双三次曲面插值过程中弦长参数化问题的探讨

在工程上,把双三次埃尔米特插值函数用于不同规则曲面的拟合,是一种简单且有效的方法。但当曲面本身产生较大扭曲时,往往会出现失真情况,对此,常采用分片拟合的方法解决。本文重点论述了如何引用弦长参数对双三次曲面的几何形状进行控制的方法,对原始的双三次埃尔米特曲面的数学模型进行了改进和补充。

Discussion on the Chord Length Parameterization in Process of Bicubic Interpolation

In engineering it is effective to apply the bicubic Hermitian interpolation function to fitting the irregular surfaces. However, the distortion often appears when the surface itself has considerable warpage. In this case seperate fitting is generally introduced. The paper puts stress on dealing with the method of controlling the geometric figure of the bicubic surface by chord length parameters. Some complements to original mathematical model of bicubic Hermitian surface have also been made.