CUED Publications database

Calculating the Rotor Between Conformal Objects

Lasenby, J and Hadfield, H and Lasenby, A (2019) Calculating the Rotor Between Conformal Objects. Advances in Applied Clifford Algebras, 29. ISSN 0188-7009

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Abstract

© 2019, The Author(s). In this paper we will address the problem of recovering covariant transformations between objects—specifically; lines, planes, circles, spheres and point pairs. Using the covariant language of conformal geometric algebra (CGA), we will derive such transformations in a very simple manner. In CGA, rotations, translations, dilations and inversions can be written as a single rotor, which is itself an element of the algebra. We will show that the rotor which takes a line to a line (or plane to a plane etc) can easily be formed and we will investigate the nature of the rotors formed in this way. If we can recover the rotor between one object and another of the same type, a useable metric which tells us how close one line (plane etc) is to another, can be a function of how close this rotor is to the identity. Using these ideas, we find that we can define metrics for a number of common problems, specifically recovering the transformation between sets of noisy objects.

Item Type: Article
Subjects: UNSPECIFIED
Divisions: Div F > Signal Processing and Communications
Depositing User: Unnamed user with email sms67@cam.ac.uk
Date Deposited: 25 Oct 2019 21:10
Last Modified: 09 Sep 2021 02:10
DOI: 10.1007/s00006-019-1014-8