Publication
Clifford’s identity and generalized Cayley-Menger determinants
Conference Article
Conference
International Symposium on Advances in Robot Kinematics (ARK)
Edition
17th
Pages
285-292
Doc link
https://doi.org/10.1007/978-3-030-50975-0_35
File
Abstract
Distance geometry is usually defined as the characterization and study of point sets in ℝk, the k-dimensional Euclidean space, based on the pairwise distances between their points. In this paper, we use Clifford’s identity to extend this kind of characterization to sets of n hyperspheres embedded in 𝕊n-3 or ℝn-3 where the role of the Euclidean distance between two points is replaced by the so-called power between two hyperspheres. By properly choosing the value of n and the radii of these hyperspheres, Clifford’s identity reduces to conditions in terms of generalized Cayley-Menger determinants which has been previously obtained on the basis of a case-by-case analysis.
Categories
robots.
Author keywords
Clifford’s identity, Cayley-Menger determinants, Distance Geometry
Scientific reference
F. Thomas and J.M. Porta. Clifford’s identity and generalized Cayley-Menger determinants, 17th International Symposium on Advances in Robot Kinematics, 2020, Ljubljana, Slovenia, in Advances in Robot Kinematics 2020, Vol 15 of Springer Proceedings in Advanced Robotics, pp. 285-292, Springer.
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