The Internet (or internet) is the global system of interconnected computer networks that uses the Internet protocol suite (TCP/IP) to communicate between networks and devices. It is a network of networks that comprises private, public, academic, business, and government networks of local to global scope, linked by electronic, wireless, and optical networking technologies. The Internet carries a vast range of information services and resources, such as the interlinked hypertext documents and applications of the World Wide Web (WWW), electronic mail, discussion groups, internet telephony, streaming media and file sharing. Most traditional communication media, including telephone, radio, television, paper mail, newspapers, and print publishing, have been transformed by the Internet, giving rise to new media such as email, online music, digital newspapers, news aggregators, and audio and video streaming websites. The Internet has enabled and accelerated new forms of personal interaction through instant messaging, Internet forums, and social networking services. Online shopping has also grown to occupy a significant market across industries, enabling firms to extend brick and mortar presences to serve larger markets. Business-to-business and financial services on the Internet affect supply chains across entire industries. The origins of the Internet date back to research that enabled the time-sharing of computer resources, the development of packet switching, and the design of computer networks for data communication. The set of communication protocols to enable internetworking on the Internet arose from research and development commissioned in the 1970s by the Defense Advanced Research Projects Agency (DARPA) of the United States Department of Defense in collaboration with universities and researchers across the United States, United Kingdom and France. The Internet has no single centralized governance in either technological implementation or policies for access and usage. Each constituent network sets its own policies. The overarching definitions of the two principal name spaces on the Internet, the Internet Protocol address (IP address) space and the Domain Name System (DNS), are directed by a maintainer organization, the Internet Corporation for Assigned Names and Numbers (ICANN). The technical underpinning and standardization of the core protocols is an activity of the non-profit Internet Engineering Task Force (IETF). == Terminology == The word internetted was used as early as 1849, meaning interconnected or interwoven. The word Internet was used in 1945 by the United States War Department in a radio operator's manual, and in 1974 as the shorthand form of Internetwork. Today, the term Internet most commonly refers to the global system of interconnected computer networks, though it may also refer to any group of smaller networks. The word Internet may be capitalized as a proper noun, although this is becoming less common. This reflects the tendency in English to capitalize new terms and move them to lowercase as they become familiar. The word is sometimes still capitalized to distinguish the global internet from smaller networks, though many publications, including the AP Stylebook since 2016, recommend the lowercase form in every case. In 2016, the Oxford English Dictionary found that, based on a study of around 2.5 billion printed and online sources, "Internet" was capitalized in 54% of cases. The terms Internet and World Wide Web are often used interchangeably; it is common to speak of "going on the Internet" when using a web browser to view web pages. However, the World Wide Web, or the Web, is only one of a large number of Internet services. It is the global collection of web pages, documents and other web resources linked by hyperlinks and URLs. == History == === 1960s === In the 1960s, computer scientists began developing systems for time-sharing of computer resources. J. C. R. Licklider proposed the idea of a universal network while working at Bolt Beranek & Newman and, later, leading the Information Processing Techniques Office at the Advanced Research Projects Agency (ARPA) of the United States Department of Defense. Research into packet switching, one of the fundamental Internet technologies, started in the work of Paul Baran at RAND in the early 1960s and, independently, Donald Davies at the United Kingdom's National Physical Laboratory in 1965. After the Symposium on Operating Systems Principles in 1967, packet switching from the proposed NPL network was incorporated into the design of the ARPANET, an experimental resource sharing network proposed by ARPA. ARPANET development began with two network nodes which were interconnected between the University of California, Los Angeles and the Stanford Research Institute on 29 October 1969. The third site was at the University of California, Santa Barbara, followed by the University of Utah. === 1970s === By the end of 1971, 15 sites were connected to the young ARPANET. Thereafter, the ARPANET gradually developed into a decentralized communications network, connecting remote centers and military bases in the United States. Other user networks and research networks, such as the Merit Network and CYCLADES, were developed in the late 1960s and early 1970s. Early international collaborations for the ARPANET were rare. Connections were made in 1973 to Norway (NORSAR and, later, NDRE) and to Peter Kirstein's research group at University College London, which provided a gateway to British academic networks, the first internetwork for resource sharing. ARPA projects, the International Network Working Group and commercial initiatives led to the development of various protocols and standards by which multiple separate networks could become a single network, or a network of networks. In 1974, Vint Cerf at Stanford University and Bob Kahn at DARPA published a proposal for "A Protocol for Packet Network Intercommunication". Cerf and his graduate students used the term internet as a shorthand for internetwork in RFC 675. The Internet Experiment Notes and later RFCs repeated this use. The work of Louis Pouzin and Robert Metcalfe had important influences on the resulting TCP/IP design. National PTTs and commercial providers developed the X.25 standard and deployed it on public data networks. === 1980s === The ARPANET initially served as a backbone for the interconnection of regional academic and military networks in the United States to enable resource sharing. Access to the ARPANET