Research Initiation: Second Order Continuous Blending of Functional Surfaces

本文讨论了混合函数的二阶连续性问题， 光顺表面只收到近似或非常 有限的解决方案，虽然，这是一个重大的挑战， 海军和航空航天表面的计算机辅助设计， 由流体动力学决定。 根据结果， 以前的研究在可变扫描几何建模，这 研究将开发一种混合策略， 数学上精确，并确保二阶连续性的 共混物 具体研究目标概括如下 （1）制定变量扫描表示法， 二阶连续混合 表面。 (2)定义二阶连续的修剪 在混合边的端点附近进行混合。 (3)制定 （可能递归）定义先前的混合 混合曲面。

The problem of second order continuity of blending and fairing surfaces has received only approximate or very restricted solutions, although, it is a major challenge in Computer Aided Design of Naval and Aerospace surfaces, where it is dictated by fluid dynamics. Based upon the result of previous research in Variable Sweep Geometric Modeling, this research will develop a blending strategy that is mathematically exact and insures second order continuity of the blend. The specific research objectives are summarized as follows: (1) Formulate the Variable Sweep representation of the second order continuous blend of two second order continuous surfaces. (2) Define trimming of the second order continuous blend near the ends of the blended edge. (3) Formulate the (possibly recursive) definition of the blend of previously blended surfaces.