Free-form additive motions using conformal geometric algebra. (May 2018)

• Record Type: Journal Article
• Authors: Hunt, Mat; Mullineux, Glen; Cripps, Robert J; Cross, Ben
• Is Part Of: Proceedings of the Institution of Mechanical Engineers. Volume 232:Number 9(2018)
• Page Start: 1560
• Page End: 1571
• Publication Date: 2018-05
• Subjects: Free-form motion -- conformal geometric algebra -- de Casteljau algorithm -- motion curves; Mechanical engineering -- Periodicals; 621.05
• DOI: 10.1177/0954406217707777
• Languages: English
• ISSNs: 0954-4062

Abstract

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.