Rvachev function

In mathematics, an R-function or Rvachev function is a 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 its arguments.

Typically, the function and its arguments are real-valued. Interpreting positive values as "true" and negative values as "false", an R-function is transformed into an equivalent Boolean function (the two functions are termed "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 the context of implicit functions and, in computer graphics, implicit surfaces. 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 [ [http://users.kpi.kharkov.ua/apm/all/rva75en.htm 75 years to Vladimir L. Rvachev] (75th anniversary biographical tribute)] in 1963 [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).] , and elaborated on by Kravchenko. They are sometimes called Rvachev's atomic functions or Kravchenko-Rvachev functions.

ee also

* Function representation

Notes

References

* [http://sal-cnc.me.wisc.edu/Research/meshless/R-functions/R-functions.html Meshfree Modeling and Analysis, R-Functions (University of Wisconsin)]

* [http://docs.lib.purdue.edu/dissertations/AAI3263546/ Pattern Recognition Methods Based on Rvachev Functions (Purdue University)]