| 摘要: |
| 有理二次三角Bézier曲线是近年来研究的一种新型曲线，证明了已知给定三维空间中不共面的4个控制顶点和它们凸包内的一点，可以唯一确定一条有理二次三角Bézier曲线，并且做了更进一步的研究，对有理二次三角Bézier曲线上一点的参数和它的2个内权因子这3个未知变量进行反求，从而得出原曲线的完整表达式.同时提出了2种简单的方法，避免了数值计算的不稳定性.最后给出了数值例子进行了验算，验算结果和实际基本吻合，具有很高的准确性. |
| 关键词: 有理二次三角Bézier 空间曲线 权因子 参数 |
| DOI： |
| 分类号: |
| 基金项目:湖南科技大学研究生创新基金资助项目（S130031）；湖南省自然科学基金资助项目（12JJA002）；湖南省教育厅资助项目（12K106） |
|
| Inversely solving the parameter and inner weight of rational quadratic trigonometric Bézier space curve |
|
|
| Abstract: |
| The rational quadratic triangular Bézier is a new curve.Given four non-coplanar vertices and a point inside the convex hull of the vertices, a rational quadratic triangular Bézier curve was uniquely determined. The question to solve the parameter of the point on the curve and the inter weights was discussed,and two simple methods were proposed to avoid numerical instabilities. Finally, numerical examples were carried out checking,and the results were consistent with reality. |
| Key words: rational quadratic trigonometric polynomial Bézier space curve weight parameter |
