic code may use Python idioms well; be natural or show fluency in the language; or conform with Python's minimalist philosophy and emphasis on readability. === Enhancement Proposals === Python Enhancement Proposals are a design document for either providing information to the Python community, or proposal for new feature in Python. PEPs are intented to explain new processes in Python, provide naming conventions or document the processes in the language. PEPs are overseen by Python Steering Council. There are 3 kinds of PEPs, with those are being standards track PEP, Informational PEP and Process PEPs which has their own unique meanings. They were firstly introduced in 2000, in
Swizzling (computer graphics)
In computer graphics, swizzles are a class of operations that transform vectors by rearranging components. Swizzles can also project from a vector of one dimensionality to a vector of another dimensionality, such as taking a three-dimensional vector and creating a two-dimensional or five-dimensional vector using components from the original vector. For example, if A = {1,2,3,4}, where the components are x, y, z, and w respectively, one could compute B = A.wwxy, whereupon B would equal {4,4,1,2}. Additionally, one could create a two-dimensional vector with A.wx or a five-dimensional vector with A.xyzwx. Combining vectors and swizzling can be employed in various ways. This is common in GPGPU applications. In terms of linear algebra, this is equivalent to multiplying by a matrix whose rows are standard basis vectors. If A = ( 1 , 2 , 3 , 4 ) T {\displaystyle A=(1,2,3,4)^{T}} , then swizzling A {\displaystyle A} as above looks like A . w w x y = [ 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 ] [ 1 2 3 4 ] = [ 4 4 1 2 ] . {\displaystyle A.\!wwxy={\begin{bmatrix}0&0&0&1\\0&0&0&1\\1&0&0&0\\0&1&0&0\end{bmatrix}}{\begin{bmatrix}1\\2\\3\\4\end{bmatrix}}={\begin{bmatrix}4\\4\\1\\2\end{bmatrix}}.}
MY F.C.
MY F.C. is a freemium app designed to organise and administer football teams. It is developed by MY F.C. Limited, a private company headquartered in Auckland, New Zealand. The app allows users to build a team by adding players and from there they can create trainings and matches, keep up with relevant news in the curated newsfeed, record statistics both individually and team based, follow the games live in the match-centre. The app also features integrated lineup builder with custom team kits. == History == Founders Sam Jenkins, Mike Simpson and Sam Jasper started MY F.C. in 2015 to help them "run their football lives". The app was launched on Android and iOS on 14 February 2017. == Accolades == MY F.C. won the first place prize at Bank of New Zealand Start-up Alley 2017 competition that aims to discover New Zealand start-ups who are doing innovative work and ready to establish themselves as long-term, sustainable businesses. The prize package included $15,000 and a trip to San Francisco.
Triller (app)
Triller is an American video-sharing social networking service that was first released for iOS and Android in 2015. The service allowed users to create and share short-form videos, including videos set to, or automatically synchronized to, music using artificial intelligence technology. It initially operated as a video editing app before adding social networking features. Triller gained prominence in 2020 as a competitor to the similar Chinese-owned app TikTok, mainly in the United States and India (after the service was banned in the latter country). The app's success would allow its parent company to expand into sports broadcasting and promotion; including the distribution of pay-per-view boxing events under the Triller Fight Club banner (such as Mike Tyson vs. Roy Jones Jr. and Jake Paul vs. Ben Askren) that incorporated live music performances and appearances by various celebrities and entertainment personalities. == History == === Launch and early years === Triller was launched in 2015 by co-founders David Leiberman and Sammy Rubin. The app was originally positioned as a video editor, using artificial intelligence to automatically edit distinct clips into music videos. They later launched Triller Famous, a page within the app that featured curated selections of user videos. In 2016, the app was purchased by Carnegie Technologies and converted into a social networking service by allowing users to follow each other and share their videos publicly. In 2019, Ryan Kavanaugh's Proxima Media made a majority investment. It is headquartered in Los Angeles, California, and is currently led by CEO Mahi de Silva. === Media exposure and controversies === On June 29, 2020, Government of India banned TikTok, among other apps stating that they were "prejudicial to [the] sovereignty and integrity" of India. Triller, which had planned to enter into the Indian market by the end of 2020, saw a spike from less than 1 million users to over 30 million users in the country overnight. In July 2020, Triller sued ByteDance, the Chinese parent company of TikTok, for infringing patents relating to video editing. In response, TikTok and ByteDance filed a lawsuit