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.

Issue Section:
Technical Papers
Keywords:
computer graphics, splines (mathematics), algebra, computational geometry
Topics:
Algebra
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