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代数三角混合Bézier型插值曲线

  

  • 出版日期:2010-12-31 发布日期:2015-08-12

Algebraic Trigonometric Blending Bézier-type Interpolation Curves

  • Online:2010-12-31 Published:2015-08-12

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摘要： 通过一类代数三角混合Bézier型基函数的定义，构造了一类C2连续的代数三角混合Bézier型插值曲线。该曲线继承了Bézier曲线的一些优良特性，并能充分克服Bézier型基函数不能精确表示二次曲线曲面以及某些超越曲线曲面的弱点。另外，利用形状控制参数可以灵活调节曲线形状，进一步增强了曲线曲面的表现能力。最后实例表明了新的插值曲线应用于几何造型的有效性。

关键词: 代数三角混合多项式, Bé, zier型曲线, 曲线插值, 形状参数

Abstract: A class of C2 continuous algebraic trigonometric blending Bézier-type interpolation curves is constructed based on the definition of free form algebraic trigonometric blending Bézier-type curves. The introduced curves inherit some characteristics which the Bézier interpolation curves have. Meanwhile, the new curves can accurately represent some conic and transcendental curves, which are more powerful than the Bézier interpolation curves. Moreover, the shapes of curves can be adjusted freely by an introduced control parameter in the base functions. At last, the illustrations show that the new interpolating curves are effective in practice on geometric modeling.

Key words: algebraic trigonometric blending polynomial, Bézier-type curve, curve interpolation, shape parameter