against Triller, alleging the litigation initiated by Triller has "cast a cloud" over TikTok's reputation and business dealings. That Summer, U.S. president Donald Trump signed an executive order which threatened to ban TikTok from operating within the United States, citing threats to national security, unless it was sold by ByteDance. The Trump administration stated that TikTok had until November 12, 2020, to assure the administration that the app did not pose any national security threats to the U.S. Following this order and news of possible purchases of TikTok's American operations by companies such as Oracle, Triller jumped from number 198 to number one in the App Store in the U.S., while TikTok dropped down to number three. The discussions surrounding TikTok's potential ban in the United States caused popular TikTok stars, including Charli D’Amelio and her family, to join Triller. Trump joined Triller himself and posted his first video on August 15, 2020. The video received over a million views within hours. On August 12, 2020, Triller partnered with B2B music company 7digital, which will provide Triller with access to its catalogue of 80 million tracks and automatically report usage data to Sony Music, Warner Music Group, Universal Music Group and Merlin Network. The number of Triller's app installations came under scrutiny when third-party analytics firm Apptopia estimated only 52 million lifetime installations of the app by August 2020, while Triller claimed 250 million. Triller threatened to sue Apptopia for publishing the report. By October 2020, Triller claimed to serve 100 million active monthly users, but this number was quickly disputed by six former employees interviewed by Business Insider. Within a few weeks of Triller's claim, employees shared screenshots of the company's internal analytics that showed less than 2.5 million active monthly users. On October 2, 2020, Triller signed licensing deals with the rights societies PRS for Music, GEMA, STIM and IMRO, and the publishers Concord, Downtown and Peermusic. On February 5, 2021, Universal Music Group (UMG) pulled its library from Triller, citing unpaid music royalties. They alleged that Triller "shamefully withheld payments owed to our artists" and refused to negotiate future music licensing. Triller responded with the assertion that "relevant artists" were already partnered with Triller, so a deal with UMG was unnecessary. The two companies reached an expanded licensing agreement in May 2021. On March 24, 2021, Triller signed a licensing agreement with the National Music Publishers' Association. == Features == The Triller app allows users to create music videos, skits, and lip-sync videos containing background music. The app's spotlight feature is its special auto-editing tool, which uses artificial intelligence to automatically stitch separate video clips together without the user having to do it themselves. The separate video clips are created to the same background music, but users are able to shoot multiple takes with different filters or edits each time. Once the auto-editing tool stitches the individual clips together, users can rearrange and replace clips as desired. Users can also customize videos by applying filters and text. When creating a video, users can choose to make a "music video" or a "social video". A "music video" allows users to add music and trim the audio to personal preference. Unlike the music video option, a "social video" does not require the user to add music in the background. The app's auto-editing tool is only used when making music videos, as it uses the background track to help arrange and synchronize the clips. Users can also link their accounts with Apple Music or Spotify to integrate their playlists. Incomplete videos that are yet to be shared appear in a user's "Projects" folder. Once finalized, a video can be shared with other users of the app or through social media platforms such as Facebook, Instagram, Twitter (X), WhatsApp, and YouTube. Any video on Triller can also be downloaded or shared through links, text messages, or direct messaging to other users within the app. The app is divided into three video feeds, consisting of videos from creators that the user follows, the "Social" feed (which showcases trending videos and those by verified users), and the "Music" feed (which exclusively features music videos). Triller accounts can be made either public or private. When the account is public, any user can view the videos on that account. When the account is private, only approved users can view the videos on that account. Users with private accounts can change the privacy settings of individual videos on their accounts from private to public, making the selected videos viewable to anyone on the app. In accordance with online child privacy laws in the United States, children under the age of 13 must receive parental consent in order to create an account on Triller. == User characteristics and behavior == In August 2020, Triller reported that it had been downloaded over 250 million times worldwide with average rating of 4.00. Mobile