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 does not change, that is, if its sign is determined solely by the signs of its arguments.[1][2]
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, y) = min(x, y) is one possible friend of the logical conjunction (AND). R-functions are used in computer graphics and geometric modeling in the context of implicit surfaces and the function representation. They also appear in certain boundary-value problems, and are also popular in certain artificial intelligence applications, where they are used in pattern recognition.
R-functions were first proposed by Vladimir Logvinovich Rvachev[3] (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, who perished in Stalin's concentration camps.