In the fields of computing and computer vision, pose (or spatial pose) represents the position and the orientation of an object, each usually in three dimensions. Poses are often stored internally as transformation matrices. The term “pose” is largely synonymous with the term “transform”, but a transform may often include scale, whereas pose does not. In computer vision, the pose of an object is often estimated from camera input by the process of pose estimation. This information can then be used, for example, to allow a robot to manipulate an object or to avoid moving into the object based on its perceived position and orientation in the environment. Other applications include skeletal action recognition. == Pose estimation == The specific task of determining the pose of an object in an image (or stereo images, image sequence) is referred to as pose estimation. Pose estimation problems can be solved in different ways depending on the image sensor configuration, and choice of methodology. Three classes of methodologies can be distinguished: Analytic or geometric methods: Given that the image sensor (camera) is calibrated and the mapping from 3D points in the scene and 2D points in the image is known. If also the geometry of the object is known, it means that the projected image of the object on the camera image is a well-known function of the object's pose. Once a set of control points on the object, typically corners or other feature points, has been identified, it is then possible to solve the pose transformation from a set of equations which relate the 3D coordinates of the points with their 2D image coordinates. Algorithms that determine the pose of a point cloud with respect to another point cloud are known as point set registration algorithms, if the correspondences between points are not already known. Genetic algorithm methods: If the pose of an object does not have to be computed in real-time a genetic algorithm may be used. This approach is robust especially when the images are not perfectly calibrated. In this particular case, the pose represent the genetic representation and the error between the projection of the object control points with the image is the fitness function. Learning-based methods: These methods use artificial learning-based system which learn the mapping from 2D image features to pose transformation. In short, this means that a sufficiently large set of images of the object, in different poses, must be presented to the system during a learning phase. Once the learning phase is completed, the system should be able to present an estimate of the object's pose given an image of the object. == Camera pose ==
Reflection (computer graphics)
Reflection in computer graphics is used to render reflective objects like mirrors and shiny surfaces. Accurate reflections are commonly computed using ray tracing whereas approximate reflections can usually be computed faster by using simpler methods such as environment mapping. Reflections on shiny surfaces like wood or tile can add to the photorealistic effects of a 3D rendering. == Approaches to reflection rendering == For rendering environment reflections there exist many techniques that differ in precision, computational and implementation complexity. Combination of these techniques are also possible. Image order rendering algorithms based on tracing rays of light, such as ray tracing or path tracing, typically compute accurate reflections on general surfaces, including multiple reflections and self reflections. However these algorithms are generally still too computationally expensive for real time rendering (even though specialized HW exists, such as Nvidia RTX) and require a different rendering approach from typically used rasterization. Reflections on planar surfaces, such as planar mirrors or water surfaces, can be computed simply and accurately in real time with two pass rendering — one for the viewer, one for the view in the mirror, usually with the help of stencil buffer. Some older video games used a trick to achieve this effect with one pass rendering by putting the whole mirrored scene behind a transparent plane representing the mirror. Reflections on non-planar (curved) surfaces are more challenging for real time rendering. Main approaches that are used include: Environment mapping (e.g. cube mapping): a technique that has been widely used e.g. in video games, offering reflection approximation that's mostly sufficient to the eye, but lacking self-reflections and requiring pre-rendering of the environment map. The precision can be increased by using a spatial array of environment maps instead of just one. It is also possible to generate cube map reflections in real time, at the cost of memory and computational requirements. Screen space reflections (SSR): a more expensive technique that traces rays come from pixel data.This requires the data of surface normal and either depth buffer (local space) or position buffer (world space).The disadvantage is that objects not captured in the rendered frame cannot appear in the reflections, which results in unresolved and or false intersections causing artefacts such as reflection vanishment and virtual