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
Authors
-
Bongardt, Bertold
-
Thomas, Federico
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.
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