A Computational Method with Maple for Finding the Maximum Curvature of a Bézier-Spline Curve
In this paper, we propose two Maple procedures and some related utilities to determine the maximum curvature of a cubic Bézier-spline curve that interpolates an ordered set of points in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">...
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MDPI AG
2023-04-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/28/2/56 |
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| author | Henk Pijls Le Phuong Quan |
| author_facet | Henk Pijls Le Phuong Quan |
| author_sort | Henk Pijls |
| collection | DOAJ |
| description | In this paper, we propose two Maple procedures and some related utilities to determine the maximum curvature of a cubic Bézier-spline curve that interpolates an ordered set of points in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mn>2</mn></msup></semantics></math></inline-formula> or <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mn>3</mn></msup></semantics></math></inline-formula>. The procedures are designed from closed-form formulas for such open and closed curves. |
| first_indexed | 2024-03-11T04:46:33Z |
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| id | doaj.art-1e19111802c44b6b822a94767aeef3d8 |
| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-11T04:46:33Z |
| publishDate | 2023-04-01 |
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| series | Mathematical and Computational Applications |
| spelling | doaj.art-1e19111802c44b6b822a94767aeef3d82023-11-17T20:19:41ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472023-04-012825610.3390/mca28020056A Computational Method with Maple for Finding the Maximum Curvature of a Bézier-Spline CurveHenk Pijls0Le Phuong Quan1Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 105-107, 3rd Floor (Entrance via Nikhef), 1098 XG Amsterdam, The NetherlandsDepartment of Mathematics, College of Natural Sciences, Cantho University, 3/2 Street, Cantho City 900000, VietnamIn this paper, we propose two Maple procedures and some related utilities to determine the maximum curvature of a cubic Bézier-spline curve that interpolates an ordered set of points in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mn>2</mn></msup></semantics></math></inline-formula> or <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mn>3</mn></msup></semantics></math></inline-formula>. The procedures are designed from closed-form formulas for such open and closed curves.https://www.mdpi.com/2297-8747/28/2/56approximationBézier-spline curvecomputer algebra systemFrenet frameinterpolationparametrization |
| spellingShingle | Henk Pijls Le Phuong Quan A Computational Method with Maple for Finding the Maximum Curvature of a Bézier-Spline Curve Mathematical and Computational Applications approximation Bézier-spline curve computer algebra system Frenet frame interpolation parametrization |
| title | A Computational Method with Maple for Finding the Maximum Curvature of a Bézier-Spline Curve |
| title_full | A Computational Method with Maple for Finding the Maximum Curvature of a Bézier-Spline Curve |
| title_fullStr | A Computational Method with Maple for Finding the Maximum Curvature of a Bézier-Spline Curve |
| title_full_unstemmed | A Computational Method with Maple for Finding the Maximum Curvature of a Bézier-Spline Curve |
| title_short | A Computational Method with Maple for Finding the Maximum Curvature of a Bézier-Spline Curve |
| title_sort | computational method with maple for finding the maximum curvature of a bezier spline curve |
| topic | approximation Bézier-spline curve computer algebra system Frenet frame interpolation parametrization |
| url | https://www.mdpi.com/2297-8747/28/2/56 |
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