Document Type


Date of Award


Degree Name

Master of Science in Applied Mathematics - (M.S.)


Mathematical Sciences

First Advisor

Denis L. Blackmore

Second Advisor

M. C. Leu

Third Advisor

Jonathan H.C. Luke


In this thesis, a method for representing swept volume based on the sweep differential equation and sweep vector field flow is developed. This method can be used to determine the boundary representation of a swept volume generated by any polygonal object undergoing a general smooth 2-D sweep. For any given sweep and object, a. set of candidate boundary points is computed using a selection criterion based on vector field behavior. The set of candidate boundary points is then trimmed in order to obtain the true boundary of the swept volume. This trimming procedure is based on some simple topological principles and it utilizes the concept of extended sweep. This method is more general and efficient than existing approaches (e. g. it can readily deal with the cases in which the swept volume area. has "holes") and can easily be extended to 3-D sweeps; the 3-D extension is discussed but only briefly. Several examples are given to illustrate the implementation of the prototype software for 2-D sweeps which has been developed in conjunction with this research.



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