An approximation method for convolution curves of regular curves and ellipses
In this paper, we present a method of $ G^2 $ Hermite interpolation of convolution curves of regular plane curves and ellipses. We show that our approximant is also a $ C^1 $ Hermite interpolation of the convolution curve. This method yields a polynomial curve if the trajectory curve is a polynomial...
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241648 |
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| author | Young Joon Ahn |
| author_facet | Young Joon Ahn |
| author_sort | Young Joon Ahn |
| collection | DOAJ |
| description | In this paper, we present a method of $ G^2 $ Hermite interpolation of convolution curves of regular plane curves and ellipses. We show that our approximant is also a $ C^1 $ Hermite interpolation of the convolution curve. This method yields a polynomial curve if the trajectory curve is a polynomial curve. Our approximation method is applied to two previous numerical examples. The results of our method are compared with those of previous methods, and the merits and demerits are analyzed. Compared with previous methods, the merits of our method are that the approximant is $ G^2 $ and $ C^1 $ Hermite interpolation, and the degree of the approximant or the required number of segments of the approximant within error tolerances is small. |
| format | Article |
| id | doaj-art-a2b78251cb034a76a1a8791459071322 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-a2b78251cb034a76a1a87914590713222025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912346063461710.3934/math.20241648An approximation method for convolution curves of regular curves and ellipsesYoung Joon Ahn0Department of Mathematics Education, Chosun University, Gwangju 61452, South KoreaIn this paper, we present a method of $ G^2 $ Hermite interpolation of convolution curves of regular plane curves and ellipses. We show that our approximant is also a $ C^1 $ Hermite interpolation of the convolution curve. This method yields a polynomial curve if the trajectory curve is a polynomial curve. Our approximation method is applied to two previous numerical examples. The results of our method are compared with those of previous methods, and the merits and demerits are analyzed. Compared with previous methods, the merits of our method are that the approximant is $ G^2 $ and $ C^1 $ Hermite interpolation, and the degree of the approximant or the required number of segments of the approximant within error tolerances is small.https://www.aimspress.com/article/doi/10.3934/math.20241648convolution approximationhermite interpolationpolynomial curvehausdorff distancesigned curvature continuity |
| spellingShingle | Young Joon Ahn An approximation method for convolution curves of regular curves and ellipses AIMS Mathematics convolution approximation hermite interpolation polynomial curve hausdorff distance signed curvature continuity |
| title | An approximation method for convolution curves of regular curves and ellipses |
| title_full | An approximation method for convolution curves of regular curves and ellipses |
| title_fullStr | An approximation method for convolution curves of regular curves and ellipses |
| title_full_unstemmed | An approximation method for convolution curves of regular curves and ellipses |
| title_short | An approximation method for convolution curves of regular curves and ellipses |
| title_sort | approximation method for convolution curves of regular curves and ellipses |
| topic | convolution approximation hermite interpolation polynomial curve hausdorff distance signed curvature continuity |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241648 |
| work_keys_str_mv | AT youngjoonahn anapproximationmethodforconvolutioncurvesofregularcurvesandellipses AT youngjoonahn approximationmethodforconvolutioncurvesofregularcurvesandellipses |