Analysis and modelling of deformed swept volumes

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Abstract

The sweep differential equation approach and the boundary-flow method developed for the analysis and representation of swept volumes are extended to include objects experiencing deformation. It is found that the theoretical framework can be generalized quite naturally to deformed swept volumes by the enlargement of the Lie group structure of the sweeps. All the usual results, including the boundary-flow formula, are shown to have extensions for swept volumes with deformation. Several special classes of deformation are identified, and their particular properties are studied insofar as they pertain to swept volumes. A program for obtaining deformed swept volumes of planar polygons is described, and is then applied to several examples to demonstrate its effectiveness.

Original languageEnglish (US)
Pages (from-to)315-326
Number of pages12
JournalComputer-Aided Design
Volume26
Issue number4
DOIs
StatePublished - Apr 1994

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering

Keywords

  • Lie groups
  • boundary-flow formulae
  • linear deformations
  • nonlinear deformations
  • similarity deformations
  • sweep differential equations

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