Square Root and Logarithm of Rotors in 3D Conformal Geometric Algebra Using Polar Decomposition
Conformal transformations are described by rotors in the conformal model of geometric algebra (CGA). In applications there is a need for interpolation of such transformations, especially for the subclass of 3D rigid body motions. This chapter gives explicit formulas for the square root and the logarithm of rotors in 3D CGA. It also classifies the types of conformal transformations and their orbits. To derive the results, we employ a novel polar decomposition for the even subalgebra of 3D CGA and an associated norm-like expression.
KeywordsConformal Transformation Rigid Body Motion Geometric Algebra Invertible Element Polar Decomposition
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