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{{Short description|Real-valued mathematical function}}
In [[Mathematics|mathematics]], an '''R-function''', or '''Rvachev function''', is a [[Real-valued function|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.<ref>V.L. Rvachev, “On the analytical description of some geometric objects”, ''Reports of Ukrainian Academy of Sciences'', vol. '''153''', no. 4, 1963, pp. 765–767 (in Russian)</ref><ref>V. Shapiro, Semi-analytic geometry with R-Functions, Acta Numerica, Cambridge University Press,  2007, 16: 239-303</ref>

Interpreting positive values as ''true'' and negative values as ''false'', an R-function is transformed into a "companion" [[Boolean function]] (the two functions are called ''friends''). For instance, the R-function ''ƒ''(''x'',&nbsp;''y'') = min(''x'',&nbsp;''y'') is one possible friend of the logical conjunction (AND). R-functions are used in [[Computer graphics|computer graphics]] and [[Geometric modeling|geometric modeling]] in the context of [[Implicit surface|implicit surface]]s and the [[Function representation|function representation]]. They also appear in certain boundary-value problems, and are also popular in certain [[Artificial intelligence|artificial intelligence]] applications, where they are used in [[Pattern recognition|pattern recognition]].

R-functions were first proposed by {{Interlanguage link multi|Vladimir Logvinovich Rvachev|ru|3=Рвачев, Владимир Логвинович}}<ref>[http://users.kpi.kharkov.ua/apm/all/rva75en.htm 75 years to Vladimir L. Rvachev] (75th anniversary biographical tribute)</ref> ({{lang-ru|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 ({{lang-ru|Логвин  Фёдорович Рвачёв}}).

== See also ==
* [[Function representation]]
*Slesarenko function (S-function)

== Notes ==
<references/>

== References ==
* [http://sal-cnc.me.wisc.edu/Research/meshless/R-functions/R-functions.html Meshfree Modeling and Analysis, R-Functions (University of Wisconsin)]
* [https://docs.lib.purdue.edu/dissertations/AAI3263546/ Pattern Recognition Methods Based on Rvachev Functions (Purdue University)]
* [http://hyperfun.org/wiki/doku.php?id=frep:main Shape Modeling and Computer Graphics with Real Functions]

[[Category:Non-classical logic]]
[[Category:Real analysis]]
[[Category:Types of functions]]

{{Sourceattribution|Rvachev function}}