was expanded in 1981 when the National Science Foundation (NSF) funded the Computer Science Network (CSNET). In 1982, the Internet Protocol Suite (TCP/IP) was standardized, which facilitated worldwide proliferation of interconnected networks. TCP/IP network access expanded again in 1986 when the National Science Foundation Network (NSFNet) provided access to supercomputer sites in the United States for researchers, first at speeds of 56 kbit/s and later at 1.5 Mbit/s and 45 Mbit/s. The NSFNet expanded into academic and research organizations in Europe, Australia, New Zealand and Japan in 1988–89. Although other network protocols such as UUCP and PTT public data networks had global reach well before this time, this marked the beginning of the Internet as an intercontinental network. Commercial Internet service providers emerged in 1989 in the United States and Australia. The ARPANET was decommissioned in 1990. === 1990s === The linking of commercial networks and enterprises by the early 1990s, as well as the advent of the World Wide Web, marked the beginning of the transition to the modern Internet. Steady advances in semiconductor technology and optical networking created new economic opportunities for commercial involvement in the expansion of the network in its core and for delivering services to the public. In mid-1989, MCI Mail and Compuserve established connections to the Internet, delivering email and public access products to the half million users of the Internet. Just months later, on 1 January 1990, PSInet launched an alternate Internet backbone for commercial use; one of the networks that added to the core of the commercial Internet of later years. In March 1990, the first high-speed T1 (1.5 Mbit/s) link between the NSFNET and Europe was installed between Cornell University and CERN, allowing much more robust communications than were capable with satellites. Later in 1990, Tim Berners-Lee began writing WorldWideWeb, the first web browser, after two years of lobbying CERN management. By Christmas 1990, Berners-Lee had built all the tools necessary for a working Web: the HyperText Transfer Protocol (HTTP) 0.9, the HyperText Markup Language (HTML), the first Web browser (which was also an HTML editor and could access Usenet newsgroups and FTP files), the first HTTP server software (later known as CERN httpd), the first web server, and the first Web pages that described the project itself. In 1991 the
Augmented Analytics
Augmented Analytics is an approach of data analytics that employs the use of machine learning and natural language processing to automate analysis processes normally done by a specialist or data scientist. The term was introduced in 2017 by Rita Sallam, Cindi Howson, and Carlie Idoine in a Gartner research paper. Augmented analytics is based on business intelligence and analytics. In the graph extraction step, data from different sources are investigated. == Defining Augmented Analytics == Machine Learning – a systematic computing method that uses algorithms to sift through data to identify relationships, trends, and patterns. It is a process that allows algorithms to dynamically learn from data instead of having a set base of programmed rules. Natural language generation (NLG) – a software capability that takes unstructured data and translates it into plain-English, readable, language. Automating Insights – using machine learning algorithms to automate data analysis processes. Natural Language Query – enabling users to query data using business terms that are either typed onto a search box or spoken. == Data Democratization == Data Democratization is the democratizing data access in order to relieve data congestion and get rid of any sense of data "gatekeepers". This process must be implemented alongside a method for users to make sense of the data. This process is used in hopes of speeding up company decision making and uncovering opportunities hidden in data. There are three aspects to democratising data: Data Parameterisation and Characterisation. Data Decentralisation using an OS of blockchain and DLT technologies, as well as an independently governed secure data exchange to enable trust. Consent Market-driven Data Monetisation. When it comes to connecting assets, there are two features that will accelerate the adoption and usage of data democratisation: decentralized identity management and business data object monetization of data ownership. It enables multiple individuals and organizations to identify, authenticate, and authorize participants and organizations, enabling them to access services, data or systems across multiple networks, organizations, environments, and use cases. It empowers users and enables a personalized, self-service digital onboarding system so that users can self-authenticate without relying on a central administration function to process their information. Simultaneously, decentralized identity management ensures the user is authorized to perform actions subject to the system’s policies based on their attributes (role, department, organization, etc.) and/ or physical location. == Use cases == Agriculture – Farmers collect data on water use, soil temperature, moisture content and crop growth, augmented analytics can be used to make sense of this data and possibly identify insights that the user can then use to make business decisions. Smart Cities – Many cities across the United States, known as Smart Cities collect large amounts of data on a daily basis. Augmented analytics can be used to simplify this data in order to increase effectiveness in city management (transportation, natural disasters, etc.). Analytic Dashboards – Augmented analytics has the ability to take large data sets and create highly interactive and informative analytical dashboards that assist in many organizational decisions. Augmented Data Discovery – Using an augmented analytics process can assist organizations in automatically finding, visualizing and narrating potentially important data correlations and trends. Data Preparation – Augmented analytics platforms have the ability to take large amounts of data and organize and "clean" the data in order for it to be usable for future analyses. Business – Businesses collect large amounts of data, daily. Some examples of types of data collected in business operations include; sales data, consumer behavior data, distribution data. An augmented analytics platform provides access to analysis of this data, which could be used in making business decisions.
