| 蒋金文.带形状参数的三角λ-Bézier曲线[J].安徽建筑大学学报,2024,32(): |
| 带形状参数的三角λ-Bézier曲线 |
| Trigonometric λ-Bézier Curves with Shape Parameter |
| 投稿时间：2023-04-12 修订日期：2023-05-11 |
| DOI： |
| 中文关键词: Bézier曲线 形状参数 递推性 |
| 英文关键词: Bézier curve Shape parameter Recurrency |
| 基金项目:安徽省高等学校自然科学基金重点项目(KJ2021A0630，KJ2021A0633，KJ2021A0634) |
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| 中文摘要: |
| 为了克服传统Bézier曲线缺乏局部调整性并且不能精确表达圆锥曲线的缺点，构造了一个带形状参数的n(n≥2)次三角λ-Bézier曲线，为了降低工作难度，各阶曲线的形状参数的取值范围保持不变。首先基函数空间选择在三角多项式空间中，利用递推性构造了λ-Bernstein基函数，进而讨论了该基函数的端点性和对称性等重要性质，并由该基函数定义了n(n≥2)次λ-Bézier曲线。另外，讨论了形状参数取不同值时对曲线形状的影响以及曲线的拼接条件：在一定的条件下，该曲线可达到G2拼接；最后，给出了张量积形式的λ-Bézier曲面以及性质。实例表明，该曲线克服了传统Bézier曲线缺乏局部调整性的缺点且能精确表达圆弧和抛物线等圆锥曲线。 |
| 英文摘要: |
| In order to overcome the shortcomings of traditional Bézier curves which lack local adjustability and cannot accurately express conic curves, a trigonometric λ-Bézier curve with n(n≥2) order shape parameter is constructed. In order to reduce the difficulty of work, the value range of shape parameters of each order curve remains unchanged.Firstly, λ-Bernstein basis function is constructed in trigonometric polynomial space by means of recursion. Then, the important properties of endpoint and symmetry of this basis function are discussed, and the n(n≥2) λ-Bézier curve is defined by this basis function.In addition, the influence of different shape parameter on the shape of the curve and the splicing conditions of the curve are discussed. Under certain conditions, the curve can achieve G2 splicing. Finally, λ-Bézier surfaces in tensor product form and their properties are given.The example shows that this curve overcomes the shortcoming of traditional Bézier curve which lacks local adjustment and can accurately express conic curves such as circular arc and parabola. |
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