This paper looks at the use of a Clifford (or geometric) algebra for handling both rotations and translations in Euclidean space. The algebra is constructed over the real numbers using four basis vectors. Three of these generate a subalgebra which models three-dimensional space; the fourth acts as a projective coordinate. Spatial displacements are represented by bivectors of a certain form. The application to the generation of smooth motions using Be´zier and B-spline techniques is illustrated.
Modeling Spatial Displacements Using Clifford Algebra
Contributed by the Mechanisms and Robotics Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received October 2002; revised September 2003. Associate Editor: C. Mavroidis.
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Mullineux, G. (September 1, 2003). "Modeling Spatial Displacements Using Clifford Algebra ." ASME. J. Mech. Des. May 2004; 126(3): 420–424. https://doi.org/10.1115/1.1701876
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