image. SSR was originally introduced as Real Time Local Reflections in CryENGINE 3. == Types of reflection == Polished - A polished reflection is an undisturbed reflection, like a mirror or chrome surface. Blurry - A blurry reflection means that tiny random bumps, or microfacets, on the surface of the material causes the reflection to be blurry. Metallic - A reflection is metallic if the highlights and reflections retain the color of the reflective object. Glossy - This term can be misused: sometimes, it is a setting which is the opposite of blurry (e.g. when "glossiness" has a low value, the reflection is blurry). Sometimes the term is used as a synonym for "blurred reflection". Glossy used in this context means that the reflection is actually blurred. === Polished or mirror reflection === Mirrors are usually almost 100% reflective. === Metallic reflection === Normal (nonmetallic) objects reflect light and colors in the original color of the object being reflected. Metallic objects reflect lights and colors altered by the color of the metallic object itself. === Blurry reflection === Many materials are imperfect reflectors, where the reflections are blurred to various degrees due to surface roughness that scatters the rays of the reflections. === Glossy reflection === Fully glossy reflection, shows highlights from light sources, but does not show a clear reflection from objects. == Examples of reflections == === Wet floor reflections === The wet floor effect is a graphic effects technique popular in conjunction with Web 2.0 style pages, particularly in logos. The effect can be done manually or created with an auxiliary tool which can be installed to create the effect automatically. Unlike a standard computer reflection (and the Java water effect popular in first-generation web graphics), the wet floor effect involves a gradient and often a slant in the reflection, so that the mirrored image appears to be hovering over or resting on a wet floor.
Rendering equation
In computer graphics, the rendering equation is an integral equation that expresses the amount of light leaving a point on a surface as the sum of emitted light and reflected light. It was independently introduced into computer graphics by David Immel et al. and James Kajiya in 1986. The equation is important in the theory of physically based rendering, describing the relationships between the bidirectional reflectance distribution function (BRDF) and the radiometric quantities used in rendering. The rendering equation is defined at every point on every surface in the scene being rendered, including points hidden from the camera. The incoming light quantities on the right side of the equation usually come from the left (outgoing) side at other points in the scene (ray casting can be used to find these other points). The radiosity rendering method solves a discrete approximation of this system of equations. In distributed ray tracing, the integral on the right side of the equation may be evaluated using Monte Carlo integration by randomly sampling possible incoming light directions. Path tracing improves and simplifies this method. The rendering equation can be extended to handle effects such as fluorescence (in which some absorbed energy is re-emitted at different wavelengths) and can support transparent and translucent materials by using a bidirectional scattering distribution function (BSDF) in place of a BRDF. The theory of path tracing sometimes uses a path integral (integral over possible paths from a light source to a point) instead of the integral over possible incoming directions. == Equation form == The rendering equation may be written in the form L o ( x , ω o , λ , t ) = L e ( x , ω o , λ , t ) + L r ( x , ω o , λ , t ) {\displaystyle L_{\text{o}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)=L_{\text{e}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)+L_{\text{r}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} L r ( x , ω o , λ , t ) = ∫ Ω f r ( x , ω i , ω o , λ , t ) L i ( x , ω i , λ , t ) ( ω i ⋅ n ) d ω i {\displaystyle L_{\text{r}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)=\int _{\Omega }f_{\text{r}}(\mathbf {x} ,\omega _{\text{i}},\omega _{\text{o}},\lambda ,t)L_{\text{i}}(\mathbf {x} ,\omega _{\text{i}},\lambda ,t)(\omega _{\text{i}}\cdot \mathbf {n} )\operatorname {d} \omega _{\text{i}}} where L o ( x , ω o , λ , t ) {\displaystyle L_{\text{o}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} is the total spectral radiance of wavelength λ {\displaystyle \lambda } directed outward along direction ω o {\displaystyle \omega _{\text{o}}} at time t {\displaystyle t} , from a particular position x {\displaystyle \mathbf {x} } x {\displaystyle \mathbf {x} } is the location in space ω o {\displaystyle \omega _{\text{o}}} is the direction of the outgoing light λ {\displaystyle \lambda } is a particular wavelength of light t {\displaystyle t} is time L e ( x , ω o , λ , t ) {\displaystyle L_{\text{e}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} is emitted spectral radiance L r ( x , ω o , λ , t ) {\displaystyle L_{\text{r}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} is reflected spectral radiance ∫ Ω … d ω i {\displaystyle \int _{\Omega }\dots \operatorname {d} \omega _{\text{i}}} is an integral over Ω {\displaystyle \Omega } Ω {\displaystyle \Omega } is the unit hemisphere centered around n {\displaystyle \mathbf {n} } containing all possible values for ω i {\displaystyle \omega _{\text{i}}} where ω i ⋅ n > 0 {\displaystyle \omega _{\text{i}}\cdot \mathbf {n} >0} f r ( x , ω i , ω o , λ , t ) {\displaystyle f_{\text{r}}(\mathbf {x} ,\omega _{\text{i}},\omega _{\text{o}},\lambda ,t)} is the bidirectional reflectance distribution function, the proportion of light reflected from ω i {\displaystyle \omega _{\text{i}}} to ω o {\displaystyle \omega _{\text{o}}} at position x {\displaystyle \mathbf {x} } , time t {\displaystyle t} , and at wavelength λ {\displaystyle \lambda } ω i {\displaystyle \omega _{\text{i}}} is the negative direction of the incoming light L i ( x , ω i , λ , t ) {\displaystyle L_{\text{i}}(\mathbf {x} ,\omega _{\text{i}},\lambda ,t)} is spectral radiance of wavelength λ {\displaystyle \lambda } coming inward toward x {\displaystyle \mathbf {x} } from direction ω i {\displaystyle \omega _{\text{i}}} at time t {\displaystyle t} n {\displaystyle \mathbf {n} } is the surface normal at x {\displaystyle \mathbf {x} } ω i ⋅ n {\displaystyle \omega _{\text{i}}\cdot \mathbf {n} } is the weakening factor of outward irradiance due to incident angle, as the light flux is smeared across a surface whose area is larger than the projected area perpendicular to the ray. This is often written as cos θ i {\displaystyle \cos \theta _{i}} . Two noteworthy features are: its linearity—it is composed only of multiplications and additions, and its spatial homogeneity—it is the same in all positions and orientations. These mean a wide range of factorings and rearrangements of the equation are possible. It is a Fredholm integral equation of the second kind, similar to those that arise in quantum field theory. Note this equation's spectral and time dependence — L o {\displaystyle L_{\text{o}}} may be sampled at or integrated over sections of the visible spectrum to obtain, for example, a trichromatic color sample. A pixel value for a single frame in an animation may be obtained by fixing t ; {\displaystyle t;} motion blur can be produced by averaging L o {\displaystyle L_{\text{o}}} over some given time interval (by integrating over the time interval and dividing by the length of the interval). Note that a solution to the rendering equation is the function L o {\displaystyle L_{\text{o}}} . The function L i {\displaystyle L_{\text{i}}} is related to L o {\displaystyle L_{\text{o}}} via a ray-tracing operation: The incoming radiance from some direction at one point is the outgoing radiance at some other point in the opposite direction. == Applications == Solving the rendering equation for any given scene is the primary challenge in realistic rendering. One approach to solving the equation is based on finite element methods, leading to the radiosity algorithm. Another approach using Monte Carlo methods has led to many different algorithms including path tracing, photon mapping, and Metropolis light transport, among others. == Limitations == Although the equation is very general, it does not capture every aspect of light reflection. Some missing aspects include the following: Transmission, which occurs when light is transmitted through the surface, such as when it hits a glass object or a water surface, Subsurface scattering, where the spatial locations for incoming and departing light are different. Surfaces rendered without accounting for subsurface scattering may appear unnaturally opaque — however, it is not necessary to account for this if transmission is included in the equation, since that will effectively include also light scattered under the surface, Polarization, where different light polarizations will sometimes have different reflection distributions, for example when light bounces at a water surface, Phosphorescence, which occurs when light or other electromagnetic radiation is absorbed at one moment and emitted at a later moment, usually with a longer wavelength (unless the absorbed electromagnetic radiation is very intense), Interference, where the wave properties of light are exhibited, Fluorescence, where the absorbed and emitted light have different wavelengths, Non-linear effects, where very intense light can increase the energy level of an electron with more energy than that of a single photon (this can occur if the electron is hit by two photons at the same time), and emission of light with higher frequency than the frequency of the light that hit the surface suddenly becomes possible, and Doppler effect, where light that bounces off an object moving at a very high speed will get its wavelength changed: if the light bounces off an object that is moving towards it, the light will be blueshifted and the photons will be packed more closely so the photon flux will be increased; if it bounces off an object moving away from it, it will be redshifted and the photon flux will be decreased. This effect becomes apparent only at speeds comparable to the speed of light, which is not the case for most rendering applications. For scenes that are either not composed of simple surfaces in a vacuum or for which the travel time for light is an important factor, researchers have generalized the rendering equation to produce a volume rendering equation suitable for volume rendering and a transient rendering equation for use with data from a time-of-flight camera.
