Swept volumes: Fundation, perspectives, and applications

Karim Abdel-Malek, Jingzhou Yang, Denis Blackmore, Ken Joy

Research output: Contribution to journalArticlepeer-review

96 Scopus citations


A survey of swept volume concepts and methods is presented. It consolidates and relates seemingly different terminology and methods. The methods are divided into five major categories: method with envelope theory, method with sweep differential equation (SDE)/sweep envelope differential equation (SEDE), method with Jacobian rank deficiency, Voxel-based method, and free-form solids' sweeping methods. Commentary is provided on three fronts, concerning the advantages and pitfalls of individual methods, the different classes of methods, and the field of swept volumes as a whole. The characteristics of the most significant methods are summarized. The applicability of this seemingly simple formulation to the fields of solid modeling, robotics, manufacturing automation, and visualization is demonstrated through results reported by the authors, each in their own field.

Original languageEnglish (US)
Pages (from-to)87-127
Number of pages41
JournalInternational Journal of Shape Modeling
Issue number1
StatePublished - Jun 2006

All Science Journal Classification (ASJC) codes

  • Software
  • Modeling and Simulation
  • Computer Vision and Pattern Recognition
  • Computer Science Applications
  • Geometry and Topology
  • Applied Mathematics


  • NC verification
  • Solid modeling
  • Swept volumes
  • Workspace analysis


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