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On Circle Intersections by Means of Distance Geometry

  • Bertold BongardtEmail author
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)

Abstract

The intersection of circles appears as a frequent subproblem in the domains of computational kinematics and geometry. For this reason, the methods for computing its solutions need to be stable and simple. This paper surveys the solution method for circle intersection given by the approach of distance geometry via Cayley–Menger bideterminants. In particular, the equivalence of the squared-quantity method to its linear-quantity counterpart is shown and novel interconnections to related concepts of Non-Euclidean geometry are worked out.

Keywords

Distance Geometry Cayley–Menger Bideterminants Circle Configurations Squared Distances Computational Kinematics 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Technische Universität Braunschweig, Institut für Robotik und ProzessinformatikBraunschweigGermany

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