The New Jersey Institute of Technology's
Electronic Theses & Dissertations Project

Title:	The flow approach to swept volume
Author:	Jiang, Haitao
View Online:	njit-etd1993-096 (ix, 75 pages ~ 2.1 MB pdf)
Department:	Department of Mathematics
Degree:	Master of Science
Program:	Applied Mathematics
Document Type:	Thesis
Advisory Committee:	Blackmore, Denis L. (Committee chair) Leu, M.C. (Committee member) Luke, Jonathan H.C. (Committee member)
Date:	1993-01
Keywords:	Differential equations Vector fields
Availability:	Unrestricted
Abstract:	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.