analytics firm Apptopia disputed the numbers and claimed they were inflated, suggesting that the app had only been downloaded 52 million times since it first launched in 2015. Apptopia pulled the report after Triller threatened to sue the company. The app has been downloaded 23.8 million times in the U.S., with users spending an average of more than 20 minutes per day. A large number of downloads come from India, where TikTok has been banned, as well as from various European and African countries. In October 2020, Triller CEO Mike Lu stated that the app has 100 million monthly active users (MAU). In February 2021, Billboard reported that Triller had "reported higher numbers of monthly active users to the public than it reports to [music] rights holders." CEO Lu argued that "there is no legal definition" of monthly and daily active users, and that "if someone is trying to compare TikTok's MAU/DAU to ours—which means they are saying we have the same definition of MAU/DAU—there is an inherent misunderstanding about Triller's business and business model. It’s like trying to compare a fish and a bicycle." In a public statement, Lu denied that the company had inflated its user metrics. Triller has attracted celebrity users like Chance the Rapper, King Von, LIl Tecca, Lil Mosey, Justin Bieber, Marshmello, The Weeknd, Alicia Keys, Cardi B, Eminem, Post Malone and Kevin Hart. The app is also used by TikTok stars such as Charli D’Amelio, Josh Richards, Noah Beck, Griffin Johnson, and Dixie D’Amelio. Triller has offered large sums of money, company equity, and advisory roles to encourage prominent TikTok users to move to Triller, such as The Sway Boys. Sway House member J
Multisample anti-aliasing
Multisample anti-aliasing (MSAA) is a type of spatial anti-aliasing, a technique used in computer graphics to remove jaggies. It is an optimization of supersampling, where only the necessary parts are sampled more. Jaggies are only noticed in a small area, so the area is quickly found, and only that is anti-aliased. == Definition == The term generally refers to a special case of supersampling. Initial implementations of full-scene anti-aliasing (FSAA) worked conceptually by simply rendering a scene at a higher resolution, and then downsampling to a lower-resolution output. Most modern GPUs are capable of this form of anti-aliasing, but it greatly taxes resources such as texture, bandwidth, and fillrate. (If a program is highly TCL-bound or CPU-bound, supersampling can be used without much performance hit.) According to the OpenGL GL_ARB_multisample specification, "multisampling" refers to a specific optimization of supersampling. The specification dictates that the renderer evaluate the fragment program once per pixel, and only "truly" supersample the depth and stencil values. (This is not the same as supersampling but, by the OpenGL 1.5 specification, the definition had been updated to include fully supersampling implementations as well.) In graphics literature in general, "multisampling" refers to any special case of supersampling where some components of the final image are not fully supersampled. The lists below refer specifically to the ARB_multisample definition. == Description == In supersample anti-aliasing, multiple locations are sampled within every pixel, and each of those samples is fully rendered and combined with the others to produce the pixel that is ultimately displayed. This is computationally expensive, because the entire rendering process must be repeated for each sample location. It is also inefficient, as aliasing is typically only noticed in some parts of the image, such as the edges, whereas supersampling is performed for every single pixel. In multisample anti-aliasing, if any of the multi sample locations in a pixel is covered by the triangle being rendered, a shading computation must be performed for that triangle. However this calculation only needs to be performed once for the whole pixel regardless of how many sample positions are covered; the result of the shading calculation is simply applied to all of the relevant multi sample locations. In the case where only one triangle covers every multi sample location within the pixel, only one shading computation is performed, and these pixels are little more expensive than (and the result is no different from) the non-anti-aliased image. This is true of the middle of triangles, where aliasing is not an issue. (Edge detection can reduce this further by explicitly limiting the MSAA calculation to pixels whose samples involve multiple triangles, or triangles at multiple depths.) In the extreme case where each of the multi sample locations is covered by a different triangle, a different shading computation will be performed for each location and the results then combined to give the final pixel, and the result and computational expense are the same as in the equivalent supersampled image. The shading calculation is not the only operation that must be performed on a given pixel; multisampling implementations may variously sample other operations such as visibility at different