Foreign key
A foreign key is a set of attributes in a table that refers to the primary key of another table, linking these two tables. In the context of relational databases, a foreign key is subject to an inclusion dependency constraint that the tuples consisting of the foreign key attributes in one relation, R, must also exist in some other (not necessarily distinct) relation, S; furthermore that those attributes must also be a candidate key in S. In other words, a foreign key is a set of attributes that references a candidate key. For example, a table called TEAM may have an attribute, MEMBER_NAME, which is a foreign key referencing a candidate key, PERSON_NAME, in the PERSON table. Since MEMBER_NAME is a foreign key, any value existing as the name of a member in TEAM must also exist as a person's name in the PERSON table; in other words, every member of a TEAM is also a PERSON. == Summary == The table containing the foreign key is called the child table, and the table containing the candidate key is called the referenced or parent table. In database relational modeling and implementation, a candidate key is a set of zero or more attributes, the values of which are guaranteed to be unique for each tuple (row) in a relation. The value or combination of values of candidate key attributes for any tuple cannot be duplicated for any other tuple in that relation. Since the purpose of the foreign key is to identify a particular row of referenced table, it is generally required that the foreign key is equal to the candidate key in some row of the primary table, or else have no value (the NULL value.). This rule is called a referential integrity constraint between the two tables. Because violations of these constraints can be the source of many database problems, most database management systems provide mechanisms to ensure that every non-null foreign key corresponds to a row of the referenced table. For example, consider a database with two tables: a CUSTOMER table that includes all customer data and an ORDER table that includes all customer orders. Suppose the business requires that each order must refer to a single customer. To reflect this in the database, a foreign key column is added to the ORDER table (e.g., CUSTOMERID), which references the primary key of CUSTOMER (e.g. ID). Because the primary key of a table must be unique, and because CUSTOMERID only contains values from that primary key field, we may assume that, when it has a value, CUSTOMERID will identify the particular customer which placed the order. However, this can no longer be assumed if the ORDER table is not kept up to date when rows of the CUSTOMER table are deleted or the ID column altered, and working with these tables may become more difficult. Many real world databases work around this problem by 'inactivating' rather than physically deleting master table foreign keys, or by complex update programs that modify all references to a foreign key when a change is needed. Foreign keys play an essential role in database design. One important part of database design is making sure that relationships between real-world entities are reflected in the database by references, using foreign keys to refer from one table to another. Another important part of database design is database normalization, in which tables are broken apart and foreign keys make it possible for them to be reconstructed. Multiple rows in the referencing (or child) table may refer to the same row in the referenced (or parent) table. In this case, the relationship between the two tables is called a one to many relationship between the referencing table and the referenced table. In addition, the child and parent table may, in fact, be the same table, i.e. the foreign key refers back to the same table. Such a foreign key is known in SQL:2003 as a self-referencing or recursive foreign key. In database management systems, this is often accomplished by linking a first and second reference to the same table. A table may have multiple foreign keys, and each foreign key can have a different parent table. Each foreign key is enforced independently by the database system. Therefore, cascading relationships between tables can be established using foreign keys. A foreign key is defined as an attribute or set of attributes in a relation whose values match a primary key in another relation. The syntax to add such a constraint to an existing table is defined in SQL:2003 as shown below. Omitting the column list in the REFERENCES clause implies that the foreign key shall reference the primary key of the referenced table. Likewise, foreign keys can be defined as part of the CREATE TABLE SQL statement. If the foreign key is a single column only, the column can be marked as such using the following syntax: Foreign keys can be defined with a stored procedure