摘要
Hassan提出的四点ternary插值细分法当细分参数在一定范围内取值时可达C2连续。为了进一步扩展其在插值曲线造型方面的能力,作者对该细分法的C0及C1连续性条件、极限函数的一阶及二阶导数等重要特性作了进一步的讨论,给出了细分法C0及C1连续的必要条件、充分条件及极限函数的一阶及二阶导数的表达式,并讨论了细分法在函数逼近、无须辅助顶点而直接插值给定型值点的光滑插值细分曲线的构造等方面的应用。
The 4-point ternary interpolatory subdivision scheme proposed by Hassan can be C^2-continuous when the subdivision parameter is chosen in a certain range. To extend its application in the modeling of smooth curves with different continuity, some other important properties of this scheme such as the conditions of C^0, C^1-continuous, and the derivatives of the limit function are analyzed in this paper. Its application in function approximation is discussed. Finally a modified 4-point ternary subdivision scheme is proposed to design smooth and open interpolatory curves without supplying any additional control points.
出处
《工程图学学报》
CSCD
北大核心
2006年第3期65-72,共8页
Journal of Engineering Graphics
基金
西北工业大学青年科技创新基金资助项目
