On a class of Bézier-like model for shape-preserving approximation. (English) Zbl 1499.65062
Summary: A class of Bernstein-like basis functions, equipped with a shape param-eter, is presented. Employing the introduced basis functions, the corresponding curve and surface in rectangular patches are defined based on some control points. It is verified that the new curve and surface have most properties of the classical Bézier curves and surfaces. The shape parameter helps to adjust the shape of the curve and surface while the control points are fixed. We prove that the proposed Bézier-like curves can preserve monotonicity and that Bézier-like surfaces can preserve axial monotonicity. Moreover, the presented curves and surfaces preserve bound constraints implied by the original data.
MSC:
| 65D17 | Computer-aided design (modeling of curves and surfaces) |
| 65D10 | Numerical smoothing, curve fitting |
| 68U05 | Computer graphics; computational geometry (digital and algorithmic aspects) |
Keywords:
blending functions; Bézier curve; shape adjustment; monotonicity preservation; shape-preserving; boundednessReferences:
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| [34] | How to cite this article B. Nouri and J. Saeidian On a class of Bézier-like model for shape-preserving approximation. Iranian Journal of Numerical Analysis and Optimization, 2022; 12(2): 449-466. doi: 10.22067/ijnao.2022.72818.1064. · Zbl 1499.65062 · doi:10.22067/ijnao.2022.72818.1064 |
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