statement. child_table: the name of the table or view that contains the foreign key to be defined. parent_table: the name of the table or view that has the primary key to which the foreign key applies. The primary key must already be defined. col3 and col4: the name of the columns that make up the foreign key. The foreign key must have at least one column and at most eight columns. == Referential actions == Because the database management system enforces referential constraints, it must ensure data integrity if rows in a referenced table are to be deleted (or updated). If dependent rows in referencing tables still exist, those references have to be considered. SQL:2003 specifies 5 different referential actions that shall take place in such occurrences: CASCADE RESTRICT NO ACTION SET NULL SET DEFAULT === CASCADE === Whenever rows in the parent (referenced) table are deleted (or updated), the respective rows of the child (referencing) table with a matching foreign key column will be deleted (or updated) as well. This is called a cascade delete (or update). === RESTRICT === A value cannot be updated or deleted when a row exists in a referencing or child table that references the value in the referenced table. Similarly, a row cannot be deleted as long as there is a reference to it from a referencing or child table. To understand RESTRICT (and CASCADE) better, it may be helpful to notice the following difference, which might not be immediately clear. The referential action CASCADE modifies the "behavior" of the (child) table itself where the word CASCADE is used. For example, ON DELETE CASCADE effectively says "When the referenced row is deleted from the other table (master table), then delete also from me". However, the referential action RESTRICT modifies the "behavior" of the master table, not the child table, although the word RESTRICT appears in the child table and not in the master table! So, ON DELETE RESTRICT effectively says: "When someone tries to delete the row from the other table (master table), prevent deletion from that other table (and of course, also don't delete from me, but that's not the main point here)." RESTRICT is not supported by Microsoft SQL 2012 and earlier. === NO ACTION === NO ACTION and RESTRICT are very much alike. The main difference between NO ACTION and RESTRICT is that with NO ACTION the referential integrity check is done after trying to alter the table. RESTRICT does the check before trying to execute the UPDATE or DELETE statement. Both referential actions act the same if the referential integrity check fails: the UPDATE or DELETE statement will result in an error. In other words, when an UPDATE or DELETE statement is executed on the referenced table using the referential action NO ACTION, the DBMS verifies at the end of the statement execution that none of the referential relationships are violated. This is different from RESTRICT, which assumes at the outset that the operation will violate the constraint. Using NO ACTION, the triggers or the semantics of the statement itself may yield an end state in which no foreign key relationships are violated by the time the constraint is finally checked, thus allowing the statement to complete successfully. === SET NULL, SET DEFAULT === In general, the action taken by the DBMS for SET NULL or SET DEFAULT is the same for both ON DELETE or ON UPDATE: the value of the affected referencing attributes is changed to NULL for SET NULL, and to the specified default value for SET DEFAULT. === Triggers === Referential actions are generally implemented as implied triggers (i.e. triggers with system-generated names, often hidden.) As such, they are subject to the same limitations as user-defined triggers, and their order of execution relative to other triggers may need to be considered; in some cases it may become necessary to replace the referential action with its equivalent user-defined trigger to ensure proper execution order, or to work around mutating-table limitations. Another important limitation appears with transaction isolation: your changes to a row may not be able to fully cascade because the row is ref
Device-independent pixel
A device-independent pixel (also: density-independent pixel, dip, dp) is a unit of length. A typical use is to allow mobile device software to scale the display of information and user interaction to different screen sizes. The abstraction allows an application to work in pixels as a measurement, while the underlying graphics system converts the abstract pixel measurements of the application into real pixel measurements appropriate to the particular device. For example, on the Android operating system a device-independent pixel is equivalent to one physical pixel on a 160 dpi screen, while the Windows Presentation Foundation specifies one device-independent pixel as equivalent to 1/96th of an inch. As dp is a physical unit it has an absolute value which can be measured in traditional units, e.g. for Android devices 1 dp equals 1/160 of inch or 0.15875 mm. While traditional pixels only refer to the display of information, device-independent pixels may also be used to measure user input such as input on a touch screen device.
