Rvachev function
In mathematics, an R-function, or Rvachev function, is a real-valued function whose sign can change if and only if the sign of one of its arguments changes, 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] in 1963, though the name, "R-functions", was given later on by E.L.Rvacheva-Yushchenko.
See also
Notes
- ^ 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)
- ^ V. Shapiro, Semi-analytic geometry with R-Functions, Acta Numerica, Cambridge University Press, 2007, 16: 239-303
- ^ 75 years to Vladimir L. Rvachev (75th anniversary biographical tribute)