A Singularity Theory Approach to Swept Volumes
An approach to the study of the topology and geometry of swept volumes is developed based on the theory of singularities of sweep mappings. It is shown how the computation of the critical point and bifurcation sets of a certain (sweep) mapping yields important information about both the local and global structure of swept volumes. For example, it is proved under mild restrictions that a swept volume can be arbitrary closely approximated by a product manifold. a computer program - incorporating singularity calculations - for the approximate analysis and representation of swept volumes is developed and applied to several examples in order to demonstrate its usefulness.
D. Blackmore et al., "A Singularity Theory Approach to Swept Volumes," International Journal of Shape Modeling, World Scientific Publishing, Jun 2000.
The definitive version is available at http://dx.doi.org/10.1142/S0218654300000089
Mechanical and Aerospace Engineering
Keywords and Phrases
Computer-Aided Geometric Design; Envelopes; Singularity Theory; Sweep Differential Equations; Swept Volume
Article - Journal
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