Hybrid machine translation
Hybrid machine translation is a method of machine translation that is characterized by the use of multiple machine translation approaches within a single machine translation system. The motivation for developing hybrid machine translation systems stems from the failure of any single technique to achieve a satisfactory level of accuracy. Many hybrid machine translation systems have been successful in improving the accuracy of the translations, and there are several popular machine translation systems which employ hybrid methods. == Approaches == === Multi-engine === This approach to hybrid machine translation involves running multiple machine translation systems in parallel. The final output is generated by combining the output of all the sub-systems. Most commonly, these systems use statistical and rule-based translation subsystems, but other combinations have been explored. For example, researchers at Carnegie Mellon University have had some success combining example-based, transfer-based, knowledge-based and statistical translation sub-systems into one machine translation system. === Statistical rule generation === This approach involves using statistical data to generate lexical and syntactic rules. The input is then processed with these rules as if it were a rule-based translator. This approach attempts to avoid the difficult and time-consuming task of creating a set of comprehensive, fine-grained linguistic rules by extracting those rules from the training corpus. This approach still suffers from many problems of normal statistical machine translation, namely that the accuracy of the translation will depend heavily on the similarity of the input text to the text of the training corpus. As a result, this technique has had the most success in domain-specific applications, and has the same difficulties with domain adaptation as many statistical machine translation systems. === Multi-Pass === This approach involves serially processing the input multiple times. The most common technique used in multi-pass machine translation systems is to pre-process the input with a rule-based machine translation system. The output of the rule-based pre-processor is passed to a statistical machine translation system, which produces the final output. This technique is used to limit the amount of information a statistical system need consider, significantly reducing the processing power required. It also removes the need for the rule-based system to be a complete translation system for the language, significantly reducing the amount of human effort and labor necessary to build the system. === Confidence-Based === This approach differs from the other hybrid approaches in that in most cases only one translation technology is used. A confidence metric is produced for each translated sentence from which a decision can be made whether to try a secondary translation technology or to proceed with the initial translation output. SMT is also used when common error patterns such as multiple repeat words appear in sequence, as is common with NMT when the attention mechanism is confused.
