Rvachev function
Real-valued mathematical function
title: "Rvachev function" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["non-classical-logic", "real-analysis", "types-of-functions", "boolean-algebra"] description: "Real-valued mathematical function" topic_path: "philosophy" source: "https://en.wikipedia.org/wiki/Rvachev_function" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0
::summary Real-valued mathematical 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 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 () in 1963, though the name, "R-functions", was given later on by Ekaterina L. Rvacheva-Yushchenko, in memory of their father, Logvin Fedorovich Rvachev ().
Notes
References
- Meshfree Modeling and Analysis, R-Functions (University of Wisconsin)
- Pattern Recognition Methods Based on Rvachev Functions (Purdue University)
References
- 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
- [http://users.kpi.kharkov.ua/apm/all/rva75en.htm 75 years to Vladimir L. Rvachev] (75th anniversary biographical tribute)
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