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authors Eastman, Charles M. and Weiler, Kevin
year 1979
title Geometric Modeling Using the Euler Operators
source 12 p. : ill. Pittsburgh: Institute of Physical Planning, Carnegie Mellon University, February, 1979. includes bibliography
summary A recent advance in the modeling of three-dimensional shapes is the joint development of bounded shape models, capable of representing complete and well-formed arbitrary polyhedra, and operators for manipulating them. Two approaches have been developed thus far in forming bounded shape models: to combine a given fixed set of primitive shapes into other possibly more complex ones using the spatial set operators, and/or to apply lower level operators that define and combine faces, edges, loops and vertices to directly construct a shape. The name that has come to be applied to these latter operators is the Euler operators. This paper offers a description of the Euler operators, in a form expected to be useful for prospective implementers and others wishing to better understand their function and behavior. It includes considerations regarding their specification in terms of being able to completely describe different classes of shapes, how to properly specify them and the extent of their well-formedness, especially in terms of their interaction with geometric operations. Example specifications are provided as well as some useful applications. The Euler operators provide different capabilities from the spatial set operators. An extensible CAD/CAM facility needs them both
keywords Euler operators, boolean operations, CSG, geometric modeling, CAD, CAM, B-rep, solid modeling, theory
series CADline
references Content-type: text/plain
last changed 2003/05/17 08:15
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