A polynomial basis with a shape parameter for curve and surface modeling

IF 5.4 3区材料科学 Q2 CHEMISTRY, PHYSICAL

ACS Applied Energy Materials Pub Date : 2024-10-26 DOI:10.1016/j.matcom.2024.10.029

Bahareh Nouri , Imre Juhász , Jamshid Saeidian

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引用次数: 0

Abstract

Based on Bernstein polynomials, a system of functions with a free parameter is proposed in the space of polynomials of degree at most

n

. The system inherits several properties of Bernstein polynomials, such as linear independence, non-negativity, partition of unity and symmetry. This new family of functions are employed to construct control point based parametric curves. The free parameter serves as a shape adjustment parameter, by means of which a one-parameter family of polynomial curves is obtained. The new family of curves is in common with Bézier curves in most of the geometric properties, providing a smooth transition between the Bézier curve and the straight line segment joining the first and last control points. Shape preserving properties, such as monotonicity preservation, as well as length, hodograph and variation diminishing are studied. The proposed basis can also be used to create tensor product surfaces. The extent to which the suggested basis generation method can be applied to other (non-polynomial) function spaces is also being investigated.

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带有形状参数的多项式基础，用于曲线和曲面建模

该系统继承了伯恩斯坦多项式的若干特性，如线性独立性、非负性、统一分割和对称性。这一新的函数族被用来构建基于控制点的参数曲线。自由参数作为形状调整参数，通过它可以得到一个单参数的多项式曲线族。新的曲线族在大多数几何特性上与贝塞尔曲线相同，提供了贝塞尔曲线与连接第一个和最后一个控制点的直线段之间的平滑过渡。我们还研究了形状保持特性，如单调性保持，以及长度、线形和变化递减。建议的基础还可用于创建张量乘积曲面。建议的基础生成方法在多大程度上可应用于其他（非多项式）函数空间也在研究之中。

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来源期刊

ACS Applied Energy Materials Materials Science-Materials Chemistry

CiteScore

10.30

自引率

6.20%

发文量

1368

期刊介绍： ACS Applied Energy Materials is an interdisciplinary journal publishing original research covering all aspects of materials, engineering, chemistry, physics and biology relevant to energy conversion and storage. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrate knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important energy applications.