R-函数理论介绍及其应用评述

An Introduction to Theory of R-Functions and A Survey on Their Applications

R-函数是一系列实函数，其函数值的符号完全取决于其各个变量的符号。一个R-函数总与一个逻辑表达式相对应，所以利用R-函数可以将形体表示成隐函数形式，由此导致它在许多领域的应用。本文概要介绍了R-函数、R-函数族与R-函数系的概念及其性质，将任意几何形体转化成隐函数形式的方法本文简要地介绍了两方面的应用：在几何造型中的应用和在边值问题求解中的应用。本文是对该领域的入门介绍，也是对其近年研究成果的评述。

An R-function is a real-valued function whose sign is completely determined by the signs of its arguments. An R-function is always corresponding to a logic predicate. Almost any geometric objects can be converted into the form of implicit functions by R-functions, leading to their applications in many fields. First, this paper introduces the concepts of R-functions, branches and systems of R-functions, and their properties. Then it explains how to get the implicit representations of geometric objects. At last, it briefly summarizes two important applications of R-functions: application in geometric modeling and application in solving boundary value problems.