Load file
A load file in the litigation community is commonly referred to as the file used to import data (coded, captured or extracted data from ESI processing) into a database; or the file used to link images. These load files carry commands, commanding the software to carry out certain functions with the data found in them. Load files are usually ASCII text files that have delimited fields of information. Such load files may have data about documents to be imported into a document management software such as Concordance or Summation. Or they may have the path or directory where images may reside so that the software can link such images to their corresponding records. Some database programs take one load file for importing images and another for importing data while others take only one load file for both pieces of information. OCR or Search-able Text which is considered "data" is also imported into most database programs via the same load files. Though some people prefer to load the OCR into their databases by running a separate command to search and find the desired text. Commonly used databases and their corresponding file extensions are: Summation (DII , CSV), Concordance (OPT, DAT), Sanction (SDT), IPRO (LFP), Ringtail (MDB) and DB/TextWorks (TXT).
Local coordinates
Local coordinates are the ones used in a local coordinate system or a local coordinate space. Simple examples: Houses. In order to work in a house construction, the measurements are referred to a control arbitrary point that will allow to check it: stick/sticks on the ground, steel bar, nails... Addresses. Using house numbers to locate a house on a street; the street is a local coordinate system within a larger system composed of city townships, states, countries, postal codes, etc. Local systems exist for convenience. On ancient times, every work was made on relative bases as there was no conception of global systems. Practically, it is better to use local systems for small works as houses, buildings... For most of the applications, it is desired the position of one element relative to one building or location, and in a more local way, relative to one furniture or person. In a regular way, you will not give your position by geographical coordinates rather than "I am 15 meters away of the entry to the building". So it is a pretty common way to locate things. It is possible to bring latitude and longitude for all terrestrial locations, but unless one has a highly precise GPS device or you make astronomical observations, this is impractical. It is much simpler to use a tape, a rope, a chain... The position information (global) should be transformed into a location. Position refers to a numeric or symbolic description within a spatial reference system, whereas location refers to information about surrounding objects and their interrelationships. (Topological space) == Use == In computer graphics and computer animation, local coordinate spaces are also useful for their ability to model independently transformable aspects of geometrical scene graphs. When modeling a car, for example, it is desirable to describe the center of each wheel with respect to the car's coordinate system, but then specify the shape of each wheel in separate local spaces centered about these points. This way, the information describing each wheel can be simply duplicated four times, and independent transformations (e.g., steering rotation) can be similarly effected. Bounding volumes of objects may be described more accurately using extents in the local coordinates, (i.e. an object oriented bounding box, contrasted with the simpler axis aligned bounding box). The trade-off for this flexibility is additional computational cost: the rendering system must access the higher-level coordinate system of the car and combine it with the space of each wheel in order to draw everything in its proper place. Local coordinates also afford digital designers a means around the finite limits of numerical representation. The tread marks on a tire, for example, can be described using millimeters by allowing the whole tire to occupy the entire range of numeric precision available. The larger aspects of the car, such as its frame, might be described in centimeters, and the terrain that the car travels on could be specified in meters. In differential topology, local coordinates on a manifold are defined by means of an atlas of charts. The basic idea behind coordinate charts is that each small patch of a manifold can be endowed with a set of local coordinates. These are collected together into an atlas, and stitched together in such a way that they are self-consistent on the manifold. In Cartography and Maps, the traditional way of works are local datum. With a local datum the land can be mapped on relative small areas as a country. With the need of global systems, the transformations on between datum became a problem, so geodetic datum have been created. More than 150 local datum have been used in the world.
