| 摘要: |
| 在给定的GC2插值条件,利用de Boor的构造平面曲线的GC2-Hermite插值方法,构造了一条具有两个自由度的三次B样条插值曲线,并证明插值曲线是局部存在的且具有4阶精度. |
| 关键词: 样条 曲线 插值 几何光滑 精度 |
| DOI： |
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| 基金项目:Supported by the National Natural Science Foundation of China under Grant Nos. 10271022, 60373093(国家自然科学基金);the Natural Science Foundation of Guangdong Province of China under Grant No.021755(广东省自然科学基金) |
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| Geometric Hermite Interpolation for Space Curves by B-Spline |
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ZHU Chun-Gang,WANG Ren-Hong
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| Abstract: |
| This paper considers the space GC2 Hermite interpolation by cubic B-spline curve which is based on de Boor’s idea for constructing the planar GC2 Hermite interpolation. In addition to position and tangent direction, the curvature vector is interpolated at each point. It is proved that under appropriate assumptions the interpolant exists locally with two degrees of freedom and the 4th order accuracy. |
| Key words: spline curve interpolation geometric smoothness accuracy |
