Generalized trigonometric curve and its spline
On the extensions of the cubic Bézier curve with four control points, to connect multiple segments with required continuity has been strongly intended and for example, tangent and curvature continuity at the start and end points are guaranteed independently by adding extra shape parameters. Contrary...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | Japanese |
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The Japan Society of Mechanical Engineers
2021-12-01
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| Series: | Nihon Kikai Gakkai ronbunshu |
| Subjects: | |
| Online Access: | https://www.jstage.jst.go.jp/article/transjsme/87/904/87_21-00154/_pdf/-char/en |
| _version_ | 1811308616190263296 |
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| author | Kenjiro T. MIURA Rudrusamy U. GOBITHAASAN Tadatoshi SEKINE Shin USUKI |
| author_facet | Kenjiro T. MIURA Rudrusamy U. GOBITHAASAN Tadatoshi SEKINE Shin USUKI |
| author_sort | Kenjiro T. MIURA |
| collection | DOAJ |
| description | On the extensions of the cubic Bézier curve with four control points, to connect multiple segments with required continuity has been strongly intended and for example, tangent and curvature continuity at the start and end points are guaranteed independently by adding extra shape parameters. Contrary to this research trend, κ-curves, which control one curvature extremum on each curve segment instead of the end points, are defined as a sequence of the quadratic Bézier curve with three control points. In this study, in order to extend κ-curves, we propose generalized trigonometric basis functions consisting of (sint,cost,1). Using these basis functions, we also define a new free-form curve named generalized trigonometric curve. We discuss its degree elevation, Miura’s triangle, Gobithaasan-Miura’s recursive algorithm, handwriting and spline. |
| first_indexed | 2024-04-13T09:26:22Z |
| format | Article |
| id | doaj.art-2e02f6dc888843cb940bbed31862fa05 |
| institution | Directory Open Access Journal |
| issn | 2187-9761 |
| language | Japanese |
| last_indexed | 2024-04-13T09:26:22Z |
| publishDate | 2021-12-01 |
| publisher | The Japan Society of Mechanical Engineers |
| record_format | Article |
| series | Nihon Kikai Gakkai ronbunshu |
| spelling | doaj.art-2e02f6dc888843cb940bbed31862fa052022-12-22T02:52:24ZjpnThe Japan Society of Mechanical EngineersNihon Kikai Gakkai ronbunshu2187-97612021-12-018790421-0015421-0015410.1299/transjsme.21-00154transjsmeGeneralized trigonometric curve and its splineKenjiro T. MIURA0Rudrusamy U. GOBITHAASAN1Tadatoshi SEKINE2Shin USUKI3Graduate School of Science and Technology, Shizuoka UniversityFaculty of Ocean Engineering and Informatics, University of Malaysia, TerengganuDepartment of Mechanical Engineering, Shizuoka UniversityResearch Institute of Electronics, Shizuoka UniversityOn the extensions of the cubic Bézier curve with four control points, to connect multiple segments with required continuity has been strongly intended and for example, tangent and curvature continuity at the start and end points are guaranteed independently by adding extra shape parameters. Contrary to this research trend, κ-curves, which control one curvature extremum on each curve segment instead of the end points, are defined as a sequence of the quadratic Bézier curve with three control points. In this study, in order to extend κ-curves, we propose generalized trigonometric basis functions consisting of (sint,cost,1). Using these basis functions, we also define a new free-form curve named generalized trigonometric curve. We discuss its degree elevation, Miura’s triangle, Gobithaasan-Miura’s recursive algorithm, handwriting and spline.https://www.jstage.jst.go.jp/article/transjsme/87/904/87_21-00154/_pdf/-char/engeneralized trigonometric splineκ-curvesdegree elevationmiura’s trianglegobithaasan-miura’s recursive algorithmspline |
| spellingShingle | Kenjiro T. MIURA Rudrusamy U. GOBITHAASAN Tadatoshi SEKINE Shin USUKI Generalized trigonometric curve and its spline Nihon Kikai Gakkai ronbunshu generalized trigonometric spline κ-curves degree elevation miura’s triangle gobithaasan-miura’s recursive algorithm spline |
| title | Generalized trigonometric curve and its spline |
| title_full | Generalized trigonometric curve and its spline |
| title_fullStr | Generalized trigonometric curve and its spline |
| title_full_unstemmed | Generalized trigonometric curve and its spline |
| title_short | Generalized trigonometric curve and its spline |
| title_sort | generalized trigonometric curve and its spline |
| topic | generalized trigonometric spline κ-curves degree elevation miura’s triangle gobithaasan-miura’s recursive algorithm spline |
| url | https://www.jstage.jst.go.jp/article/transjsme/87/904/87_21-00154/_pdf/-char/en |
| work_keys_str_mv | AT kenjirotmiura generalizedtrigonometriccurveanditsspline AT rudrusamyugobithaasan generalizedtrigonometriccurveanditsspline AT tadatoshisekine generalizedtrigonometriccurveanditsspline AT shinusuki generalizedtrigonometriccurveanditsspline |