Visualization (graphics)
Visualization (or visualisation in Commonwealth English; see spelling differences), also known as graphics visualization, is any technique for creating images, diagrams, or animations to communicate a message. Visualization through visual imagery has been an effective way to communicate both abstract and concrete ideas since the dawn of humanity. Examples from history include cave paintings, Egyptian hieroglyphs, Greek geometry, and Leonardo da Vinci's revolutionary methods of technical drawing for engineering purposes that actively involve scientific requirements. Visualization today has ever-expanding applications in science, education, engineering (e.g., product visualization), interactive multimedia, medicine, etc. Typical of a visualization application is the field of computer graphics. The invention of computer graphics (and 3D computer graphics) may be the most important development in visualization since the invention of central perspective in the Renaissance period. The development of animation also helped advance visualization. == Overview == The use of visualization to present information is not a new phenomenon. It has been used in maps, scientific drawings, and data plots for over a thousand years. Examples from cartography include Ptolemy's Geographia (2nd century AD), a map of China (1137 AD), and Minard's map (1861) of Napoleon's invasion of Russia a century and a half ago. Most of the concepts learned in devising these images carry over in a straightforward manner to computer visualization. Edward Tufte has written three critically acclaimed books that explain many of these principles. Computer graphics has from its beginning been used to study scientific problems. However, in its early days the lack of graphics power often limited its usefulness. The recent emphasis on visualization started in 1987 with the publication of Visualization in Scientific Computing, a special issue of Computer Graphics. Since then, there have been several conferences and workshops, co-sponsored by the IEEE Computer Society and ACM SIGGRAPH, devoted to the general topic, and special areas in the field, for example volume visualization. Most people are familiar with the digital animations produced to present meteorological data during weather reports on television, though few can distinguish between those models of reality and the satellite photos that are also shown on such programs. TV also offers scientific visualizations when it shows computer drawn and animated reconstructions of road or airplane accidents. Some of the most popular examples of scientific visualizations are computer-generated images that show real spacecraft in action, out in the void far beyond Earth, or on other planets. Dynamic forms of visualization, such as educational animation or timelines, have the potential to enhance learning about systems that change over time. Apart from the distinction between interactive visualizations and animation, the most useful categorization is probably between abstract and model-based scientific visualizations. The abstract visualizations show completely conceptual constructs in 2D or 3D. These generated shapes are completely arbitrary. The model-based visualizations either place overlays of data on real or digitally constructed images of reality or make a digital construction of a real object directly from the scientific data. Scientific visualization is usually done with specialized software, though there are a few exceptions, noted below. Some of these specialized programs have been released as open source software, having very often its origins in universities, within an academic environment where sharing software tools and giving access to the source code is common. There are also many proprietary software packages of scientific visualization tools. Models and frameworks for building visualizations include the data flow models popularized by systems such as AVS, IRIS Explorer, and VTK toolkit, and data state models in spreadsheet systems such as the Spreadsheet for Visualization and Spreadsheet for Images. == Applications == === Scientific visualization === As a subject in computer science, scientific visualization is the use of interactive, sensory representations, typically visual, of abstract data to reinforce cognition, hypothesis building, and reasoning. Scientific visualization is the transformation, selection, or representation of data from simulations or experiments, with an implicit or explicit geometric structure, to allow the exploration, analysis, and understanding of the data. Scientific visualization focuses and emphasizes the representation of higher order data using primarily graphics and animation techniques. It is a very important part of visualization and maybe the first one, as the visualization of experiments and phenomena is as old as science itself. Traditional areas of scientific visualization are flow visualization, medical visualization, astrophysical visualization, and chemical visualization. There are several different techniques to visualize scientific data, with isosurface reconstruction and direct volume rendering being the more common. === Data and information visualization === Data visualization is a related subcategory of visualization dealing with statistical graphics and geospatial data (as in thematic cartography) that is abstracted in schematic form. Information visualization concentrates on the use of computer-supported tools to explore large amount of abstract data. The term "information visualization" was originally coined by the User Interface Research Group at Xerox PARC and included Jock Mackinlay. Practical application of information visualization in computer programs involves selecting, transforming, and representing abstract data in a form that facilitates human interaction for exploration and understanding. Important aspects of information visualization are dynamics of visual representation and the interactivity. Strong techniques enable the user to modify the visualization in real-time, thus affording unparalleled perception of patterns and structural relations in the abstract data in question. === Educational visualization === Educational visualization is using