Publication

On ellipse intersections by means of distance geometry

Conference Article

Conference

IFToMM World Congress on Mechanism and Machine Science (IFToMM)

Edition

16th

Pages

533-543

Doc link

https://doi.org/10.1007/978-3-031-45705-0_52

File

Download the digital copy of the doc pdf document

Authors

Abstract

The problem of intersecting two ellipses arises as a frequent subproblem in computational kinematics and geometry. In this paper, an efficient solution method to this problem is presented using the concept of the power of a point with respect to an ellipse. The point-ellipse power appears in Distance Geometry as a generalization to the squared distance between two points. For establishing the intersection method, several algebraic forms of ellipses are reviewed and the interoperability of distinct deffinitions for the power of points and ellipses are outlined.

Categories

control theory, pattern recognition.

Author keywords

distance geometry, ellipse constellations, squared distances, computational kinematics, power of a point with respect to an ellipse

Scientific reference

B. Bongardt and F. Thomas. On ellipse intersections by means of distance geometry, 16th IFToMM World Congress on Mechanism and Machine Science, 2023, Tokyo (Japan), Vol 147 of Mechanisms and Machine Science, pp. 533-543, 2023, Springer, Cham.