sampling levels. == Advantages == The pixel shader usually only needs to be evaluated once per pixel for every triangle covering at least one sample point. The edges of polygons (the most obvious source of aliasing in 3D graphics) are anti-aliased. Since multiple subpixels per pixel are sampled, polygonal details smaller than one pixel that might have been missed without MSAA can be captured and made a part of the final rendered image if enough samples are taken. == Disadvantages == === Alpha testing === Alpha testing is a technique common to older video games used to render translucent objects by rejecting pixels from being written to the framebuffer. If the alpha value of a translucent fragment (pixel) is below a specified threshold, it will be discarded. Because this is performed on a pixel by pixel basis, the image does not receive the benefits of multi-sampling (all of the multisamples in a pixel are discarded based on the alpha test) for these pixels. The resulting image may contain aliasing along the edges of transparent objects or edges within textures, although the image quality will be no worse than it would be without any anti-aliasing. Translucent objects that are modelled using alpha-test textures will also be aliased due to alpha testing. This effect can be minimized by rendering objects with transparent textures multiple times, although this would result in a high performance reduction for scenes containing many transparent objects. === Aliasing === Because multi-sampling calculates interior polygon fragments only once per pixel, aliasing and other artifacts will still be visible inside rendered polygons where fragment shader output contains high frequency components. === Performance === While less performance-intensive than SSAA (supersampling), it is possible in certain scenarios (scenes heavy in complex fragments) for MSAA to be multiple times more intensive for a given frame than post processing anti-aliasing techniques such as FXAA, SMAA and MLAA. Early techniques in this category tend towards a lower performance impact, but suffer from accuracy problems. More recent post-processing based anti-aliasing techniques such as temporal anti-aliasing (TAA), which reduces aliasing by combining data from previously rendered frames, have seen the reversal of this trend, as post-processing AA becomes both more versatile and more expensive than MSAA, which cannot antialias an entire frame alone. == Sampling methods == === Point sampling === In a point-sampled mask, the coverage bit for each multisample is only set if the multisample is located inside the rendered primitive. Samples are never taken from outside a rendered primitive, so images produced using point-sampling will be geometrically correct, but filtering quality may be low because the proportion of bits set in the pixel's coverage mask may not be equal to the proportion of the pixel that is actually covered by the fragment in question. === Area sampling === Filtering quality can be improved by using area sampled masks. In this method, the number of bits set in a coverage mask for a pixel should be proportionate to the actual area coverage of the fragment. This will result in some coverage bits being set for multisamples that are not actually located within the rendered primitive, and can cause aliasing and other artifacts. == Sample patterns == === Regular grid === A regular grid sample pattern, where multisample locations form an evenly spaced grid throughout the pixel, is easy to implement and simplifies attribute evaluation (i.e. setting subpixel masks, sampling color and depth). This method is computationally expensive due to the large number of samples. Edge optimization is poor for screen-aligned edges, but image quality is good when the number of multisamples is large. === Sparse regular grid === A sparse regular grid sample pattern is a subset of samples that are chosen from the regular grid sample pattern. As with the regular grid, attribute evaluation is simplified due to regular spacing. The method is less computationally expensive due to having a fewer samples. Edge optimization is good for screen aligned edges, and image quality is good for a moderate number of multisamples. === Stochastic sample patterns === A stochastic sample pattern is a random distribution of multisamples throughout the pixel. The irregular spacing of samples makes attribute evaluation complicated. The method is cost efficient due to low sample count (compared to regular grid patterns). Edge optimization with this method, although sub-optimal for screen aligned edges. Image quality is excellent for a moderate number of samples. == Quality == Compared to supersampling, multisample anti-aliasing can provide similar quality at higher performance, or better quality for the same performance. Further improved results can be achieved by using rotated grid subpixel masks. The additional bandwidth required by multi-sampling is reasonably low if Z and colour compression are available. Most modern GPUs support 2×, 4×, and 8× MSAA samples. Higher values result in better quality, but are slower.