a simulation to create an image of something so it can be taught about. This is very useful when teaching about a topic that is difficult to otherwise see, for example, atomic structure, because atoms are far too small to be studied easily without expensive and difficult to use scientific equipment. === Knowledge visualization === The use of visual representations to transfer knowledge between at least two persons aims to improve the transfer of knowledge by using computer and non-computer-based visualization methods complementarily. Thus properly designed visualization is an important part of not only data analysis but knowledge transfer process, too. Knowledge transfer may be significantly improved using hybrid designs as it enhances information density but may decrease clarity as well. For example, visualization of a 3D scalar field may be implemented using iso-surfaces for field distribution and textures for the gradient of the field. Examples of such visual formats are sketches, diagrams, images, objects, interactive visualizations, information visualization applications, and imaginary visualizations as in stories. While information visualization concentrates on the use of computer-supported tools to derive new insights, knowledge visualization focuses on transferring insights and creating new knowledge in groups. Beyond the mere transfer of facts, knowledge visualization aims to further transfer insights, experiences, attitudes, values, expectations, perspectives, opinions, and estimates in different fields by using various complementary visualizations. See also: picture dictionary, visual dictionary === Product visualization === Product visualization involves visualization software technology for the viewing and manipulation of 3D models, technical drawing and other related documentation of manufactured components and large assemblies of products. It is a key part of product lifecycle management. Product visualization software typically provides high levels of photorealism so that a product can be viewed before it is actually manufactured. This supports functions ranging from design and styling to sales and marketing. Technical visualization is an important aspect of product development. Originally technical drawings were made by hand, but with the rise of advanced computer graphics the drawing board has been replaced by computer-aided design (CAD). CAD-drawings and models have several advantages over hand-made drawings such as the possibility of 3-D modeling, rapid prototyping, and simulation. 3D product visualization promises more interactive experiences for online shoppers, but also challenges retailers to overcome hurdles in the production of 3D content, as large-scale 3D content production can be extremel
Trello
Trello is a web-based, kanban-style list-making application developed by Atlassian. Created in 2011 by Fog Creek Software, it was spun out to form the basis of a separate company in New York City in 2014 and sold to Atlassian in January 2017. == History == The name Trello is derived from the word trellis, which had been a code name for the project at its early stages. Trello was released at a TechCrunch event by Fog Creek founder Joel Spolsky. In September 2011 Wired magazine named the application one of "The 7 Coolest Startups You Haven't Heard of Yet". Lifehacker said "it makes project collaboration simple and kind of enjoyable". In 2014, it raised US$10.3 million in funding from Index Ventures and Spark Capital. Prior to its acquisition, Trello had sold 22% of its shares to investors, with the remaining shares held by founders Michael Pryor and Joel Spolsky. In May 2016, Trello claimed it had more than 1.1 million daily active users and 14 million total signups. In May 2015, Trello expanded internationally with localized interfaces for Brazil, Germany, and Spain. In 2016 Trello launched the Power-Up platform, allowing 3rd party developers to build and distribute extensions known as Power-Ups to Trello. Initial integrations included Zendesk, SurveyMonkey and Giphy. By January 2022 there were a total of 247 power-ups listed in the Power-Up directory. On 9 January 2017, Atlassian announced its intent to acquire Trello for $425 million. The transaction was made with $360 million in cash and $65 million in shares and options. In December 2018, Trello announced its acquisition of Butler, a company that developed a leading power-up for automating tasks within a Trello board. Trello announced 35 million users in March 2019 and 50 million users in October 2019. In 2020 Craig Jones, then cybersecurity operations director at Sophos, found that the company exposed the personally identifiable information (PII) data of its users, exposed through public Trello boards; the researcher first tweeted about this issue in the year 2018. On 16 January 2024 Trello suffered a data breach containing over 15 million unique email addresses, names and usernames, when the data was posted on a popular hacking forum. The data was obtained by enumerating a publicly accessible resource using email addresses from previous breach corpuses; it was then added on 22 January 2024 to the famous website collecting data breaches "Have I Been Pwned?". == Uses == Users can create task boards with different columns and move the tasks between them. Typically columns include task statuses such as To Do, In Progress, Done. The tool can be used for personal and business purposes including real estate management, software project management, school bulletin boards, lesson planning, accounting, web design, gaming, and law office case management. == Architecture == According to a Fog Creek blog post in January 2012, the client was a thin web layer which downloads the main app, written in CoffeeScript and compiled to minified JavaScript, using Backbone.js, HTML5 .pushState(), and the Mustache templating language. The server was built on top of MongoDB, Node.js and a modified version of Socket.io. == Reception == On 26 January 2017, PC Magazine gave Trello a 3.5 / 5 rating, calling it "flexible" and saying that "you can get rather creative", while noting that "it may require some experimentation to figure out how to best use it for your team and the workload you manage."
