Free-form additive motions using conformal geometric algebra

Glen Mullineux, Mat Hunt, Robert Cripps, Benjamin Cross

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Free-form motions in B-spline form can be created from a number of prescribed control poses using the de Casteljau algorithm. With poses dened using conformal geometric algebra (CGA), it is natural to combine poses multiplicatively. Additive combinations oer alternative freedoms in design and avoid dealing with non-integer exponents. This paper investigates additive combinations and shows how to modify the conventional CGA denitions to allow such combinations to be well-dened. The additive and multiplicative approaches are compared and in general they generate similar motions, with the additive approach oering computational simplicity.
Original languageEnglish
Pages (from-to)1560-1571
JournalInstitution of Mechanical Engineers. Proceedings. Part C: Journal of Mechanical Engineering Science
Issue number9
Early online date2 May 2017
Publication statusPublished - May 2018


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

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering


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