Kinematic chain
In mechanical engineering, a kinematic chain is an assembly of rigid bodies connected by joints to provide constrained motion that is the mathematical model for a mechanical system. As the word chain suggests, the rigid bodies, or links, are constrained by their connections to other links. An example is the simple open chain formed by links connected in series, like the usual chain, which is the kinematic model for a typical robot manipulator. Mathematical models of the connections, or joints, between two links are termed kinematic pairs. Kinematic pairs model the hinged and sliding joints fundamental to robotics, often called lower pairs and the surface contact joints critical to cams and gearing, called higher pairs. These joints are generally modeled as holonomic constraints. A kinematic diagram is a schematic of the mechanical system that shows the kinematic chain. The modern use of kinematic chains includes analysis of Linkages (mechanical), compliance that arises from flexure joints in precision mechanisms, link compliance in compliant mechanisms and micro-electro-mechanical systems, and cable compliance in cable robotic and tensegrity systems. == Mobility formula == The degrees of freedom, or mobility, of a kinematic chain is the number of parameters that define the configuration of the chain. A system of n rigid bodies moving in space has 6n degrees of freedom measured relative to a fixed frame. This frame is included in the count of bodies, so that mobility does not depend on link that forms the fixed frame. This means the degree-of-freedom of this system is M = 6(N − 1), where N = n + 1 is the number of moving bodies plus the fixed body. Joints that connect bodies impose constraints. Specifically, hinges and sliders each impose five constraints and therefore remove five degrees of freedom. It is convenient to define the number of constraints c that a joint imposes in terms of the joint's freedom f, where c = 6 − f. In the case of a hinge or slider, which are one-degree-of-freedom joints, have f = 1 and therefore c = 6 − 1 = 5. The result in general where d {\displaystyle d} is the degrees of freedom for the mobility of a kinematic chain formed from n moving links and j joints each with freedom fi, i = 1, 2, …, j, is given by M = d n − ∑ i = 1 j ( d − f i ) = d ( N − 1 − j ) + ∑ i = 1 j f i {\displaystyle M=dn-\sum _{i=1}^{j}(d-f_{i})=d(N-1-j)+\sum _{i=1}^{j}f_{i}} Where N is the total number of links and includes the fixed link. Spacial linkages used d = 6 {\displaystyle d=6} and planar linkages use d = 3 {\displaystyle d=3} . This result is known as the Chebychev–Grübler–Kutzbach criterion. == Analysis of kinematic chains == The constraint equations of a kinematic chain couple the range of movement allowed at each joint to the dimensions of the links in the chain, and form algebraic equations that are solved to determine the configuration of the chain associated with specific values of input parameters, called degrees of freedom. The constraint equations for a kinematic chain are obtained using rigid transformations [Z] to characterize the relative movement allowed at each joint and separate rigid transformations [X] to define the dimensions of each link. In the case of a serial open chain, the result is a sequence of rigid transformations alternating joint and link transformations from the base of the chain to its end link, which is equated to the specified position for the end link. A chain of n links connected in series has the kinematic equations, [ T ] = [ Z 1 ] [ X 1 ] [ Z 2 ] [ X 2 ] ⋯ [ X n − 1 ] [ Z n ] , {\displaystyle [T]=[Z_{1}][X_{1}][Z_{2}][X_{2}]\cdots [X_{n-1}][Z_{n}],\!} where [T] is the transformation locating the end-link—notice that the chain includes a "zeroth" link consisting of the ground frame to which it is attached. These equations are called the forward kinematics equations of the serial chain. Kinematic chains of a wide range of complexity are analyzed by equating the kinematics equations of serial chains that form loops within the kinematic chain. These equations are often called loop equations. The complexity (in terms of calculating the forward and inverse kinematics) of the chain is determined by the following factors: Its topology: a serial chain, a parallel manipulator, a tree structure, or a graph. Its geometrical form: how are neighbouring joints spatially connected to each other? Explanation Two or more rigid bodies in space are collectively called a rigid body system. We can hinder the motion of these independent rigid bodies with kinematic constraints. Kinematic constraints are constraints between rigid bodies that result in the decrease of the degrees of freedom of rigid body system. == Synthesis of kinematic chains == The constraint equations of a kinematic chain can be used in reverse to determine the dimensions of the links from a specification of the desired movement of the system. This is termed kinematic synthesis. Perhaps the most developed formulation of kinematic synthesis is for four-bar linkages, which is known as Burmester theory. Ferdinand Freudenstein is often called the father of modern kinematics for his contributions to the kinematic synthesis of linkages beginning in the 1950s. His use of the newly developed computer to solve Freudenstein's equation became the prototype of computer-aided design systems. This work has been generalized to the synthesis of spherical and spatial mechanisms.