Collision detection
Collision detection is the computational problem of detecting an intersection of two or more objects in virtual space. More precisely, it deals with the questions of if, when, and where two or more objects intersect. Collision detection is a classic problem of computational geometry with applications in computer graphics, physical simulation, video games, robotics (including autonomous driving), and computational physics. Collision detection algorithms can be divided into operating on 2D or 3D spatial objects. == Overview == Collision detection is closely linked to calculating the distance between objects, as objects collide when the distance between them is less than or equal to zero. Negative distances indicate that one object has penetrated another. Performing collision detection requires more context than just the distance between the objects. Accurately identifying the points of contact on both objects' surfaces is also essential for computing a physically accurate collision response. The complexity of this task increases with the level of detail in the objects' representations: the more intricate the model, the greater the computational cost. Collision detection frequently involves dynamic objects, adding a temporal dimension to distance calculations. Instead of simply measuring distance between static objects, collision detection algorithms often aim to determine whether the objects' motion will bring them to a point in time when their distance is zero—an operation that adds significant computational overhead. In collision detection involving multiple objects, a naive approach would require detecting collisions for all pairwise combinations of objects. As the number of objects increases, the number of required comparisons grows rapidly: for n {\displaystyle n} objects, n ( n − 1 ) / 2 {n(n-1)}/{2} intersection tests are needed with a naive approach. This quadratic growth makes such an approach computationally expensive as n {\displaystyle n} increases. Due to the complexity mentioned above, collision detection is a computationally intensive process. Nevertheless, it is essential for interactive applications like video games, robotics, and real-time physics engines. To manage these computational demands, extensive efforts have gone into optimizing collision detection algorithms. A commonly used approach towards accelerating the required computations is to divide the process into two phases: the broad phase and the narrow phase. The broad phase aims to answer the question of whether objects might collide, using a conservative but efficient approach to rule out pairs that clearly do not intersect, thus avoiding unnecessary calculations. Objects that cannot be definitively separated in the broad phase are passed to the narrow phase. Here, more precise algorithms determine whether these objects actually intersect. If they do, the narrow phase often calculates the exact time and location of the intersection. == Broad phase == This phase aims at quickly finding objects or parts of objects for which it can be quickly determined that no further collision test is needed. A useful property of such approach is that it is output sensitive. In the context of collision detection this means that the time complexity of the collision detection is proportional to the number of objects that are close to each other. An early example of that is the I-COLLIDE where the number of required narrow phase collision tests was O ( n + m ) {\displaystyle O(n+m)} where n {\displaystyle n} is the number of objects and m {\displaystyle m} is the number of objects at close proximity. This is a significant improvement over the quadratic complexity of the naive approach. === Spatial partitioning === Several approaches can be grouped under the spatial partitioning umbrella, which includes octrees (for 3D), quadtrees (for 2D), binary space partitioning (or BSP trees) and other, similar approaches. If one splits space into a number of simple cells, and if two objects can be shown not to be in the same cell, then they need not be checked for intersection. Dynamic scenes and deformable objects require updating the partitioning which can add overhead. === Bounding volume hierarchy === Bounding Volume Hierarchy (BVH) is a tree structure over a set of bounding volumes. Collision is determined by doing a tree traversal starting from the root. If the bounding volume of the root doesn't intersect with the object of interest, the traversal can be