Implicit functions with guaranteed differential properties

Abstract

Theory of R-functions [12] provides the methodology for constructing exact implicit functions for any semianalytic set. This paper systematically explores and compares the known constructions in terms of their differential properties and explains how such functions may be constructed automatically from CSG and boundary representations of solids. The constructed functions may be automatically differentiated and integrated and have many important applications in meshfree engineering analysis, motion planning, and scientific visualization.