Rigid-Body Transforms Using Symbolic Infinitesimals


There is a requirement to be able to represent three-dimensional objects and their transforms in many applications, including computer graphics and mechanism and machine design. A geometric algebra is constructed which can model three-dimensional geometry and rigid-body transforms. The representation is exact since the square of one of the basis vectors is treated symbolically as being infinite. The non-zero, even-grade elements of the algebra represent precisely all rigid-body transforms. By allowing the transform to vary, smooth motions are obtained. This can be achieved using Bézier and B-spline combinations of even-grade elements.


Control Point Basis Vector Geometric Algebra Curve Segment Smooth Motion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The work reported in the paper was carried within the Innovative Design and Manufacturing Research Centre at the University of Bath, and the second author is funded by a studentship provided via the Centre. The Centre is funded by the Engineering and Physical Sciences Research Council (EPSRC), and this support is gratefully acknowledged.


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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Innovative Design and Manufacturing Research Centre, Department of Mechanical EngineeringUniversity of BathBathUK

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