mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, an

R-function In mathematics, an R-function, or Rvachev function, is a real-valued function whose sign does not change if none of the signs of its arguments change; that is, its sign is determined solely by the signs of its arguments. Interpreting positive val ...

, or Rvachev function, is a

real-valued function In mathematics, a real-valued function is a function whose values are real numbers. In other words, it is a function that assigns a real number to each member of its domain. Real-valued functions of a real variable (commonly called ''real f ...

whose sign does not change if none of the signs of its arguments change; that is, its sign is determined solely by the signs of its arguments. Interpreting positive values as ''true'' and negative values as ''false'', an R-function is transformed into a "companion"

Boolean function In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually , or ). Alternative names are switching function, used especially in older computer science literature, and truth function ...

(the two functions are called ''friends''). For instance, the R-function ''ƒ''(''x'', ''y'') = min(''x'', ''y'') is one possible friend of the logical conjunction (AND). R-functions are used in

computer graphics Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great de ...

and

geometric modeling __NOTOC__ Geometric modeling is a branch of applied mathematics and computational geometry that studies methods and algorithms for the mathematical description of shapes. The shapes studied in geometric modeling are mostly two- or three-dimensio ...

in the context of

implicit surface In mathematics, an implicit surface is a surface in Euclidean space defined by an equation : F(x,y,z)=0. An ''implicit surface'' is the set of zeros of a function of three variables. ''Implicit'' means that the equation is not solved for ...

s and the

function representation Function Representation (FRep or F-Rep) is used in solid modeling, volume modeling and computer graphics. FRep was introduced in "Function representation in geometric modeling: concepts, implementation and applications" as a uniform representatio ...

. They also appear in certain

boundary-value problem In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to t ...

s, and are also popular in certain

artificial intelligence Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animals and humans. Example tasks in which this is done include speech ...

applications, where they are used in

pattern recognition Pattern recognition is the automated recognition of patterns and regularities in data. It has applications in statistical data analysis, signal processing, image analysis, information retrieval, bioinformatics, data compression, computer graphics ...

. R-functions were first proposed by {{Interlanguage link multi, Vladimir Logvinovich Rvachev, ru, 3=Рвачев, Владимир Логвинович75 years to Vladimir L. Rvachev
(75th anniversary biographical tribute) (russian: Влади́мир Логвинович Рвачёв) in 1963, though the name, "R-functions", was given later on by Ekaterina L. Rvacheva-Yushchenko, in memory of their father, Logvin Fedorovich Rvachev (russian: Логвин Фёдорович Рвачёв).

Notes

References

Meshfree Modeling and Analysis, R-Functions (University of Wisconsin)

Pattern Recognition Methods Based on Rvachev Functions (Purdue University)

Shape Modeling and Computer Graphics with Real Functions
Non-classical logic Real analysis Types of functions

See also

Notes

References