R-function
Encyclopedia
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.
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 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.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, an R-function, or Rvachev function, is a real-valued function
Real-valued function
In mathematics, a real-valued function is a function that associates to every element of the domain a real number in the image....
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.
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
Computer graphics
Computer graphics are graphics created using computers and, more generally, the representation and manipulation of image data by a computer with help from specialized software and hardware....
and geometric modeling
Geometric modeling
Geometric modeling is a branch of applied mathematics and computational geometry that studies methods and algorithms for the mathematical description of shapes....
in the context of implicit surfaces and the function representation
Function representation
Function Representation is used in solid modeling, volume modeling and computer graphics. FRep was introduced in "Function representation in geometric modeling: concepts, implementation and applications" as a uniform representation of multidimensional geometric objects...
. They also appear in certain boundary-value problems, and are also popular in certain artificial intelligence
Artificial intelligence
Artificial intelligence is the intelligence of machines and the branch of computer science that aims to create it. AI textbooks define the field as "the study and design of intelligent agents" where an intelligent agent is a system that perceives its environment and takes actions that maximize its...
applications, where they are used in pattern recognition
Pattern recognition
In machine learning, pattern recognition is the assignment of some sort of output value to a given input value , according to some specific algorithm. An example of pattern recognition is classification, which attempts to assign each input value to one of a given set of classes...
.
R-functions were first proposed by Vladimir Logvinovich Rvachev 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.