User-defined function
A user-defined function (UDF) is a function provided by the user of a program or environment, in a context where the usual assumption is that functions are built into the program or environment. UDFs are usually written for the requirement of its creator. == BASIC language == In some old implementations of the BASIC programming language, user-defined functions are defined using the "DEF FN" syntax. More modern dialects of BASIC are influenced by the structured programming paradigm, where most or all of the code is written as user-defined functions or procedures, and the concept becomes practically redundant. == COBOL language == In the COBOL programming language, a user-defined function is an entity that is defined by the user by specifying a FUNCTION-ID paragraph. A user-defined function must return a value by specifying the RETURNING phrase of the procedure division header and they are invoked using the function-identifier syntax. See the ISO/IEC 1989:2014 Programming Language COBOL standard for details. As of May 2022, the IBM Enterprise COBOL for z/OS 6.4 (IBM COBOL) compiler contains support for user-defined functions. == Databases == In relational database management systems, a user-defined function provides a mechanism for extending the functionality of the database server by adding a function, that can be evaluated in standard query language (usually SQL) statements. The SQL standard distinguishes between scalar and table functions. A scalar function returns only a single value (or NULL), whereas a table function returns a (relational) table comprising zero or more rows, each row with one or more columns. User-defined functions in SQL are declared using the CREATE FUNCTION statement. For example, a user-defined function that converts Celsius to Fahrenheit (a temperature scale used in USA) might be declared like this: Once created, a user-defined function may be used in expressions in SQL statements. For example, it can be invoked where most other intrinsic functions are allowed. This also includes SELECT statements, where the function can be used against data stored in tables in the database. Conceptually, the function is evaluated once per row in such usage. For example, assume a table named Elements, with a row for each known chemical element. The table has a column named BoilingPoint for the boiling point of that element, in Celsius. The query would retrieve the name and the boiling point from each row. It invokes the CtoF user-defined function as declared above in order to convert the value in the column to a value in Fahrenheit. Each user-defined function carries certain properties or characteristics. The SQL standard defines the following properties: Language - defines the programming language in which the user-defined function is implemented; examples include SQL, C, C# and Java. Parameter style - defines the conventions that are used to pass the function parameters and results between the implementation of the function and the database system (only applicable if language is not SQL). Specific name - a name for the function that is unique within the database. Note that the function name does not have to be unique, considering overloaded functions. Some SQL implementations require that function names are unique within a database, and overloaded functions are not allowed. Determinism - specifies whether the function is deterministic or not. The determinism characteristic has an influence on the query optimizer when compiling a SQL statement. SQL-data access - tells the database management system whether the function contains no SQL statements (NO SQL), contains SQL statements but does not access any tables or views (CONTAINS SQL), reads data from tables or views (READS SQL DATA), or actually modifies data in the database (MODIFIES SQL DATA). User-defined functions should not be confused with stored procedures. Stored procedures allow the user to group a set of SQL commands. A procedure can accept parameters and execute its SQL statements depending on those parameters. A procedure is not an expression and, thus, cannot be used like user-defined functions. Some database management systems allow the creation of user defined functions in languages other than SQL. Microsoft SQL Server, for example, allows the user to use .NET languages including C# for this purpose. DB2 and Oracle support user-defined functions written in C or Java programming languages. === SQL Server 2000 === There are three types of UDF in Microsoft SQL Server 2000: scalar functions, inline table-valued functions, and multistatement table-valued functions. Scalar functions return a single data value (not a table) with RETURNS clause. Scalar functions can use all scalar data types, with exception of timestamp and user-defined data types. Inline table-valued functions return the result set of a single SELECT statement. Multistatement table-valued functions return a table, which was built with many TRANSACT-SQL statements. User-defined functions can be invoked from a query like built‑in functions such as OBJECT_ID, LEN, DATEDIFF, or can be executed through an EXECUTE statement like stored procedures. Performance Notes: User-defined functions are subroutines made of one or more Transact-SQL statements that can be used to encapsulate code for reuse. It takes zero or more arguments and evaluates a return value. Has both control-flow and DML statements in its body similar to stored procedures. Does not allow changes to any Global Session State, like modifications to database or external resource, such as a file or network. Does not support output parameter. DEFAULT keyword must be specified to pass the default value of parameter. Errors in UDF cause UDF to abort which, in turn, aborts the statement that invoked the UDF. === Apache Hive === Apache Hive defines, in addition to the regular user-defined functions (UDF), also user-defined aggregate functions (UDAF) and table-generating functions (UDTF). Hive enables developers to create their own custom functions with Java. === Apache Doris === Apache Doris, an open-source real-time analytical database, allows external users to contribute their own UDFs written in C++ to it.