Free-form additive motions using conformal geometric algebra

Mat Hunt, Glen Mullineux, Robert J. Cripps, Ben Cross

Research output: Contribution to journalArticlepeer-review

1 Citation (SciVal)


Free-form motions in B-spline form can be created from a number of prescribed control poses using the de Casteljau algorithm. With poses defined using conformal geometric algebra, it is natural to combine poses multiplicatively. Additive combinations offer alternative freedoms in design and avoid dealing with noninteger exponents. This paper investigates additive combinations and shows how to modify the conventional conformal geometric algebra definitions to allow such combinations to be well-defined. The additive and multiplicative approaches are compared and in general they generate similar motions, with the additive approach offering computational simplicity.

Original languageEnglish
Pages (from-to)1560-1571
Number of pages12
JournalProceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
Issue number9
Early online date2 May 2017
Publication statusPublished - 1 May 2018


  • Free-form motion
  • conformal geometric algebra
  • de Casteljau algorithm
  • motion curves

ASJC Scopus subject areas

  • Mechanical Engineering


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