Advanced ellipse overlap computation based on segment area of circles
To address the numerical limitations that may arise when calculating the overlapping area of two ellipses using algebraic and numerical methods, we propose a novel approach aimed at improving numerical accuracy. Given two ellipses of either the standard or general types, a quaternary equation can be...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-04-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016825001528 |
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| author | Minhye Kim Yongkuk Kim Giphil Cho |
| author_facet | Minhye Kim Yongkuk Kim Giphil Cho |
| author_sort | Minhye Kim |
| collection | DOAJ |
| description | To address the numerical limitations that may arise when calculating the overlapping area of two ellipses using algebraic and numerical methods, we propose a novel approach aimed at improving numerical accuracy. Given two ellipses of either the standard or general types, a quaternary equation can be derived for the intersection points of the two ellipses. By solving this equation, we classify the methods for calculating the area into five types and proposed area calculation approaches for each type. In addition, we propose a method for calculating the area of a segment of an ellipse without integration. This method calculates the area of a segment of a circle with the major axis of the ellipse as its diameter and multiplies the ratio of the major axis to the minor axis. The proposed method for calculating the overlapping area of two ellipses does not require integration, enabling straightforward computation while providing high accuracy. We compared our method with the traditional Monte Carlo method and found that when the relative error is 0.0245, our method operates approximately 6 times faster. Our research applies to fields like robotics, GIS, industrial clustering, and biology, with strong potential in medical imaging and diagnosis. |
| format | Article |
| id | doaj-art-4bc001e1e3e14c938602a890827d71c1 |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-4bc001e1e3e14c938602a890827d71c12025-02-09T04:59:46ZengElsevierAlexandria Engineering Journal1110-01682025-04-01119425436Advanced ellipse overlap computation based on segment area of circlesMinhye Kim0Yongkuk Kim1Giphil Cho2Department of Mathematics, Kyungpook National University, Daegu 41566, Republic of KoreaDepartment of Mathematics, Kyungpook National University, Daegu 41566, Republic of KoreaDepartment of Artificial Intelligence & Software, Kangwon National University, Samcheok-si, Gangwon-do 25913, Republic of Korea; Corresponding author.To address the numerical limitations that may arise when calculating the overlapping area of two ellipses using algebraic and numerical methods, we propose a novel approach aimed at improving numerical accuracy. Given two ellipses of either the standard or general types, a quaternary equation can be derived for the intersection points of the two ellipses. By solving this equation, we classify the methods for calculating the area into five types and proposed area calculation approaches for each type. In addition, we propose a method for calculating the area of a segment of an ellipse without integration. This method calculates the area of a segment of a circle with the major axis of the ellipse as its diameter and multiplies the ratio of the major axis to the minor axis. The proposed method for calculating the overlapping area of two ellipses does not require integration, enabling straightforward computation while providing high accuracy. We compared our method with the traditional Monte Carlo method and found that when the relative error is 0.0245, our method operates approximately 6 times faster. Our research applies to fields like robotics, GIS, industrial clustering, and biology, with strong potential in medical imaging and diagnosis.http://www.sciencedirect.com/science/article/pii/S1110016825001528EllipseOverlapping areaSegmentIntersection pointCircleClassification |
| spellingShingle | Minhye Kim Yongkuk Kim Giphil Cho Advanced ellipse overlap computation based on segment area of circles Alexandria Engineering Journal Ellipse Overlapping area Segment Intersection point Circle Classification |
| title | Advanced ellipse overlap computation based on segment area of circles |
| title_full | Advanced ellipse overlap computation based on segment area of circles |
| title_fullStr | Advanced ellipse overlap computation based on segment area of circles |
| title_full_unstemmed | Advanced ellipse overlap computation based on segment area of circles |
| title_short | Advanced ellipse overlap computation based on segment area of circles |
| title_sort | advanced ellipse overlap computation based on segment area of circles |
| topic | Ellipse Overlapping area Segment Intersection point Circle Classification |
| url | http://www.sciencedirect.com/science/article/pii/S1110016825001528 |
| work_keys_str_mv | AT minhyekim advancedellipseoverlapcomputationbasedonsegmentareaofcircles AT yongkukkim advancedellipseoverlapcomputationbasedonsegmentareaofcircles AT giphilcho advancedellipseoverlapcomputationbasedonsegmentareaofcircles |