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Describing a Set of Points with Elliptical Areas: Mathematical Description and Verification on Operational Tests of Technical Devices


[ 1 ] Instytut Konstrukcji Maszyn, Wydział Inżynierii Mechanicznej, Politechnika Poznańska | [ P ] employee

Scientific discipline (Law 2.0)

[2.9] Mechanical engineering

Year of publication


Published in

Applied Sciences

Journal year: 2022 | Journal volume: vol. 12 | Journal number: iss. 1

Article type

scientific article

Publication language


  • method of data description
  • exploitation research
  • point cloud
  • research analysis

EN The purpose of this article was to present an algorithm for creating an ellipse for any data set represented on a two-dimensional reference frame. The study objective was to verify the developed method on real results of experimental tests with different subject matter. This article contains a mathematical algorithm to describe a set of points with elliptical areas. In addition, four results of tests with different subject matter are cited, based on which the developed method was verified. The verification of the method included checking the deviation of the geometric dimensions of the ellipse, the number of points contained within the ellipse, and the area of the ellipse. The implemented research methodology allowed to demonstrate the possibility of using the method of describing a set of points with elliptical areas, in order to determine quantitative parameters evaluating the results of the test. The presented results show the method’s applicability for the results obtained in four different operational tests: measurement of the human body’s gravity center position for a person propelling a wheelchair, measurement of marker position using motion capture methods, measurement of particulate emissions when using equipment powered by an internal combustion engine, and measurement of the muscle activity of the upper limb when propelling a hybrid manual-electric wheelchair. The performed experiments demonstrated that the method allows to describe about 85% of all measurement points with an ellipse.

Pages (from - to)

445-1 - 445-18





article number: 445

License type

CC BY (attribution alone)

Open Access Mode

open journal

Open Access Text Version

final published version

Date of Open Access to the publication

at the time of publication

Full text of article

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