stopped. If, however there is an intersection, the traversal proceeds and checks the branches for each there is an intersection. Branches for which there is no intersection with the bounding volume can be culled from further intersection test. Therefore, multiple objects can be determined to not intersect at once. BVH can be used with deformable objects such as cloth or soft-bodies but the volume hierarchy has to be adjusted as the shape deforms. For deformable objects we need to be concerned about self-collisions or self intersections. BVH can be used for that end as well. Collision between two objects is computed by computing intersection between the bounding volumes of the root of the tree as there are collision we dive into the sub-trees that intersect. Exact collisions between the actual objects, or its parts (often triangles of a triangle mesh) need to be computed only between intersecting leaves. The same approach works for pair wise collision and self-collisions. === Exploiting temporal coherence === During the broad-phase, when the objects in the world move or deform, the data-structures used to cull collisions have to be updated. In cases where the changes between two frames or time-steps are small and the objects can be approximated well with axis-aligned bounding boxes, the sweep and prune algorithm can be a suitable approach. Several key observation make the implementation efficient: Two bounding-boxes intersect if, and only if, there is overlap along all three axes; overlap can be determined, for each axis separately, by sorting the intervals for all the boxes; and lastly, between two frames updates are typically small (making sorting algorithms optimized for almost-sorted lists suitable for this application). The algorithm keeps track of currently intersecting boxes, and as objects move, re-sorting the intervals helps keep track of the status. === Pairwise pruning === Once a pair of physical bodies has been selected for further investigation, collisions need to be checked more carefully. However, in many applications, individual objects (if they are not too deformable) are described by a set of smaller primitives, mainly triangles. So there are two sets of triangles, S = S 1 , S 2 , … , S n {\displaystyle S={S_{1},S_{2},\dots ,S_{n}}} and T = T 1 , T 2 , … , T n {\displaystyle T={T_{1},T_{2},\dots ,T_{n}}} (for simplicity, each set has the same number of triangles.) The obvious thing to do is to check all triangles S j {\displaystyle S_{j}} against all triangles T k {\displaystyle T_{k}} for collisions, but this involves n 2 {\displaystyle n^{2}} comparisons, which is highly inefficient. If possible, it is desirable to use a pruning algorithm to reduce the number of pairs of triangles that need to be checked. The most widely used family of algorithms is known as the hierarchical bounding volumes method. As a preprocessing step, for each object (e.g., S {\displaystyle S} and T {\displaystyle T} ) calculates a hierarchy of bounding volumes. Then, at each time step, when collisions need to be checked between S {\displaystyle S} and T {\displaystyle T} , the hierarchical bounding volumes are used to reduce the number of pairs of triangles under consideration. For simplicity, provide an example using bounding spheres, although it has been noted that spheres are undesirable in many cases. If E {\displaystyle E} is a set of triangles, a bounding sphere is pre-calculated. B ( E ) {\displaystyle B(E)} . There are many ways of choosing B ( E ) {\displaystyle B(E)} , B ( E ) {\displaystyle B(E)} is a sphere that completely contains E {\displaystyle E} and is as small as possible. Ahead of time, B ( S ) {\displaystyle B(S)} and B ( T ) {\displaystyle B(T)} can be computed. Clearly, if these two spheres do not intersect (and that is very easy to test), then neither do S {\displaystyle S} and T {\displaystyle T} . This is not much better than an n-body pruning algorithm, however. If E = E 1 , E 2 , … , E m {\displaystyle E={E_{1},E_{2},\dots ,E_{m}}} is a set of triangles, then split it into two halves L ( E ) := E 1 , E 2 , … , E m / 2 {\displaystyle L(E):={E_{1},E_{2},\dots ,E_{m/2}}} and R ( E ) := E m / 2 + 1 , … , E m − 1 , E m {\displaystyle R(E):={E_{m/2+1},\dots ,E_{m-1},E_{m}}} . Apply this to S {\displaystyle S} and T {\displaystyle T} , and calculate (ahead of time) the bounding spheres B ( L ( S ) ) , B ( R ( S ) ) {\displaystyle B(L(S)),B(R(S))} and B ( L ( T ) ) , B ( R ( T ) ) {\displaystyle B(L(T)),B(R(T))} . T