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- Title
Fast closest logarithm algorithm in the special orthogonal group.
- Authors
ESCANDE, ADRIEN
- Abstract
For interpolating between elements of SO(n), it is attractive to work in n, passing from one space to the other via the exponential map. However, the logarithm is a multi-valued map and the choice of a particular image affects the quality of the interpolation. In this paper, we propose a fast and accurate algorithm to compute the image that seems the most appropriate for interpolation: given Q ∈ SO(n) and A ∈ n, our algorithm returns the logarithm of Q which is the closest to A, under minimal conditions on Q. We carefully study the mathematical properties of our problem to establish the algorithm, discuss its implementation and demonstrate its efficiency.
- Subjects
LOGARITHMS; ALGORITHMS; ORTHOGONALIZATION; MATHEMATICAL analysis; PROBLEM solving
- Publication
IMA Journal of Numerical Analysis, 2016, Vol 36, Issue 2, p675
- ISSN
0272-4979
- Publication type
Article
- DOI
10.1093/imanum/drv027