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Semi-analytic geometry with R-functions

Published online by Cambridge University Press:  24 April 2007

Vadim Shapiro
Affiliation:
Mechanical Engineering & Computer Sciences, University of Wisconsin, Madison, 1513 University Avenue, Madison, Wisconsin 53706, USA E-mail: vshapiro@engr.wisc.edu

Abstract

V. L. Rvachev called R-functions ‘logically charged functions’ because they encode complete logical information within the standard setting of real analysis. He invented them in the 1960s as a means for unifying logic, geometry, and analysis within a common computational framework – in an effort to develop a new computationally effective language for modelling and solving boundary value problems. Over the last forty years, R-functions have been accepted as a valuable tool in computer graphics, geometric modelling, computational physics, and in many areas of engineering design, analysis, and optimization. Yet, many elements of the theory of R-functions continue to be rediscovered in different application areas and special situations. The purpose of this survey is to expose the key ideas and concepts behind the theory of R-functions, explain the utility of R-functions in a broad range of applications, and to discuss selected algorithmic issues arising in connection with their use.

Type
Research Article
Copyright
© 2007 Cambridge University Press

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